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Digix
2008-Nov-09, 12:32 AM
I ran into some problems on this famous paradox.
if you move fast time is supposed to slow down.

so lets say what will happen in this case:

I have one stationary clock and another one is sent some to distance away and it returns back to same point.
later we compare them and do they show different time ?

Some Time ago I expected that they should show different time, but now I think that they will show exactly same time like no relativity ever existed.
because all effects will cancel if you return to the same point.

hhEb09'1
2008-Nov-09, 02:05 AM
Some Time ago I expected that they should show different time, but now I think that they will show exactly same time like no relativity ever existed.
because all effects will cancel if you return to the same point.I'm not sure why you'd think that. The effect, as you've described it, is special relativity, and Einstein described the effect in his first paper in 1905. They will not show the same time, at least at the level of the effect--and experiments have agreed.

sirius0
2008-Nov-09, 02:31 AM
The Same Point is the point here. You are considering a return to the same point. But it hasn't, it is at a different point in the four dimensional sense. Both clocks have left that original point "somewhere back there" on their individual time lines. The usual set up is for the clock that is "stationary" to be assigned coordinate time because it will have the longest proper time possible for the twins scenario you describe. Whilst the traveled clock will have less time elapsed meaning it was observed to be time-dilated by the "stationary clock" Also SR is largely about speed, a scalar, so the direction relative to you doesn't matter, so a difference is not cancelled out.

TobiasTheViking
2008-Nov-09, 02:33 AM
The one that have changed reference frames(the one that moved) will be behind the one that stayed behind.

If you have clock a and b, and they start in the same reference frame(same speed and position), one accelerates at 1g for a week, does nothing for a week, then decelerates for a week. Now that clock will be behind the one left behind..

Now if the OTHER clock does the same thing, then when they meet up they will show the same time. But if the one that traveled first travels back, it will still be behind.

spratleyj
2008-Nov-09, 03:06 AM
I ran into some problems on this famous paradox.
if you move fast time is supposed to slow down.

so lets say what will happen in this case:

I have one stationary clock and another one is sent some to distance away and it returns back to same point.
later we compare them and do they show different time ?

Some Time ago I expected that they should show different time, but now I think that they will show exactly same time like no relativity ever existed.
because all effects will cancel if you return to the same point.

Why would you think that? As another member has already pointed out speed is a scalar... It has nothing to do with location, rather it's all about speed. Perhaps, you should read up on special relativity.

Kebsis
2008-Nov-09, 06:11 AM
Lets say two clocks are set to exactly the same time. Neither will wear down with time or anything. One clock is left on Earth, while the other is sent out into the cosmos at some non-relativistic speed, say 20k mph. The clock going out into space spends 2 billion years going out, and then 2 billion years returning to Earth.

Should the clocks still show the same time?

Digix
2008-Nov-09, 11:47 AM
Why would you think that? As another member has already pointed out speed is a scalar... It has nothing to do with location, rather it's all about speed. Perhaps, you should read up on special relativity.

Speed i usually vector so I don't see a reason why it should be scalar here
and if we think in that way then time will slow down when distance increases, and it will speed up if it increases. all that because of simple Dopler shift. which can explain everything on all relativity cases.

in case if we assume that speed is scalar, I don't see any way to solve problem with invariance. neither observer can tell who is moving and who is not.
acceleration cant be used for that, because we can accelerate for few minutes and then fly free for many years. And relativity does not mention acceleration anywhere too.

in case if all this happens because of acceleration, then just putting clock into centrifuge should slow down it indefinitely, since acceleration is constant for unlimited time.

I'm not sure why you'd think that. The effect, as you've described it, is special relativity, and Einstein described the effect in his first paper in 1905. They will not show the same time, at least at the level of the effect--and experiments have agreed.
actually I don't know any experiment where one of 2 clocks travels somewhere and returns, it would be nice to see what happens.
experiments where clock trawled only one direction doest count since effect will not cancel in that way
since to read data from clock you must catch your clock so all experiments will be performed on decreasing distance or else if clock is running away you cant catch and measure it.

Digix
2008-Nov-09, 11:58 AM
The one that have changed reference frames(the one that moved) will be behind the one that stayed behind.

If you have clock a and b, and they start in the same reference frame(same speed and position), one accelerates at 1g for a week, does nothing for a week, then decelerates for a week. Now that clock will be behind the one left behind..

Now if the OTHER clock does the same thing, then when they meet up they will show the same time. But if the one that traveled first travels back, it will still be behind.

again, how that acceleration incorporates into relativity?
none of the formulas mentions acceleration, and acceleration is also non constant but only temporary so after acceleration process ended all observers are equal and are free to think that they are stationary and another observer is moving.

sirius0
2008-Nov-09, 01:09 PM
Lets say two clocks are set to exactly the same time. Neither will wear down with time or anything. One clock is left on Earth, while the other is sent out into the cosmos at some non-relativistic speed, say 20k mph. The clock going out into space spends 2 billion years going out, and then 2 billion years returning to Earth.

Should the clocks still show the same time?

Valuable question because it points out that the Lorentz is always there even at non-relativistic speeds although the effect is very small.

The clock that traveled 4Gyears relative to an observer that is stationary WRT to a clock on earth will have had less time elapse.
The equation being 4GyearsX Squareroot(1-(8940.8^2/c^2))= not quite 4Gyears. It comes down to the precision of the calculator used but 8940^2/c^2 is very small. Nevertheless 4Gyears should be plenty enough time for a small dilation at non-relativistic speeds to be seen; especially given the clocks would be 12hr or 24hr

Edit: Managed to get3.999999998 billion years, approx 73days (Edit correction 730 days being two years, sorry :))shorter time on the clock that travelled not counting leap years

sirius0
2008-Nov-09, 01:29 PM
No Digix. It has to be scalar. Your scenario would have two people waiting on two train stations with synchronised watches seeing two different effects for a relativistic train travelling between those two stations. But observers stationary relative to one another must agree on what they observe.

Digix
2008-Nov-09, 01:50 PM
No Digix. It has to be scalar. Your scenario would have two people waiting on two train stations with synchronised watches seeing two different effects for a relativistic train travelling between those two stations. But observers stationary relative to one another must agree on what they observe.

no that is incorrect approximation because if you have synchronized watches then you are only measuring distance decrease mode. in that case it will look like non stationary clock became slower.

but the whole idea is if I not use any clock synchronization. just 2 watches, (not 3) and you do all measuring in the starting point.

alternative question would be if I put some clock into centrifuge and rotate it there for some time, will it slow down?

Tensor
2008-Nov-09, 02:56 PM
Speed i usually vector so I don't see a reason why it should be scalar here

Digix, speed is a scalar. Velocity is a vector. Vectors have a direction and a magnatude. In the case of velocity, that magnitude is the scalar, speed.

Digix
2008-Nov-09, 03:00 PM
Valuable question because it points out that the Lorentz is always there even at non-relativistic speeds although the effect is very small.

The clock that traveled 4Gyears relative to an observer that is stationary WRT to a clock on earth will have had less time elapse.
The equation being 4GyearsX Squareroot(1-(8940.8^2/c^2))= not quite 4Gyears. It comes down to the precision of the calculator used but 8940^2/c^2 is very small. Nevertheless 4Gyears should be plenty enough time for a small dilation at non-relativistic speeds to be seen; especially given the clocks would be 12hr or 24hr

Edit: Managed to get3.999999998 billion years, approx 73days shorter time on the clock that travelled not counting leap years

I atempted to calculate effect again and it really does not cancel
so seems that moving clock will lag afterall.

but again how to solve invariance problem here speed just cant have any effect.
so it means that all is because of acceleration.

Digix
2008-Nov-09, 03:05 PM
Digix, speed is a scalar. Velocity is a vector. Vectors have a direction and a magnatude. In the case of velocity, that magnitude is the scalar, speed.

In any case it impossible to run in place so speed must be vector, unless we invent tome strange concept with no meaning.
how can you be moving with no direction?

Tensor
2008-Nov-09, 03:05 PM
again, how that acceleration incorporates into relativity?
none of the formulas mentions acceleration, and acceleration is also non constant but only temporary

Special Relativity, as originally written by Einstein, doesn't incorporate acceleration. That was one of the reasons for his efforts to produce General Relativity (GR). GR, does incorporate acceleration, which is why most people would say the acceleration is covered under GR. However, Special Relativity can handle acceleration. All you have to do is calculate the acceleration during each time slice, then integrate all those time slices over the the total acceleration time.

so after acceleration process ended all observers are equal and are free to think that they are stationary and another observer is moving.

While the observers are now stationary, they took different world lines to get to that place from the original starting point. The observer whose world line included acceleration is the one whose time passed slower.

cosmocrazy
2008-Nov-09, 03:17 PM
In any case it impossible to run in place

Digix
2008-Nov-09, 03:30 PM
Special Relativity, as originally written by Einstein, doesn't incorporate acceleration. That was one of the reasons for his efforts to produce General Relativity (GR). GR, does incorporate acceleration, which is why most people would say the acceleration is covered under GR. However, Special Relativity can handle acceleration. All you have to do is calculate the acceleration during each time slice, then integrate all those time slices over the the total acceleration time.
Ok, thank you. Now I finally managed to understand all that nonsense :)
so basically SR is just some approximation and real effects are because of that unmentioned acceleration
Ok, now everything is almost fine.

Digix
2008-Nov-09, 03:31 PM
verry funny... :lol:

Tensor
2008-Nov-09, 03:36 PM
In any case it impossible to run in place so speed must be vector, unless we invent tome strange concept with no meaning.
how can you be moving with no direction?

No, check any begining physics book. The definition of a scalar is a one component quantity (a magnitude) that is invariant under rotations. Speed fits this definition as the quantity will stay the same no matter which direction you go. A vector has two components. A magnitude and a direction. In the case of velocity, it has two components. It has speed and a direction.

Tensor
2008-Nov-09, 03:47 PM
Ok, thank you. Now I finally managed to understand all that nonsense :)
so basically SR is just some approximation and real effects are because of that unmentioned acceleration
Ok, now everything is almost fine.

Be careful here. SR is not just an approximation. In the case of an observer going out and back, you have to calculate five different time effects. The original acceleration, the first coasting, the acceleration to turn around, the second coasting, and the final acceleration to arrive at the final point. All of those combine to determine how fast the observer aged. The acceleration will just tell you which of the observer's ages the least. The time during coasting parts can be calculated as relative motion using only the original SR equations.

Digix
2008-Nov-09, 03:50 PM
No, check any begining physics book. The definition of a scalar is a one component quantity (a magnitude) that is invariant under rotations. Speed fits this definition as the quantity will stay the same no matter which direction you go. A vector has two components. A magnitude and a direction. In the case of velocity, it has two components. It has speed and a direction.

well yes, logically this is correct but practically I cant imagine such situation
it is like voltage only can be between 2 points and it cant be in single point.

also back to the relativity
Do I understand correctly now.

if you accelerate in one direction then time slows down and it speed up if you accelerate in another direction, if there is no acceleration time speed does not change.
basically time speed is just matter of energetic potential. like in gravity, if you move up time accelerates for you if you move down it slows down.

Digix
2008-Nov-09, 03:54 PM
Be careful here. SR is not just an approximation. In the case of an observer going out and back, you have to calculate five different time effects. The original acceleration, the first coasting, the acceleration to turn around, the second coasting, and the final acceleration to arrive at the final point. All of those combine to determine how fast the observer aged. The acceleration will just tell you which of the observer's ages the least. The time during coasting parts can be calculated as relative motion using only the original SR equations.

I want to use only most fundamental theories and get rid of all redundancy. Since such thing as SR really mess up everything they give good results but they destroy logic.

Tensor
2008-Nov-09, 04:10 PM
I want to use only most fundamental theories and get rid of all redundancy. Since such thing as SR really mess up everything they give good results but they destroy logic.

But, there is a reason for using them. Have you ever seen the math required for GR? Here (http://archive.ncsa.uiuc.edu/Cyberia/NumRel/mathmine1.html) is the first page of the equations used in two spatial dimensions (feel free to click to see the other two pages). The full three dimensional equations are even worse. Now, you must admit, if you can use the more simpler SR equations (a good high school math student would be able to), why not use them.

Tensor
2008-Nov-09, 04:19 PM
Do I understand correctly now.

if you accelerate in one direction then time slows down and it speed up if you accelerate in another direction, if there is no acceleration time speed does not change.
basically time speed is just matter of energetic potential. like in gravity, if you move up time accelerates for you if you move down it slows down.

Not quite. Any acceleration, in any direction, will slow down time. The greater the acceleration, the slower the time. This fits with the greater gravity slowing time more. In addition,relative motion, between inertial observers, also slows time.

Jeff Root
2008-Nov-09, 04:25 PM
Digix,

It is quite easy to set up the twin "paradox" in a way that completely
avoids acceleration. The clocks are already in relative motion and are
compared at the instant they pass. Acceleration is not essential to
understanding time dilation. It is pure special relativity.

-- Jeff, in Minneapolis

hhEb09'1
2008-Nov-09, 04:40 PM
Special Relativity, as originally written by Einstein, doesn't incorporate acceleration. OK
That was one of the reasons for his efforts to produce General Relativity (GR). GR, does incorporate acceleration, which is why most people would say the acceleration is covered under GR. However, Special Relativity can handle acceleration. All you have to do is calculate the acceleration during each time slice, then integrate all those time slices over the the total acceleration time. Which is pretty much how Einstein presented it in his first paper on special relativity.

Tensor
2008-Nov-09, 04:47 PM
OKWhich is pretty much how Einstein presented it in his first paper on special relativity.

Yabut, how many people actually know this? ;)

Ken G
2008-Nov-09, 05:05 PM
It is quite easy to set up the twin "paradox" in a way that completely
avoids acceleration. The clocks are already in relative motion and are
compared at the instant they pass. Acceleration is not essential to
understanding time dilation. But acceleration is essential for understanding the twin paradox, which involves not just time dilation. That's the point of it-- most people "get" time dilation at some level, but they think it's a "paradox" because it is symmetric with both observers-- both observers think the other is younger. But in the twin "paradox", one is definitely younger, because they have been reunited. This is why the resolution of the paradox absolutely does require acceleration, or gravity.

Jeff Root
2008-Nov-09, 06:15 PM
In that case, can we go back in time before I posted that, please? I must
have had some other "paradox" in mind, if acceleration is essential to the
"twin paradox". Thinking about it for a few seconds, I don't know how to
get two clocks to tick at identical rates if they are in relative motion but
one is not accelerated, so, uh, yeah... Sorry about that. Just go back
two hours, that's all.

... However... You could eliminate the turnaround at the far end of the
trip by having a third clock already in motion. That reduces the number
of acceleration events from three to two. If that has any value...

-- Jeff, in Minneapolis

Ken G
2008-Nov-09, 06:20 PM
It's a useful mistake that underscores the difference between the twin paradox and time dilation.

hhEb09'1
2008-Nov-09, 06:51 PM
... However... You could eliminate the turnaround at the far end of the
trip by having a third clock already in motion. That reduces the number
of acceleration events from three to two. If that has any value...You mean like this (http://mentock.home.mindspring.com/twins.htm)?

There, consider all three, Ann, Bob, and Carl, to never accelerate, but only to stay in constant inertial motion and pass each other at the appropriate times.

Digix
2008-Nov-09, 07:01 PM
But, there is a reason for using them. Have you ever seen the math required for GR? Here (http://archive.ncsa.uiuc.edu/Cyberia/NumRel/mathmine1.html) is the first page of the equations used in two spatial dimensions (feel free to click to see the other two pages). The full three dimensional equations are even worse. Now, you must admit, if you can use the more simpler SR equations (a good high school math student would be able to), why not use them.
all multidimensional calculations are mathematically complex if you try brute force them
but we can reduce them to one dimension ant then everything should be no harder than SR
Td = 1 + gh / c2
from here
http://en.wikipedia.org/wiki/Gravitational_time_dilation
seems no more complex than SR equations and in case of thought experiments we always chose very simple situations
in case of real calculations we can use derived formulas that have known but not unlimited application range.

Not quite. Any acceleration, in any direction, will slow down time. The greater the acceleration, the slower the time. This fits with the greater gravity slowing time more. In addition,relative motion, between inertial observers, also slows time.

well that wont work, because if we accelerated and your time slowed we need to stop with reverse acceleration and restore time flow back. or else nonsense will happen

same is valid on gravity all objects above observers have acceleration down that its in the direction to observer, and all objects below observer have acceleration down too, ant that is from observer

Digix
2008-Nov-09, 07:07 PM
Digix,
It is quite easy to set up the twin "paradox" in a way that completely
avoids acceleration. The clocks are already in relative motion and are
compared at the instant they pass. Acceleration is not essential to
understanding time dilation. It is pure special relativity.
-- Jeff, in Minneapolis

that will not work. If you perform synchronization without acceleration there will be no time dilation at all. (remember that you must synchronize not only start times but also time speeds too or else this is not full synchronization)

Gigabyte
2008-Nov-09, 07:16 PM
My brain hurts.

hhEb09'1
2008-Nov-09, 09:00 PM
that will not work. If you perform synchronization without acceleration there will be no time dilation at all. (remember that you must synchronize not only start times but also time speeds too or else this is not full synchronization)Not going to work either

If one twin is three feet tall and still sucking his thumb, and the other is starting to go gray and think about retirement, it doesn't make much sense to say they're both twenty years old, just to make the clocks match. :)

We define our clocks by physical processes, the second (http://en.wikipedia.org/wiki/Second) is now "the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom". We can't change that.

Digix
2008-Nov-09, 09:17 PM
you miss here one pointn that you cant place twin into spaceship and make it fly at near light speed with no acceleration.
maibe some teleportation could do the trick, but we don't know how it will work.

We define our clocks by physical processes, the second is now "the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom". We can't change that.
ok, you got a way around it.
but how do you tell which clock is moving and which one is stationary then?
lets say you drift in space and another spaceship is flying by.
when you are close to each other you reset your timers.
and so which one will go faster?

hhEb09'1
2008-Nov-09, 09:38 PM
you miss here one pointn that you cant place twin into spaceship and make it fly at near light speed with no acceleration.
maibe some teleportation could do the trick, but we don't know how it will work.I'm just talking about clocks, really

ok, you got a way around it.
but how do you tell which clock is moving and which one is stationary then?
lets say you drift in space and another spaceship is flying by.
when you are close to each other you reset your timers.
and so which one will go faster?They'll both see each other as going slow. If one turns around and heads back to catch the other one, when it arrives it'll find it was slow.

cjameshuff
2008-Nov-09, 09:46 PM
If one twin is three feet tall and still sucking his thumb, and the other is starting to go gray and think about retirement, it doesn't make much sense to say they're both twenty years old, just to make the clocks match. :)

And in any case, you can't make all clocks match (unless they're on VCRs or DVD players, in which case they'll typically all be blinking 12:00 at various rates). There is no consistent way to establish an absolute time. Digix's comment about "synchronizing the time speeds too" makes me think he's still stuck on this concept. (Which is perfectly understandable, given how firmly founded our concept of time is on everyday experiences...it can be hard to convince oneself that a universal clock, and thus simultaneity across reference frames, doesn't exist.)

but how do you tell which clock is moving and which one is stationary then?
lets say you drift in space and another spaceship is flying by.
when you are close to each other you reset your timers.
and so which one will go faster?

Each will see the other as being dilated.

Consider a spaceship flying past a planet toward another spaceship that's approaching the planet, both going at the same speed relative to the planet, in opposite directions. The outgoing spaceship accelerates, then synchronizes its clock as it passes the planet post-acceleration. The incoming spaceship synchronizes its clock with the outgoing spaceship as they pass, then broadcasts its time to the planet as it flies past.

The relative velocity between the two spacecraft is higher than that between either and the planet, so each sees the other spacecraft as being more dilated than the planet. The planet and the spacecraft see each other as having the same dilation. The time given by the inbound spacecraft will be lagged. The inbound spacecraft will see the lag as having happened on the outbound spacecraft, which from its point of view is dilated more than the planet. The outbound spacecraft will see it as having happened on the inbound spacecraft, for the same reason, and the planet will see it as happening over the whole trip. The clocks don't match, but none of them are wrong.

Digix
2008-Nov-09, 09:59 PM
I'm just talking about clocks, reallyThey'll both see each other as going slow. If one turns around and heads back to catch the other one, when it arrives it'll find it was slow.

so it depends on acceleration, because to turn back you need to stop and accelerate in opposite direction.

Ken G
2008-Nov-09, 10:03 PM
You mean like this (http://mentock.home.mindspring.com/twins.htm)?

There, consider all three, Ann, Bob, and Carl, to never accelerate, but only to stay in constant inertial motion and pass each other at the appropriate times.Unfortunately, the claim in that explanation, that acceleration is not involved in achieving or resolving the paradox, is flat out wrong. Every scenario they discuss which would seemingly lead to a "paradox", i.e., a pair of twins meeting at two events, does indeed involve acceleration. Alternatively, the scenario they mention involving a "messenger" does not lead to any paradoxes, because we have no reason to expect any of the clocks to agree, and no one ever meets a younger twin. Their math is correct, but their claims are misguided. In brief, if you connect two reference frames in relative motion into one reference frame, which is what they do, you have the definition of acceleration.

Digix
2008-Nov-09, 10:07 PM
And in any case, you can't make all clocks match (unless they're on VCRs or DVD players, in which case they'll typically all be blinking 12:00 at various rates). There is no consistent way to establish an absolute time. Digix's comment about "synchronizing the time speeds too" makes me think he's still stuck on this concept. (Which is perfectly understandable, given how firmly founded our concept of time is on everyday experiences...it can be hard to convince oneself that a universal clock, and thus simultaneity across reference frames, doesn't exist.)
why do you think so? If I said about time speed synchronization that means exactly that time is not universal or else why do you need synchronization?

Each will see the other as being dilated.

Consider a spaceship flying past a planet toward another spaceship that's approaching the planet, both going at the same speed relative to the planet, in opposite directions. The outgoing spaceship accelerates, then synchronizes its clock as it passes the planet post-acceleration. The incoming spaceship synchronizes its clock with the outgoing spaceship as they pass, then broadcasts its time to the planet as it flies past.

The relative velocity between the two spacecraft is higher than that between either and the planet, so each sees the other spacecraft as being more dilated than the planet. The planet and the spacecraft see each other as having the same dilation. The time given by the inbound spacecraft will be lagged. The inbound spacecraft will see the lag as having happened on the outbound spacecraft, which from its point of view is dilated more than the planet. The outbound spacecraft will see it as having happened on the inbound spacecraft, for the same reason, and the planet will see it as happening over the whole trip. The clocks don't match, but none of them are wrong.
I understand that, but I wanted to find the cause of time dilation.
and it seems to be acceleration which is same as in gravitational time dilation.
in that case I can get rid of another theory making physic simpler.

timb
2008-Nov-09, 10:14 PM
Unfortunately, the claim in that explanation, that acceleration is not involved in achieving or resolving the paradox, is flat out wrong. Every scenario they discuss which would seemingly lead to a "paradox", i.e., a pair of twins meeting at two events, does indeed involve acceleration. Alternatively, the scenario they mention involving a "messenger" does not lead to any paradoxes, because we have no reason to expect any of the clocks to agree, and no one ever meets a younger twin. Their math is correct, but their claims are misguided.

I disagree. It's still a "paradox", it just doesn't involve twins. Call it the transitive clock setting paradox if you like. There is a reason to expect the clocks to agree: they are accurate clocks and have been synchronized. If I synchronize clocks A and B, then synchronize clocks B and C, I expect A and C to be synchronized.

Digix
2008-Nov-09, 10:20 PM
I disagree. It's still a "paradox", it just doesn't involve twins. Call it the transitive clock setting paradox if you like. There is a reason to expect the clocks to agree: they are accurate clocks and have been synchronized. If I synchronize clocks A and B, then synchronize clocks B and C, I expect A and C to be synchronized.

that will not work if you have clock a synchronize it with clock b, accelerate clock B and synchronize with clock C then A and C will not match for sure.
without acceleration or without universal time it will not work without acceleration

hhEb09'1
2008-Nov-09, 10:24 PM
Unfortunately, the claim in that explanation, that acceleration is not involved in achieving or resolving the paradox, is flat out wrong. Every scenario they discuss which would seemingly lead to a "paradox", i.e., a pair of twins meeting at two events, does indeed involve acceleration. Alternatively, the scenario they mention involving a "messenger" does not lead to any paradoxes, because we have no reason to expect any of the clocks to agree, and no one ever meets a younger twin. Their math is correct, but their claims are misguided. In brief, if you connect two reference frames in relative motion into one reference frame, which is what they do, you have the definition of acceleration.How do you connect two reference frames into one reference frame, especially if they're going in opposite directions? :)

There is no paradox. Period. And neither Ann nor Carl are accelerated. As far as the clocks are concerned, the result is the same, whether we use Bob's clock or Carl's clock on the return. It's the same analysis that Einstein included in his original 1905 special relativity paper, from the beginning.
without acceleration or without universal time it will not work without accelerationIt works, as Ken G says, but he just doesn't consider it a paradox then.

Ken G
2008-Nov-09, 10:32 PM
I disagree. It's still a "paradox", it just doesn't involve twins.The "paradox" you get is no different from the symmetry of time dilation. Two clocks, in relative motion, will think the other is running slowly (in the common wording). If you view that as a "paradox", then that is the only one you can get without acceleration. If, on the other hand, you think that is palatable because the two clocks are only at the same place and time once, so lose any requirement to agree with each other, then it is only a "paradox" if the two senses of time are somehow reunited at a later event. That always requires either acceleration, or gravity.

If I synchronize clocks A and B, then synchronize clocks B and C, I expect A and C to be synchronized.Not if the clocks being synchronized are in relative motion, since then there's no reason to expect them to stay synchronized-- unless you think time dilation itself is a paradox (but that is not the twin paradox, which is supposed to be surprising even after you accept time dilation). The "transitive" paradox is nothing but time dilation, but the twin paradox is more than just that.

Digix
2008-Nov-09, 10:45 PM
Ken G says, but he just doesn't consider it a paradox then.

of course time dilation will happen but the whole point is that you need to meet in the end. And if we ignore acceleration then everything is perfectly symmetric.

I was thinking a lot how to break that symmetry even came into conclusion that entire SR may be wrong since there was jut no way to tell who is stationary and who is moving.

hhEb09'1
2008-Nov-09, 11:02 PM
That always requires either acceleration, or gravity.Not acceleration of a physical object, though. None of Ann, Bob, or Carl, are accelerated, nor are their clocks. That's the beauty of it. And even if Bob were to return with Carl, his clock would match Carl's all along the way, but no physical clock has to be accelerated.
even came into conclusion that entire SR may be wrong since there was jut no way to tell who is stationary and who is moving.That's ridiculous though, special relativity has been verified many times over. If you want to pursue that, we'll have to take it to ATM.

pzkpfw
2008-Nov-09, 11:29 PM
I've read that acceleration isn't the "important" thing.

I tried a short google, but couldn't find one of the pages I've read, so I'll summarise what I think I've seen:

1. E Earth in freefall around Sun.
|
2. ---a----------------> Alice zooms past earth
| |
3. | <------b---- Bob zooms past Alice
|
4. <--c------- Bob zooms past Earth

Notes on diagram:

"a" and "b" are clock synchronisation events.

Alice and Bob are never accelerating - they are (in the time of this "experiment") already moving at some "speed".

At "c", Bob's clock will aparently show a smaller time than the Earth clock.

---

What I've read says that it's not the acceleration that resolves the "paradox", but that one of the clocks is in one reference frame but the other is in a changing reference frame.

[That acceleration is what would cause one actual physical clock to change frames, does not mean it's the acceleration itself that has the effect (resolves the "paradox").]

Is that wrong?

cjameshuff
2008-Nov-09, 11:38 PM
I was thinking a lot how to break that symmetry even came into conclusion that entire SR may be wrong since there was jut no way to tell who is stationary and who is moving.

Nobody's stationary. There's no such thing as stationary. However, one of the clocks stays in the same inertial frame, while the other changes frames, whether through sitting on an accelerating spaceship or having its setting copied between passing spaceships.

Ken G
2008-Nov-10, 12:54 AM
How do you connect two reference frames into one reference frame, especially if they're going in opposite directions? By claiming that the "messenger clock" somehow maintains the time stream of the clock it is "messenging". That connects the motion of the two clocks (one clock and its "messenger") into a single time stream-- and it is the time stream of an accelerated frame.

There is no paradox. Period. And neither Ann nor Carl are accelerated. In the correct formulation, there is a seeming paradox, because it goes deeper than time dilation-- expressly because Ann or Carl are accelerated. That's exactly why the "messenger" version is really nothing more than time dilation-- which is viewed as a weaker paradox expressly because it satisfies the very same symmetry principle that the twin paradox does not satisfy-- because of the acceleration.

Of course there are no real paradoxes here, but there are seeming paradoxes that stem from time dilation, and there are deeper seeming paradoxes that stem from acceleration. The first class is just the usual non-absolute time business, the second class are the "twin paradoxes". This is just what that other description fails to recognize.

Ken G
2008-Nov-10, 01:05 AM
- they are (in the time of this "experiment") already moving at some "speed".

At "c", Bob's clock will aparently show a smaller time than the Earth clock.
But that's just simple time dilation (if that can be viewed as simple). The twin paradox is a deeper issue, because the symmetry of the time dilation is broken.

What I've read says that it's not the acceleration that resolves the "paradox", but that one of the clocks is in one reference frame but the other is in a changing reference frame.The paradox is resolved by the way simultaneity shifts when you change reference frame, i.e., when you accelerate.

hhEb09'1
2008-Nov-10, 01:19 AM
By claiming that the "messenger clock" somehow maintains the time stream of the clock it is "messenging".That is never claimed. I'm not even sure what it means.
In the correct formulation,In the correct formulation? This is the original. :)
there is a seeming paradox, It's all relative right? "Seeming paradox" means "no paradox" except to those it "seems"?
because it goes deeper than time dilation-- expressly because Ann or Carl are accelerated.If we're talking about the same thing, neither Ann nor Carl are accelerated at any point in the thought experiment. And, when Carl is involved, neither is Bob, nor their clocks.
Of course there are no real paradoxes here, but there are seeming paradoxes that stem from time dilation, and there are deeper seeming paradoxes that stem from acceleration. The first class is just the usual non-absolute time business, the second class are the "twin paradoxes". This is just what that other description fails to recognize.This is the first I've heard of levels of paradoxes. Isn't it all in the mind of the beholder? Because there are no paradoxes, in this case?

And even if Bob were to return with Carl, his clock would match Carl's all along the way, but no physical clock has to be accelerated.

hhEb09'1
2008-Nov-10, 01:26 AM
Of course there are no real paradoxes here, but there are seeming paradoxes that stem from time dilation, and there are deeper seeming paradoxes that stem from acceleration. The first class is just the usual non-absolute time business, the second class are the "twin paradoxes". This is just what that other description fails to recognize.That's one of the interesting things about this example. It doesn't matter whether Bob returns with Carl or not. The reading on the clock that ends up back at Ann's is the same.

I'm not sure why you think they are fundamentally different.

Ken G
2008-Nov-10, 01:58 AM
That is never claimed. It is certainly claimed. That's the whole idea of the paradox. Let me put this more simply-- what breaks the symmetry between the clocks? The one clock "hands off" to the other. We can pretend that's not acceleration, but it is, it's an acceleration of the point of view. Points of view are what relativity is all about.
"Seeming paradox" means "no paradox" except to those it "seems"?Correct. That's not obvious?

This is the first I've heard of levels of paradoxes.If you can't see that the twin paradox is a deeper paradox than time dilation, owing to the break in symmetry, I'm not sure I can explain it to you. But I know you will figure it out.

Digix
2008-Nov-10, 02:00 AM
.That's ridiculous though, special relativity has been verified many times over. If you want to pursue that, we'll have to take it to ATM.
I know that, but it was very long time ago when i read about it first time, I do not object it now.
however relativity is also only one of possible physical models and there are other ways to do same.

its like we now discussed, SR effects can be better explained by GR model. in absolutely different way that has no direct logical relation to SR

SR is good, but if you start thinking more you always end in this paradox.

and in case of ATM theories I think I have one too, but it needs more careful checking.

Digix
2008-Nov-10, 02:09 AM
Nobody's stationary. There's no such thing as stationary. However, one of the clocks stays in the same inertial frame, while the other changes frames, whether through sitting on an accelerating spaceship or having its setting copied between passing spaceships.

that is obvious, but SR does not mention acceleration. without acceleration it impossible to tell if you ever moved anywhere. so all time dilation stuff becomes total nonsense. because it is basically imagined in this way

we put 2 twins in the boxes, move one box around a little and then put them back. nobody of these twins know anything about the journey (because theory does not mentions acceleration we ignore it) ,and they surprise that by some unknown reason one is younger than another.

without acceleration everything is perfectly symmetric.

timb
2008-Nov-10, 02:24 AM
The "paradox" you get is no different from the symmetry of time dilation. Two clocks, in relative motion, will think the other is running slowly (in the common wording). If you view that as a "paradox", then that is the only one you can get without acceleration. If, on the other hand, you think that is palatable because the two clocks are only at the same place and time once, so lose any requirement to agree with each other, then it is only a "paradox" if the two senses of time are somehow reunited at a later event. That always requires either acceleration, or gravity.

Not if the clocks being synchronized are in relative motion, since then there's no reason to expect them to stay synchronized-- unless you think time dilation itself is a paradox (but that is not the twin paradox, which is supposed to be surprising even after you accept time dilation). The "transitive" paradox is nothing but time dilation, but the twin paradox is more than just that.

Why is it more than just that, rather than less? Do people think that the acceleration in the twin paradox (TP) should somehow cancel out the time dilation? on the contrary, they usually attribute the time dilation to the acceleration! What went out and came back different than a Newtonian would expect in the TCSP is information. In the TP it is a human. In the TCSP someone can say "the second clock's time went out and came back, but from its point of view it was the first clock time that went out and came back, so the times should be the same", analogously to the naive response to the TP.

Consider the gedanken experiment where the situation is as in the TCSP, but instead, or as well as, transmitting a time between space vehicles as they pass (real close), they beam one of the twins from vehicle to vehicle. A human is, after all, merely a lump of atoms plus information, and identical atoms are indistinguishable while information can be recorded and transmitted. As in the TP, when the second twin meets his brother he finds himself the younger. This clarifies the situation and suggests that it is not the acceleration, per se, that causes the difference, but the change(s) in reference frame.

Jeff Root
2008-Nov-10, 02:42 AM
Red Spray Paint,

When I started reading the story of Ann, Bob, and Carl that you linked
(very concise!), I was expectant that it would support my original thought
that the twins paradox could be explained without acceleration. Alas, it
has the failing pointed out by Ken and Digix: The clocks cannot be
synchronized when they are in relative motion.

I made that mistake here a few months ago in an argument about
teleportation, FTL, and causality. All I did was "synchronize" the clocks
at a single instant in time, so that they read the same as they passed.
That is not synchronization.

Making the clocks to the standard "universal" definition of the second
does not synchronize the clocks, either. If the clockmaker makes two
clocks in two reference frames moving relative to each other, the clocks
cannot tick at the same rate. Each sees the other as ticking slower!
They are not synchronizeable even though they were made to the same
standard. You have to put the two clocks at rest relative to each other
before you can synchronize them. Then it is necessary to accelerate
one in order to move them apart.

-- Jeff, in Minneapolis

hhEb09'1
2008-Nov-10, 03:47 AM
It is certainly claimed. That's the whole idea of the paradox.Well, I don't know where. As I said, I don't even know what it means, so I don't know why I'd claim it, especially since I think that there is no paradox.
Let me put this more simply-- what breaks the symmetry between the clocks? The one clock "hands off" to the other. We can pretend that's not acceleration, but it is, it's an acceleration of the point of view. Points of view are what relativity is all about.Nonsense. It's about observations, idnit? All physics is observations? :)

There just is no physical object that is accelerated in that thought experiment, which could be physically realizeable.
Correct. That's not obvious?But I'm not the one making a distinction between "seeming paradoxes" and "no paradoxes" or "deep paradoxes" (which also seem to be no paradox)

If you can't see that the twin paradox is a deeper paradox than time dilation, owing to the break in symmetry, I'm not sure I can explain it to you. But I know you will figure it out.I figure both are not paradoxes.

When I started reading the story of Ann, Bob, and Carl that you linked
(very concise!), I was expectant that it would support my original thought
that the twins paradox could be explained without acceleration. Alas, it
has the failing pointed out by Ken and Digix: The clocks cannot be
synchronized when they are in relative motion.Thanks! (BTW, here's another (http://mentock.home.mindspring.com/twin2.htm))

I thought you'd found a place where'd I'd tripped up. I wrote that years ago, when I was younger and more agile, but when I read your post I started thinking maybe I'd used a different meaning of the word synchronize. But I notice I didn't even do that--I made no attempt to synchronize the clocks, in that story. I gotta go back and pat myself on the back, tomorrow.
Making the clocks to the standard "universal" definition of the second
does not synchronize the clocks, either.Clearly, I wasn't trying to synchronize the clocks--as you say, that'd be impossible :)

Ken G
2008-Nov-10, 04:00 AM
Why is it more than just that, rather than less? Do people think that the acceleration in the twin paradox (TP) should somehow cancel out the time dilation? People invariably only include the time dilation, which is why they get a paradox. The resolution comes from the shift in simultaneity that is present whenever an observer accelerates.

Perhaps I should start from the beginning, because I think there is a lot of confusion on this thread about what the twin paradox actually is. I would like to make these points:

1) I think we all recognize there is no actual problem, the issue is that one reaches false conclusions when one makes false assumptions. We generally call that a "paradox" only when the false assumptions are so subtle that they seem perfectly inoccuous.

2) There are three big surprises about time in relativity, and the first is simply time dilation-- clocks run slow when they are moving relative to the observer making that determination. But time dilation is not the twin paradox, because time dilation, in the absence of gravity or acceleration, only presents surprising conclusions for clocks that are separating in space. As such, it is easy to "duck" any disconnects in the perception of time by simply blaming the concept of "nowness" (simultaneity) as it extends between vastly separated clocks. There is even a convention of simultaneity that is used in relativity, and it is easy to blame the convention. There doesn't need to be anything "real" about time dilation, until....

3) The "twin paradox" brings in yet two more surprising elements of time, and these are quite central to that "paradox". The first is that two people can meet at two different events, and have aged a different amount between those events. You see, now we cannot say that the problem is any simultaneity convention, or the accumulation of huge distances between the people-- we really have an inescapable difference in the elapsed time. But this requires either acceleration or gravity, or it simply could never occur.

4) Even this is not yet the full "twin paradox", which has one more surprise in store for us. Imagine a third observer, Danielle, who stays always directly between Alice and Bob. Note that Danielle can map out the distance to Alice as a function of Danielle's time, call that function a(t), and the distance to Bob, call that b(t). Note that a(t) and b(t) are zero at both the start and the end of the experiment. But what's more, a(t) and b(t) are precisely the same functions, they are identical (by construction-- Danielle is at the center between Alice and Bob). Yet, Alice is older than Bob at the end! What breaks that symmetry? Their dynamical behavior, relative to Danielle, is identical in every way-- except one: the presence of proper acceleration or gravity. There is simply no other way that Danielle can explain the difference in their ages, when a(t) and b(t) are identical functions.

So that's the full "twin paradox", the breaking of the symmetry of a(t) and b(t) via the recognition of proper acceleration. There's no way to say you are looking at the twin paradox without that element, it simply isn't much of a paradox if you are using "messenger clocks". By that I mean simply, the subtlety of the wrong assumptions that lead to the paradox is vastly greater in the real twin paradox-- it is simply the assumption that you don't need to care about the presence or absence of proper acceleration (or gravity). The acceleration is absolutely crucial, because ignoring it is the whole source of the paradox, it is the false assumption: that acceleration doesn't matter in determining the elapsed time along a world line.

pzkpfw
2008-Nov-10, 04:26 AM
The acceleration is absolutely crucial, because ignoring it is the whole source of the paradox, it is the false assumption: that acceleration doesn't matter in determining the elapsed time along a world line.

I'm not sure that post really explains what the paradox "is". I'd boil it down to:

1. Observers in relative motion observe each others' clock to be running (equally) slower than their own.
2. BUT, when the twin who left, returns - he or she will have aged less.

That's the "paradox" in a nutshell. (i.e. The contradiction of those two facts).

...and, you don't need acceleration to resolve that; just the changing reference frame of the travelling twin/clock/...

DrRocket
2008-Nov-10, 04:47 AM
I'm not sure that post really explains what the paradox "is". I'd boil it down to:

1. Observers in relative motion observe each others' clock to be running (equally) slower than their own.
2. BUT, when the twin who left, returns - he or she will have aged less.

That's the "paradox" in a nutshell. (i.e. The contradiction of those two facts).

...and, you don't need acceleration to resolve that; just the changing reference frame of the travelling twin/clock/...

You do need acceleration to resolve the issue. And here is why:

The "paradox" arises from the application of special relativity in the formulation of the question (if you do the whole problem using general relativity then you don't run into a "paradox" at all). Special relativity is formulated to be applied in inertial reference frames, and only in inertial reference frames.

In the twin paradox there is one twin whose frame of reference is clearly inertial -- the twin who remains behind. The traveling twin must leave (one acceleration) stop and turn around (the critical acceleration) return and stop (a third acceleration). Those accelerations clearly and unambiguously demonstrate that his reference frame is not inertial and that you cannot apply special relativity directly in that frame. Thus there is a preferred reference frame for the twin "paradox" and it is the the reference frame of the non-traveling twin.

Ken G
2008-Nov-10, 04:55 AM
...and, you don't need acceleration to resolve that; just the changing reference frame of the travelling twin/clock/... By "changing reference frame", I take it you mean... acceleration. There is no other type of changing frame that leads to a paradox, if one does not already count time dilation as a paradox. Time dilation means that clocks, once synchronized, do not stay synchronized. That's simply not the twin paradox, because it requires a convention for simultaneity-- whereas the twin paradox does not. Or you can look at it the way DrRocket describes it above, which is also completely correct. Or look at it this way-- if acceleration (or gravity) were impossible, there would never be any twin paradox. There would just be the simple fact that there is no "transitivity" in synchronization of clocks-- because of time dilation, they don't stay synchronized. But thinking that time dilation is all you need is what gives you the twin paradox.

Ken G
2008-Nov-10, 05:06 AM
That's one of the interesting things about this example. It doesn't matter whether Bob returns with Carl or not. The reading on the clock that ends up back at Ann's is the same.If it is still not clear from what I said above, it matters dramatically whether or not Bob returns with Carl-- you have put your finger squarely on the crucial issue, but reached the wrong conclusion about it. Because if Bob does not return with Carl, there simply is no twin paradox. What does Alice care about Carl's clock? Alice cares about Bob's clock, Bob is her twin. If only Carl returns, Carl cannot claim his clock agrees with Bob's, for it doesn't! All he can claim is that it was once synchronized to Bob-- but Alice will quite correctly note it no longer has any connection to Bob's clock because Carl's clock will no longer be synchronized to Bob's, unless Bob does come back with Carl. This is the whole point, and why it is no kind of twin paradox if Bob does not return with Carl.

pzkpfw
2008-Nov-10, 05:15 AM
From what I've read, if one postulates a means to synchronise clocks, then it all works out for already-moving non-accelerating objects. The relevant factor is the changing reference frames (not how they were changed).

Does lack of a convention for simulataenity (which I fully accept since participation in a "FTL communication" thread) invalidate the use of clock sychronisation in the thought experiment?

(Or, to put it another way, while we know "instant" teleportation can't really happen, why not invoke it, in the thought experiment, to allow Bob to return with Carl?

The little pictures showing Bob's world line as longer than Alices, even with sharp points where the reference frames change, still works out fine with Bob's time elapsed being less.

| \
| \
| \
| /
| /
| /
A B

or

| \ /
| \ /
| \/ __ C gets B's clock reading
| /\ (or Bob teleports to Carls ship)
| / \
| / \
A B C

)

P.S. Publius! Van Rijn!

Ken G
2008-Nov-10, 05:34 AM
From what I've read, if one postulates a means to synchronise clocks, then it all works out for already-moving non-accelerating objects. The relevant factor is the changing reference frames (not how they were changed).I think what you are overlooking is that the twin paradox is not that Alice calculates she will age faster than would a series of inertial clocks whose motion is tangential to a world line that connects two events in Alice's life. That's just time dilation-- Alice knows those clocks will show less total elapsed time, it's simply not the twin paradox.

The twin paradox comes in when there's really a twin, there's really a Bob who is also present at those two events in Alice's life. If you know nothing of acceleration, you are forced to conclude that Bob should have a symmetric expectation to Alice, that a series of inertial clocks tangential to Alice's apparent motion (seen from Bob's accelerating frame) should be dilated and should dictate that Alice will be the younger one. The resolution of the paradox is that that sequence of clocks will not track Alice's time at all, because to seem inertial from Bob's accelerating point of view, those clocks have to actually be accelerating, and as such will not reliably track Alice's time no matter how short the intervals chosen. That is why the twin paradox is all about acceleration.

Does lack of a convention for simulataenity (which I fully accept since participation in a "FTL communication" thread) invalidate the use of clock sychronisation in the thought experiment?For time dilation, you need a synchronization convention. You can make time dilation go away by using a different convention. But you cannot make the twin paradox go away, because anything you do to your synchronization convention "comes out in the wash" when acceleration is consistently included. This is the usual debate about whether general relativity is only about gravity, or about gravity and acceleration. If you assume the standard simultaneity convention, then general relativity is only about gravity, but if the "general" means you are generalizing to any simultaneity convention, then general relativity is also about acceleration.

(Or, to put it another way, while we know "instant" teleportation can't really happen, why not invoke it, in the thought experiment, to allow Bob to return with Carl?)Because we know instant teleportation can't really happen. Thought experiments don't mean we can suspend the laws of physics, they just mean we can probe those laws without actually doing the experiment.

pzkpfw
2008-Nov-10, 05:52 AM
I think what you are overlooking is that the twin paradox is not that Alice calculates she will age faster than would a series of inertial clocks whose motion is tangential to a world line that connects two events in Alice's life. That's just time dilation-- Alice knows those clocks will show less total elapsed time, it's simply not the twin paradox.

That's very much not what I think the Twins Paradox is, see post #61.

Nor, even if that were the case, do I think the answer is "simply time dilation".

To my understanding, again, the point of the twins paradox is that each of two relatively moving observers observe each others clock going equally slower than their own (time dilation coupled with the each-observers-point-of-view-is-equally-relevant thing). So when one twin zooms away (and returns), one would initially (naively?) think it shouldn't matter which is "really" moving and which stayed home; but one of them does actually age less. That's the paradox. The answer being that one stays in one intertial frame, and the other doesn't. That acceleration is needed to make the second experience different inertial frames doesn't seem to be the point - as shown by thought experiments invoking clock synchronisation and already-moving ships.

Because we know instant teleportation can't really happen. Thought experiments don't mean we can suspend the laws of physics, they just mean we can probe those laws without actually doing the experiment.

Is there no way we can find to synchronise clocks between two passing ships?

Does it really matter that there is a physical Bob or just a clock (or clock setting) representing him?

Jeff Root
2008-Nov-10, 06:21 AM
A third clock (C) can be set in motion beforehand so that it ought to
be synchronized when it gets into Alice's frame. The synchronization
is checked at the end of the demonstration, rather than at the instant
of time transfer from clock B to clock C. That reduces the number of
accelerations from three to two, between the three reference frames.

-- Jeff, in Minneapolis

Tensor
2008-Nov-10, 12:55 PM
This is the usual debate about whether general relativity is only about gravity, or about gravity and acceleration.

I'm not sure why you think there is a debate. Among GR scholars, GR is about gravity and any kind of motion. Einstein's original purpose in generalizing SR was, indeed, to generalize it to any motion, be it, accelerated, constant, rotational, or arbitrary. He was able to include gravity only because of his discovery of the equivalence principle. If you go back and read his original explainations of GR, you will find that they used rotating disks and rotational motion, with no mention of gravity.

Ken G
2008-Nov-10, 03:23 PM
To my understanding, again, the point of the twins paradox is that each of two relatively moving observers observe each others clock going equally slower than their own (time dilation coupled with the each-observers-point-of-view-is-equally-relevant thing). So when one twin zooms away (and returns), one would initially (naively?) think it shouldn't matter which is "really" moving and which stayed home; but one of them does actually age less. [i]OK, then we agree on what the paradox is. It follows directly that acceleration is the key.

The answer being that one stays in one intertial frame, and the other doesn't. That acceleration is needed to make the second experience different inertial frames doesn't seem to be the point - as shown by thought experiments invoking clock synchronisation and already-moving ships.If one stays in an inertial frame, and the other doesn't, then you are talking about acceleration. Which is indeed the key issue.

Is there no way we can find to synchronise clocks between two passing ships?You can synchronize them when they pass, but they don't stay synchronized, due to time dilation. So you can't generate a paradox that way-- time dilation is only half the paradox, the part that works out fine without acceleration, and leads Alice to expect Bob to be younger, but does not lead Bob to expect to be older than Alice. Without that last bit, there simply is no paradox.

Does it really matter that there is a physical Bob or just a clock (or clock setting) representing him?No, but if there is one clock representing Bob, it has to accelerate. And if there is a "messenger clock", then you are doing Alice's calculation, not Bob's-- Bob does not think that messenger clock stays synchronized with his, only Alice thinks that.

Ken G
2008-Nov-10, 04:02 PM
I'm not sure why you think there is a debate. I think there's a debate because there is a debate. No one debates how do to general relativity, but just what is meant by the "general" part is indeed a matter of point of view. Some would say it means that we can treat gravity-- and it is quite common to find statements to the effect that general relativity is just special relativity plus gravity. This is because it is false that you cannot do special relativity from an accelerated reference frame, you simply have to treat the accelerated frame as a series of tangential inertial frames with clocks synchronized as they pass. That completely generates general relativity with no gravity, i.e., it can treat any kind of motion, but by replacing it with a series of inertial-frame calculations.

But what it does not do is give you any clock synchronization convention. It still treats inertial frames specially, in the synchronization convention. So if one wants to use any coordinates, not just those built around the inertial synchronization, then you need the machinery of general relativity if you want to treat it all seamlessly, rather than always converting to tangential inertial frames. Thus, if the "general" means that inertial motion is not treated as in any way special, including in the synchronization, then you'd have a need for general relativity even without gravity.

I guess the point I'm making is that special relativity can do any calculation that general relativity can, if there is no gravity. But acceleration needs to be treated specially, and if you don't, you get the twin paradox. That's really what the thread is about, why acceleration is a crucial part of that paradox-- the issue of what the general means in general relativity is a minor issue here.

Einstein's original purpose in generalizing SR was, indeed, to generalize it to any motion, be it, accelerated, constant, rotational, or arbitrary. The question may be asked, had there been no such thing as gravity, would we need to create general relativity? Certainly no new problems become solvable.

If you go back and read his original explainations of GR, you will find that they used rotating disks and rotational motion, with no mention of gravity.All of which can be addressed with special relativity. Hence the debate of what general relativity really means. If you take a philosophical perspective, typical of Einstein, you'd say it doesn't matter if it allows for no new calculations, what matters is you can do them all the same way. If you take an empirical standpoint, a theory that makes all the same predictions as a previous one is not a new theory at all.

sirius0
2008-Nov-10, 10:33 PM
One person's gravity is another's acceleration. Principle of equivalence.

timb
2008-Nov-10, 11:48 PM
People invariably only include the time dilation, which is why they get a paradox. The resolution comes from the shift in simultaneity that is present whenever an observer accelerates.

What i (and, I think, others) are arguing is that acceleration is just the means to change reference frames, and it is not the acceleration per se that causes the time difference. The "it's the acceleration wot dun it" reasoning that leads to the conclusion that the time difference (as measured by clocks or twins' wrinkles) is all down to the acceleration. Obviously , they reason, the rate of time dilation is proportional to acceleration. AFAIK this is wrong and the A-B-C "clock synchronization" paradox is an attempt to demonstrate this.

Perhaps I should start from the beginning, because I think there is a lot of confusion on this thread about what the twin paradox actually is. I would like to make these points:

1) I think we all recognize there is no actual problem, the issue is that one reaches false conclusions when one makes false assumptions. We generally call that a "paradox" only when the false assumptions are so subtle that they seem perfectly inoccuous.

2) There are three big surprises about time in relativity, and the first is simply time dilation-- clocks run slow when they are moving relative to the observer making that determination. But time dilation is not the twin paradox, because time dilation, in the absence of gravity or acceleration, only presents surprising conclusions for clocks that are separating in space. As such, it is easy to "duck" any disconnects in the perception of time by simply blaming the concept of "nowness" (simultaneity) as it extends between vastly separated clocks. There is even a convention of simultaneity that is used in relativity, and it is easy to blame the convention. There doesn't need to be anything "real" about time dilation, until....

3) The "twin paradox" brings in yet two more surprising elements of time, and these are quite central to that "paradox". The first is that two people can meet at two different events, and have aged a different amount between those events. You see, now we cannot say that the problem is any simultaneity convention, or the accumulation of huge distances between the people-- we really have an inescapable difference in the elapsed time. But this requires either acceleration or gravity, or it simply could never occur.

4) Even this is not yet the full "twin paradox", which has one more surprise in store for us. Imagine a third observer, Danielle, who stays always directly between Alice and Bob. Note that Danielle can map out the distance to Alice as a function of Danielle's time, call that function a(t), and the distance to Bob, call that b(t). Note that a(t) and b(t) are zero at both the start and the end of the experiment. But what's more, a(t) and b(t) are precisely the same functions, they are identical (by construction-- Danielle is at the center between Alice and Bob). Yet, Alice is older than Bob at the end! What breaks that symmetry? Their dynamical behavior, relative to Danielle, is identical in every way-- except one: the presence of proper acceleration or gravity. There is simply no other way that Danielle can explain the difference in their ages, when a(t) and b(t) are identical functions.

I may have missed something here, but if a(t)=b(t) then Danielle isn't in a constant inertial frame either (because Bob isn't).

So that's the full "twin paradox", the breaking of the symmetry of a(t) and b(t) via the recognition of proper acceleration. There's no way to say you are looking at the twin paradox without that element, it simply isn't much of a paradox if you are using "messenger clocks". By that I mean simply, the subtlety of the wrong assumptions that lead to the paradox is vastly greater in the real twin paradox-- it is simply the assumption that you don't need to care about the presence or absence of proper acceleration (or gravity). The acceleration is absolutely crucial, because ignoring it is the whole source of the paradox, it is the false assumption: that acceleration doesn't matter in determining the elapsed time along a world line.

Yes, but... you get the same answer (time difference) with the "messenger clocks", don't you? The intention is to measure the comoving duration of an out and back journey at relativistic speeds without the messy accelerations. When the signal from Carl's clock arrives and it's a year behind Alice's, she think's "wow! if Bob had jumped off his spaceship into Carl's, he'd be a year younger than me!". Maybe too contrived a paradox.

Durakken
2008-Nov-11, 12:01 AM
The reason the clocks read differently is because the clock that is moving is getting to the future faster by moving faster >.> As silly as it sounds it rings of truth ^.^

Digix
2008-Nov-11, 12:47 AM
What i (and, I think, others) are arguing is that acceleration is just the means to change reference frames, and it is not the acceleration per se that causes the time difference. The "it's the acceleration wot dun it" reasoning that leads to the conclusion that the time difference (as measured by clocks or twins' wrinkles) is all down to the acceleration. Obviously , they reason, the rate of time dilation is proportional to acceleration. AFAIK this is wrong and the A-B-C "clock synchronization" paradox is an attempt to demonstrate this.

that seems ok, acceleration is cause for time dilation exactly same as in case of gravity. But it it not that time dilation is proportional to acceleration directly, it is proportional to acceleration potential (acceleration * distance) if you accelerate time slows down if you decelerate it speeds sup
after we integrate that we get same as SR suggests

alainprice
2008-Nov-11, 01:16 AM
I could send a probe off into space on a gravitational assist maneuver with the nearest black hole. Once the probe has been released from the ship carrying it into space, we synchronize the clocks(one on the ship, the other in my lab on earth).

The ship ballistically flies off, approaches the BH, and then swings around due to the intense gravity. Luckily for us, this assist maneuver has sent the probe right back towards earth.

According to the earthbound observer, he has been under constant acceleration of 9.8 m/s2.

According to the probe, there never was an acceleration felt. We on earth disagree. While the reference frame is inertial, it accelerates towards the BH at all times. Who's right? If acceleration is the answer, the clock on earth has been running slower, since it has the same relative speeds being computed, AND acceleration. Let me stress that 1 year of 1g will give higher velocities than a BH fly-by. We can say the earth gravity is weak, but over time, it dwarfs the assist maneuver forces. Let's add that this experiment took 10 years of flight time to realize.

Yet somehow, the probe will have the 'slower' clock.

As KenG is trying to point out, it's not a hard connection between acceleration and the clock. The probe coasted the whole way. An acceleration in the future cannot modify what happened on my clock in the past. This examples seems to imply the opposite if I agree with certain people's reasoning. The acceleration phase around the BH is what caused the clock to shift by the amount observed. Not exactly! Relativity caused the difference. The relative speed we started with along with a change in reference frame makes the time differential permanent.

The relativity of simultaneity is often underrated for these examples. Just because some reasoning in SR fails, does not mean we need to resort to GR to find the answer. Often times, breaking down the problem and solving with SR yields correct predictions.

It's hard to explain myself when there is such misuse of the concepts of relativity. I don't see how this is going to be explained without saying, go back and read the manual.

Ken G
2008-Nov-11, 03:10 AM
What i (and, I think, others) are arguing is that acceleration is just the means to change reference frames, and it is not the acceleration per se that causes the time difference. Changing reference frame is accelerating, there's no distinction-- if we are talking about acceleration of an observer (and we are). Relativity is always about what the observers are doing, not the objects-- perhaps you mean that the acceleration of objects that are not observers is not what matters, and with that I agree. Relativity is about reference frames, and changing reference frames is about acceleration of an observer. There simply is no twin paradox if all observers are inertial and experience no gravity, that's the point. The "messenger" approach described in hhEb09'1's link is simply not the twin paradox, because Bob has no connection to Carl's clock in that formulation other than that he was once synchronized to it. Bob will never think he is younger than Alice, Alice will never think she is younger than Bob. No paradox at all, just time dilation.

The "it's the acceleration wot dun it" reasoning that leads to the conclusion that the time difference (as measured by clocks or twins' wrinkles) is all down to the acceleration.Clocks can get time differences for all kinds of reasons, including simple time dilation. But time dilation by itself is never the twin paradox. You always wait until after someone understands time dilation before you introduce the twin paradox to them, because they will always fall for it until they understand the fact that acceleration also changes the way we interpret the workings of time in the standard global simultaneity convention. Any explanation that includes nothing but time dilation, like the Alice-Bob-Carl one, fails to generate a paradox for students who understand time dilation. But the correct formulation succeeds at generating a paradox for such students, until they understand the role of simultaneity shifts when an observer accelerates. I suspect this is exactly what a lot of people on this thread are not understanding, so they miss how crucial it is.

I may have missed something here, but if a(t)=b(t) then Danielle isn't in a constant inertial frame either (because Bob isn't).You haven't missed anything. Danielle is definitely not in an inertial frame-- that's the whole point, the role of her acceleration. If one forgets the significance of her acceleration, one reaches a paradox that a(t) and b(t) are identical, but their time elapsed is different. That's the twin paradox in its essence.

Yes, but... you get the same answer (time difference) with the "messenger clocks", don't you?You can always get the right answer on all inertial clocks, just with time dilation. There is no issue with that, and it is not the twin paradox.

The intention is to measure the comoving duration of an out and back journey at relativistic speeds without the messy accelerations. No, that is not the intention-- for that is a simple calculation that does not invoke the twin paradox. To see that, simply note that in the A-B-C formulation, Bob will always think Alice is younger than Bob. The Carl clock does nothing to change that-- it's not the twin paradox until Bob must conclude that he is younger than Alice.

grav
2008-Nov-11, 06:04 AM
Wow, what an interesting thread! I had been using an "instant" acceleration to find time dilations incorporating turnarounds and such, which would be an infinite acceleration, but ironically no GR would be required since it does so in zero time and therefore zero time lag of that zero time due to time dilation, so it need not be considered. I really like the "trade-off" between reference frames used in this thread, though. It's much more obvious that no actual acceleration is required. It also makes it much more obvious what might really be taking place here.

In that site Hh linked to, it claimed that if 8 years passes for Bob at 80% time dilation, then Alice will observe 10 years have passed and be 2 years older when Bob returns. I don't see that, though. It can just as easily be claimed that if 8 years passes for Bob, then from Bob's perspective, 6.4 years will have passed for Alice, and Bob would be 1.6 years older than Alice upon return. So something appears to be missing there.

It is often said that the difference in ages depends upon who actually does the accelerating. But this thread shows that isn't so, but simply depends upon who switches frames, although the term acceleration can almost be defined loosely as who switches frames, I suppose, but apparently not even the observer themself needs to switch frames, only the frame carried by the clock.

Okay, so we have two initial observers, Alice and Bob. Neither needs to accelerate; we can just consider Alice as our stationary observer along a stationary line of clocks, and Bob has always been travelling inertially at some relative speed toward Alice. When Bob reaches Alice, Bob synchronizes his clock to hers. Then Bob continues to travel as he has always done, now away from Alice. At some point, Bob encounters Carl, also travelling inertially toward Alice in the opposite direction of Bob. When they coincide, Carl synchronizes his clock with what Bob's reads. Then Carl continues to travel until he reaches Alice and they compare times.

Now here's the thing. When Bob and Alice were travelling away from each other, both observe a lesser time on the other's clock. The same thing would happen if Bob instantly turned around and came back. So if this was all there was to it, each should read a lesser time than the other when they meet back up. Of course, this can't happen. So what else is taking place? A simultaneity shift between frames. When Bob travels away from Alice, the times on both clocks read less than the other. But when Bob turns around, he switches frames, and Alice is instantly thrown future-forward in Bob's worldline. That is to say, while all of the clocks along Alice's stationary line remain synchronized to Alice, Bob would say that the clocks in front of him always have a greater reading than those in back. So when Bob turns around, the clocks that were in front are now in back, and vice versa, so what once read greater is now less and the lesser times now read greater.

That might be a little confusing, I know. I had trouble with it at first, but I ran many scenarios for it and it seems to check out perfectly. My main complaint was that events that are happening now for Alice have already happened for Bob ahead of his line of travel, almost sounding as if Bob might see events before they occur, but the time of flight of light takes care of that, since light will still take time to reach the observer, events are always actually observed in the past.

So what about the trade-off between Bob and Carl? Well, at the instant Bob and Carl pass, Carl synchronizes his clock to Bob's. However, the time between them only remains the same at the point where they coincide. Since they are travelling in opposite directions, then while clocks in the stationary line read a greater time in front of his line of travel according to Bob, those same clocks read a lesser time according to Carl. However, both will actually read the same times at the moment they pass due to the time of flight effects, but that is because the clocks were already future-forward for Bob and past for Carl, but the light had not yet caught up to either one yet. I hope I explained that well enough.

Anyway, getting to the point, if Bob travels away from Alice for 4 years at 80% time dilation, then 3.2 years has passed for Alice according to Bob, and vice versa. Bob then switches off the clock reading to Carl who is travelling in the opposite direction. So although the clock reading is the same for Bob and Carl in the same place, Bob would view Alice as being past while Carl views Alice, being some distance in front of him, as being future-forward, the difference in the simultaneity shift between the two frames then being 2*d v/ (c^2-v^2). Since Carl views Alice as being future-forward by this amount greater than Bob in a different reference frame, this is how much older Alice becomes in the new reference frame. Carl then travels toward Alice for 4 years at 80% time dilation, making the overall difference in clock readings become 2*d v / (c^2 - v^2) - 2* (1 - .8) * (4 years) that Alice's is greater than Carl's. If Bob had instantly turned around, the readings would be the same and Alice would be that much older than Bob. The actual result of the formula would depend upon whether or not the distance travelled should be Lorentz contracted.

grav
2008-Nov-11, 07:38 AM
I just realized that since Alice never switches reference frames, then the time dilation observed by her of Bob must be the resulting time lag between their ages. So if Bob ages 8 years during the trip at 80% time dilation both ways, and Alice observes this, then Alice must have aged 10 years. Simple as that.

So incorporating that knowledge into the formula from the last post, from Bob's perspective, we have a resulting time lag between them due to both time dilation and a simultaneity shift on Bob's part of tl = 2 d v / (c^2 - v^2) - 2 (1 - .8) (4 years), where Bob's time one way is t = 4 years, the distance travelled is d = v t, and .8 is the time dilation L = sqrt[1 - (v/c)^2]. So we get

2 d v / (c^2 - v^2) - 2 (1 - .8) (4 years)
= 2 [ (vt) v / (c^2 - v^2) - (1 - L) t]
= 2 t [ v^2 / (c^2 - v^2) - (c^2 - v^2) / (c^2 - v^2) + L]
= 2 t [ (2 (v/c)^2 - 1) / (1 - (v/c)^2) + sqrt(1 - (v/c)^2)]

Looks like a strange formula but we know that Alice's age must be 2 years greater than Bob's when they reunite, while the time dilation Bob observes of Alice is that of 80% of 4 years, so only 6.4 years observed passing for Alice. That means that the simultaneity shift that takes place for Bob must tack on an additional time lag of 3.6 years in order to result in the 10 years of aging for Alice. The time lag due to the simultaneity shift, then, would be 2 d v / (c^2 - v^2) = 2 v^2 t /(c^2 - v^2) = 2 t / [(c/v)^2 - 1] = 3.6 years. 2 t = 8 years, so 1 / [(c/v)^2 - 1] should be .45 . But 1 / [(c/v)^2 - 1] = .5625, so apparently we must use the Lorentz contraction for the distance travelled by Bob after all. I wasn't sure about that in my last post. So when we do that, we get L / [(c/v)^2 - 1] = .45 as it should be, and the overall formula for the time lag between the ages of Alice and Bob due to time dilation and a simultaneity shift, from Bob's perspective, becomes 2 t [ L (v/c)^2 / (1 - (v/c)^2) - (1 - L)] = 2 t (L - 1 + (v/c)^2) / (1 - (v/c)^2) = 2 t [L / (1 - (v/c)^2) - 1] = 2 t [1 / L - 1] = 2 t [(1 - L) / L].

Ken G
2008-Nov-11, 12:27 PM
In that site Hh linked to, it claimed that if 8 years passes for Bob at 80% time dilation, then Alice will observe 10 years have passed and be 2 years older when Bob returns. I don't see that, though. It can just as easily be claimed that if 8 years passes for Bob, then from Bob's perspective, 6.4 years will have passed for Alice, and Bob would be 1.6 years older than Alice upon return. So something appears to be missing there.Yes, it is-- acceleration! The twin paradox itself is missing there, as is the crucial acceleration that gives rise to it. The problem is not how to calculate what Alice thinks is going on, the "tradeoff" does that quite easily using nothing but time dilation. But that's not the twin paradox. The "paradox" requires that we consider what Bob thinks is going on-- and the A-B-C tradeoff scenario fails to do that.

To clarify this, let's ask what Bob does think is going on in the A-B-C tradeoff scenario. After 8 years of Bob's life, Carl zooms by. Bob now thinks Alice is 6.4 years older. Bob gives Carl his watch, which reads 8 years. Now Bob thinks his watch is moving even faster than Alice, so from this point on, it will be time dilated even more than Alice will. So as Alice ages the additional 13.6 years that Bob thinks she ages on the return trip of the watch, the watch will only register 8 more years of elapsed time. At the end of that trip, Alice has aged 20 years, the watch reads 16 years, and Bob says he has aged 25 years! So, where is there a twin paradox in that simple excursion into time dilation?

It is often said that the difference in ages depends upon who actually does the accelerating. But this thread shows that isn't soYikes, this is exactly the error in the thread I'm working to correct! If people come away from this thread with the conclusion grav is asserting here, then not only is the conclusion wrong, but the role of the thread has been to sow, rather than stamp out, misconception. What an unpleasant outcome for a forum Q&A thread! I'm trying hard to avoid that.

...but simply depends upon who switches frames, although the term acceleration can almost be defined loosely as who switches frames, I suppose,Word (except for the "almost" and "loosely" bits).

... but apparently not even the observer themself needs to switch frames, only the frame carried by the clock.No, if the observer themself does not switch frames, then Bob always thinks he is older than Alice and there is no twin paradox appearing at all.

When Bob travels away from Alice, the times on both clocks read less than the other. But when Bob turns around, he switches frames, and Alice is instantly thrown future-forward in Bob's worldline. Right, it's acceleraton! Bob's acceleration, that's the whole key. You have it exactly right, why did it lead you above to the wrong conclusion?

So what about the trade-off between Bob and Carl? Well, at the instant Bob and Carl pass, Carl synchronizes his clock to Bob's.True, but that does not mean Bob and Carl have the same global sense of time, and indeed they do not-- expressly because here Bob has not accelerated. You understand the first part of that, now just recognize the importance of the second part. But at least your description shows you fully understand the relativity involved, and the importance of global simultaneity shifts between different reference frames. All you've overlooked is that there is no twin paradox if Bob just hands off his clock, because there will still only be time dilation for Alice, Bob, and Carl, and none of them will reach any contradictions if they forget to include acceleration because there is no acceleration. The twin paradox, on the other hand, is the erroneous conclusion you reach about how other people should have aged if you overlook the importance of your own acceleration (or the gravity).

grav
2008-Nov-11, 01:38 PM
Right, it's acceleraton! Bob's acceleration, that's the whole key. You have it exactly right, why did it lead you above to the wrong conclusion?Well, it's seems to me to be like one of those logic problem assertions for sets. While acceleration always means and can be defined as a switching of frames of reference, that doesn't necessarily translate to mean that a switching of frames of reference must always involve an acceleration, as has been demonstrated in this thread. So acceleration is included in the set for switching frames, but not entirely vice versa. I think after this thread, I will now just say that the resulting time lag depends upon who (or what) switches frames, as the simultaneity shift between frames appears to be the real key here, as you have also pointed out earlier. Any acceleration that takes place does not really even figure significantly into the solution unless it occurs over an extended period of time, as that time of acceleration is then dilated according to the integrated instantaneous speeds (unless we incorporate the simultaneity shift into the formula for the time dilation due to the acceleration as well). As far as the difference in physical ages between Bob and Alice goes though, of course, Bob would actually have to return, which requires an acceleration, as you say. If Bob just hands off the time on his clock and keeps going, then no simultaneity shift occurs for Bob, and he will always remain older than Alice from his point of view, the same as Alice is older than him from what she observes according to SR.

Ken G
2008-Nov-11, 04:08 PM
As far as the difference in ages goes though, of course, Bob would actually have to return, which requires an acceleration, as you say. Right. In other words, as far as the twin paradox (which is all about that asymmetrical difference in age) goes, Bob would actually have to accelerate. That's my entire point.

If Bob just hands off the time on his clock and keeps going, then no simultaneity shift occurs for Bob, and he will always remain older than Alice from his point of view, the same as Alice is older than him from what she observes according to SR.Exactly, no twin paradox, just the usual time dilation issue. Both twins have a symmetric experience here, as we might expect twins to have-- no paradox.

pzkpfw
2008-Nov-11, 08:24 PM
In post #70 you say you agree, but then turn it around again with :

So, where is there a twin paradox in that simple excursion into time dilation?

It still seems to me that you have a more complex than required "version" of the twins' paradox. (It may be better, more detailed, invoking a deeper understanding of relativity and such - but still - more complex than needed.)

Q: Is it or is it not true that:

For any two observers in relative motion, each will observe the others clock running slower than their own.

At my simple level, that's it. That's all that is needed to "create" the apparent "paradox". Alice, Bob, Carl are all zooming around, or not. They are in relative motion, so they all see each others clocks running slower than their own. The apparent "paradox" is: why does one actually age more than the other?

The "paradox" can be resolved without invoking acceleration, by use of messenger clocks. The crux being that while all observers are in relative motion, one stays in a single reference frame and the other observer (or their clock) changes frame.

I don't understand why you write this off as "simple time dilation". Maybe it's a really easy, obvious, simple explanation - but that doesn't make it invalid, does it?

I think the underlying issue is: the subtle distinction between: a) acceleration being used to change frames, and b) that acceleration itself being a specific cause of an effect.

Messenger clock answers seem to show that a) is irrelevant; and if it isn't then all this is a debate over semantics anyway.

On the other hand, if b) is true, does that mean it's part of i) a more detailed version of the twins paradox - or ii) does it specifically replace and invalidate my simpler understanding of it?

I apologise in advance; I expect I'm causing frustration (let's talk about how many event horizons a black hole has...).

dhd40
2008-Nov-11, 09:19 PM
Q: Is it or is it not true that:

For any two observers in relative motion, each will observe the others clock running slower than their own.

To me this looks like a description of the Doppler effect.
But how about this: There´s a clock at the Earth´s equator, and a clock on a GPS satellite (in an equatorial trajectory approx. 20200 km above Earth´s surface).
If we forget about gravitational influences, the GPS clock, following SR, should run slow by approx. 7100 ns/d (nanoseconds/day) as compared to the clock on Earth due to the different speeds (velocities): 460 m/s vs 3900 m/s
And these 7100 ns/d will add up day by day

Therefore, if you brought back the GPS satellite to Earth, the two clocks would show a clear time difference, depending on how long the satellite was orbiting Earth.

Whether the GPS clock would be "younger" than the earthbound clock ... I have some doubts about this :)

sirius0
2008-Nov-11, 09:40 PM
And these 7100 ns/d will add up day by day

Therefore, if you brought back the GPS satellite to Earth, the two clocks would show a clear time difference, depending on how long the satellite was orbiting Earth.

Whether the GPS clock would be "younger" than the earthbound clock ... I have some doubts about this :)

GPS sat would be younger as it is the one to change frames. Whilst in orbit it had an angular component that is acceleration or you could approach it from gravity. But I am not to sure of the strength of what I am saying here, so I await a blasting!:)

dhd40
2008-Nov-11, 10:11 PM
GPS sat would be younger as it is the one to change frames. Whilst in orbit it had an angular component that is acceleration or you could approach it from gravity. But I am not to sure of the strength of what I am saying here, so I await a blasting!:)

If you approached it from gravity, you (on the GPS sat) would look much older (approx. 45000 ns/day!) :whistle:

mugaliens
2008-Nov-11, 10:15 PM
I think the easiest way to understand the twin "paradox" is to put it in it's simplest terms:

1. Two twins in two space ships in empty space. They synchronize clocks.

2. One twin remains where he is (no acceleration of any kind).

3. The second twin rockets away at 1 G for 1 day (shipboard clock), decelerates at 1 G for one day, reaccelerates at 1 G back towards his twin, then decelerates again, coming back to rest alongside his twin.

4. To the moving twin, 4 days have passed, exactly.

5. To the stationary twin, how many days have passed? Is it more than 4 days? Exactly 4 days? Or less than 4 days?

I would contend that it's more than 4 days. And thus, the "paradox," is no more.

mugaliens
2008-Nov-11, 10:18 PM
Addendum: Any time dilation effects due to gravitationl gradients would be multiplicative. As the gravitational gradient changes over time, as does the acceleration and relative velocities, it involves differential calculus, and is best left to a computer to crunch the numbers.

cjameshuff
2008-Nov-11, 10:19 PM
To me this looks like a description of the Doppler effect.

Doppler effect depends on velocity of approach or separation, time dilation only depends on relative velocity. Two ships passing by each other and not compensating for Doppler effect will see each other blue-shifted and dilated as they approach, time dilated only as they pass, and red-shifted and dilated as they separate. Only the time dilation causes actual differences between clocks that take different paths through space-time before meeting again, and it generally seems to be that when thought experiments refer to what one "sees", it means after compensating for lag and Doppler effect.

Whether the GPS clock would be "younger" than the earthbound clock ... I have some doubts about this :)

If you mean you doubt whether the velocity time dilation or gravitational time dilation dominates...that's a sensible question. Here's an analysis that indicates that it is the gravitational time dilation that dominates, making the ground based clock the slow one:
http://triangulum.nl/Werkgroepen/documentatie%20werkgroepen/GPS%20essay.pdf

If you mean you doubt whether either is younger than the other...clocks are based off physical processes. Time dilation affects everything we can use to measure the passage of time. And due to the relativity of simultaneity, it is impossible to even define a consistent "absolute age" for objects, just as it is impossible to define an absolute time.

SeanF
2008-Nov-11, 10:20 PM
Hey, I just saw this thread! :)

Ken G, I think you're making a mistake when you tie the simultaneity difference to acceleration. I mean, Special Relativity is all about comparing two reference frames that are in relative motion to each other. If you consider changing from looking at one frame to looking at the other frame to be "acceleration," then all of it - even basic time dilation - would be acceleration, wouldn't it?

We can synchronize two clocks, A and B, as long as they are stationary relative to each other - even if they are spatially separated. We can have two people (Ann and Bob) who are born at the two clocks simultaneously, in that reference frame.

We can have a third person, Carl, who is born at the same point in space-time as Ann's birth, but on a ship that is in relative motion to Ann and Bob. When Carl's ship reaches Bob, Carl will be younger than Bob. Isn't that effectively the "twin paradox," without any acceleration?

Now, you're right, of course, that the issue is simultaneity. Carl will insist both he and Ann were born after Bob was. But it is a simultaneity issue with simple relative motion, not an issue with acceleration.

Durakken
2008-Nov-11, 10:45 PM
It's actually really easy to explain...

First I think you guys are using the word relative pretty horribly, or at least one person is. What you mean is when two bodies are moving at different velocities relative to each other one is must be moving slower and the other is moving faster. However if two bodies are moving at the same velocity then they are both standing still. It's only with reference points that we can begin to understand speed at all.

That being said it has nothing to do with why two identical clocks that move at different speeds would read differently. The reason is that an increase in speed effects time space, increasing gravity and slowing time in that specific area through some reason i don't know cuz I just know the basics... The gravities and flow of time is different in the two different areas and thus one clock runs slower than the other...or faster, depending on how you look at it.

When the two clocks "stop" or return to velocities that are equal they read seperate times because even though they started at the same time the flow of time was altered in their local areas separately. At the moment they begin going at the same velocity their flow of time is equalized and begin ticking at the same intervals.

The OP assumes that once both clocks both return to the same velocity they both read the same time though. This is wrong. They read different times but tick at the same rate...assuming their tick is perfect and never slow or speed up.

So in the end the reason it all works is more or less because because they are moving faster through time...You know... one might make an argument that there is a balance that the faster one goes the slower time goes for them and if one were to go fast enough time would reverse >.>

sirius0
2008-Nov-11, 10:45 PM
I think the easiest way to understand the twin "paradox" is to put it in it's simplest terms:

1. Two twins in two space ships in empty space. They synchronize clocks.

2. One twin remains where he is (no acceleration of any kind).

3. The second twin rockets away at 1 G for 1 day (shipboard clock), decelerates at 1 G for one day, reaccelerates at 1 G back towards his twin, then decelerates again, coming back to rest alongside his twin.

4. To the moving twin, 4 days have passed, exactly.

5. To the stationary twin, how many days have passed? Is it more than 4 days? Exactly 4 days? Or less than 4 days?

I would contend that it's more than 4 days. And thus, the "paradox," is no more.
I also think both would agree that the younger one used more fuel. All acceleration requires energy, hmmmmm.

Durakken
2008-Nov-11, 10:56 PM
I just thought of something... why is it that a moving object which would have to be losing mass be creating more gravity than something that is standing still >.> That sounds weird to me.

pzkpfw
2008-Nov-11, 11:27 PM
It's actually really easy to explain...

You've covered what time dilation is (or might be) but I think you've missed what makes the "paradox" get called a "paradox" in the first place.

...which is that each observers view is equally valid.

(Bob in the spaceship can view himself as standing still, and Alice, sitting on Earth as zooming away then coming back again. Bob's view is entirely valid, because there is no absolute reference frame which which to say it's Alice or Bob who is moving "faster". So why doesn't Alice, on "spaceship Earth", come back younger? While there is relative motion between them - they each see each others clock as running slower than their own. It makes no difference who is "faster" or "really moving".)

The twins paradox is not about time dilation, as such, but about the apparent lack of symmetry - given that all points of view are equal.

The answer (as I understand it) is not that Bob moves "faster" but that Bobs' reference frame changes, and as a result he moves further through space-time.

(While Bob in a spaceship uses acceleration to change frames, messenger clocks synchronised in some way, don't need to invoke acceleration, to shift reference frames.)

grav
2008-Nov-11, 11:38 PM
We can synchronize two clocks, A and B, as long as they are stationary relative to each other - even if they are spatially separated. We can have two people (Ann and Bob) who are born at the two clocks simultaneously, in that reference frame.

We can have a third person, Carl, who is born at the same point in space-time as Ann's birth, but on a ship that is in relative motion to Ann and Bob. When Carl's ship reaches Bob, Carl will be younger than Bob. Isn't that effectively the "twin paradox," without any acceleration?Hmm, that's very interesting also. It appears we cannot now even say that the resulting time lag depends upon who is switching frames, much less accelerating, since there is not even any frame switching occurring in your example, only a comparison between frames with time dilation and a simultaneity effect taking place. So what could we say now that might help to clarify who ages less?

Durakken
2008-Nov-11, 11:47 PM
That's wrong.

A paradox is two opposite things being held as being true when there is no possible way for it to be.

If someone suddenly starts walking on the ceiling it's their floor because of their perspective but that does not make it a paradox that the other views it the opposing way.

And as far as what you're talking about speeds great enough to create this illusion have less to do with speed than it does with distance and area. Not the speeds at which they travel... In other words, it's several different things that create your so called paradox than it is just plain physics.

pzkpfw
2008-Nov-11, 11:49 PM
A paradox is two opposite things being held as being true when there is no possible way for it to be.

But that's exactly what I've been saying:

1. All points of view are equal and it doesn't matter who is "really" faster - they all see each others clock slower.

2. Bob ends up younger than Alice.

Those are the two opposite things that make this a "paradox" in the first place.

(Or to put it another way: what are the "two opposite things" that you think are what gets the "twins paradox" get called a "paradox"?)

Durakken
2008-Nov-11, 11:58 PM
No what you are saying is that something that is moving away at increased speed appears to be moving slower from the perspective of viewer that is watching that something but the truth of the matter is that anything that can move at speed and still be seen must be pretty big or moving across a distance from a far enough distance so one can track. What you are perceiving is not any sort of paradox but rather an illusion created by the perspective of the viewer due to tracking that object while ignoring the background OR having such a large background that is far enough away that it is outside our average range of reference.

That is why from the side that is moving faster technically it would be moving slower unless your say a car appears to be moving slower than you when you are on a bike...

pzkpfw
2008-Nov-12, 12:03 AM
No what you are saying is that something that is moving away at increased speed appears to be moving slower from the perspective of viewer that is watching that something but the truth of the matter is that anything that can move at speed and still be seen must be pretty big or moving across a distance from a far enough distance so one can track. What you are perceiving is not any sort of paradox but rather an illusion created by the perspective of the viewer due to tracking that object while ignoring the background OR having such a large background that is far enough away that it is outside our average range of reference.

That is why from the side that is moving faster technically it would be moving slower unless your say a car appears to be moving slower than you when you are on a bike...

That's way off. I'm not talking about perspective or visual illusion.

I'm talking about time dilation due to the speed of light being constant for any observer.

The bit you are missing, still, is that according to relativity, it doesn't matter which observer is doing the observing; they will see/calculate/consider the others clock to be slower than their own.

This is not about perspective or optical illusion.

This is relativity.

Ken G
2008-Nov-12, 12:13 AM
It still seems to me that you have a more complex than required "version" of the twins' paradox.When I agreed with you earlier, it was when you said that in the twin paradox, one twin "really does" age less. That is the crux of the twin paradox, and it simply never occurs without acceleration of an observer. That's not more complex than required, it is the twin paradox-- one twin really does age less. Otherwise, there's no paradox, it's just two people thinking the other is younger (that's time dilation, which also is a bit paradoxical, but it's not the significantly more subtle twin paradox because it doesn't break any symmetry between twins.)

Q: Is it or is it not true that:

For any two observers in relative motion, each will observe the others clock running slower than their own.
Yes, but that is symnetric between twins, so is not the twin paradox. It's just time dilation, which if you like, is only one pillar of the twin paradox (the other being acceleration of a twin, which breaks the symmetry).

At my simple level, that's it. That's all that is needed to "create" the apparent "paradox". It may seem paradoxical, but the twin paradox is something very different, and more difficult to explain. You starr by explaining time dilation, and once someone has that down, then you bring in the twin paradox, which establishes the additional effects of acceleration (or gravity).

Alice, Bob, Carl are all zooming around, or not. They are in relative motion, so they all see each others clocks running slower than their own. The apparent "paradox" is: why does one actually age more than the other?But that's the whole flaw in the Alice, Bob, Carl scenario-- none of them "actually" age more. They are all completely correct in thinking they each age the most, that's why it's just not the twin paradox. You are talking about nothing other than time dilation, that's why the Alice-Bob-Carl scenario misses the point. Time dilation is strange, but it's not a paradox, because no one ever said that there had to be one person who actually aged more-- unless there's acceleration, and then there really has to be one who ages more. It's a higher-order surprise in relativity than simple time dilation, and it's called a paradox because people who don't understand the importance of acceleration will think that the twin paradox is pure time dilation, and will thus reason to a contradiction (the symmetry of the twins).

I don't understand why you write this off as "simple time dilation". Maybe it's a really easy, obvious, simple explanation - but that doesn't make it invalid, does it?Time dilation is a perfectly good explanation-- of something other than the twin paradox! The twin paradox itself comes from using only time dilation and nothing else, it is not resolved by that. Its purpose is to get beyond time dilation into understanding global simultaneity shifts, which start out purely as a convention but end up getting "fixed" into the reality when there's acceleration of an observer.
Messenger clock answers seem to show that a) is irrelevant; and if it isn't then all this is a debate over semantics anyway.You cannot arrive at the twin paradox by using messenger clocks, but that doesn't mean they resolve it-- it means they are irrelevant to it. You described the paradox perfectly well yourself:

1. All points of view are equal and it doesn't matter who is "really" faster - they all see each others clock slower.

2. Bob ends up younger than Alice.
Point 2 is exactly what does not happen in the messenger-clock scenario, as it lacks acceleration of Bob. Thus the A-B-C scenario is simply not the twin paradox, and it is completely described by time dilation-- and it can only lead to the twin paradox if B goes with C rather than handing off his watch to C.

On the other hand, if b) is true, does that mean it's part of i) a more detailed version of the twins paradox - or ii) does it specifically replace and invalidate my simpler understanding of it?
I think we had better understand what is meant by the twin paradox. What is meant is not that two twins each think the other is younger (which is all you ever get with the A-B-C scenario), but rather than two twins agree that one is younger-- so how did that happen? Acceleration (or gravity).

I apologise in advance; I expect I'm causing frustration (let's talk about how many event horizons a black hole has...).No frustration, I'm just trying to find the crux of the disconnect here.

pzkpfw
2008-Nov-12, 12:27 AM
Sorry, have to get back to work (it's 1:30 pm my time), so this is a quickie (I don't mean to be rude and skip most of your post - will come back to it):

No frustration, I'm just trying to find the crux of the disconnect here.

Agreed.

What is meant is not that two twins each think the other is younger (which is all you ever get with the A-B-C scenario), but rather than two twins agree that one is younger-- so how did that happen? Acceleration (or gravity).

In my concept of the twins paradox, it is also about both twins agreeing that one has aged differently. The "paradoxical" part is that by the principle of equivalence, they shouldn't. It's the changing of reference frames that resolves the issue (or explains it). That may or may not have been caused by acceleration.

Sam5
2008-Nov-12, 12:33 AM
It still seems to me that you have a more complex than required "version" of the twins' paradox.

When I agreed with you earlier, it was when you said that in the twin paradox, one twin "really does" age less. That is the crux of the twin paradox, and it simply never occurs without acceleration of an observer.

Ken, you are quite correct.

The original 1905 SR paper always leads to a paradox, if one tries to think of what BOTH of two equal observers “see” or “observe” while “moving relatively” and while neither is accelerating, because, both will see themselves as being the “stationary” one, and they will see the other as being the “moving” one. That is why this debate about the 1905 paper has been going on for more than 100 years.

Since acceleration and gravity are disregarded in the 1905 paper, and only “relative motion” is considered, that’s what creates the “paradox”. In order to try to get rid of the “paradox”, Einstein himself had to add acceleration and gravity to his 1905 thought experiments, and he did that in a science-magazine article he wrote in 1918. The article was translated into English only in 2002, and it’s still not widely known. I mentioned this a few years ago, back before the English version was available on the internet. But now, it is finally on the internet.

Einstein wrote this article in a “dialogue” conversational style, much like Galileo’s “Dialogue Concerning the Two Chief World Systems”. In this article, “Critic” is someone who criticizes the 1905 paper, while “Relativist” is Einstein. Of course Einstein wrote both parts of the conversation:

Einstein, 1918:

Durakken
2008-Nov-12, 12:37 AM
The thing about relativity is that it claims that both objects are speeding away from each other at the exact same speed which is semi true, but then people try to apply this to the clock thing which isn't.

If I was attached to a point in space between two objects. One that flies away while the other stays still I would see that both object move away at the same pace if I am attached to the point exactly in the middle no matter what. This isn't because the non-moving object is moving but because from my perspective if i stayed in between them as one increases it's distance i have to too. That however doesn't mean the both have the same velocity and it is this Velocity that actually alters the flow of time...

The real interesting thing to look at is if you have a warp drive vessel traveling at say 2 times the speed of light and a thrust drive engine that travels at the same speed going right next to each other...what happens ^.^

Ken G
2008-Nov-12, 01:35 AM
In my concept of the twins paradox, it is also about both twins agreeing that one has aged differently. It is absolutely all about just that. That's exactly what you will never find happening in these other versions that don't include acceleration of one of the parties.

That may or may not have been caused by acceleration.
No, it is always caused by only acceleration (or gravity).

Ken G
2008-Nov-12, 02:00 AM
Ken G, I think you're making a mistake when you tie the simultaneity difference to acceleration.No, the twin paradox is more than just simultaneity differences, which are essentially purely conventional. The "closed loop" character of the paradox is absolutely essential, which requires acceleration or gravity, because that's the topology that makes the conventional elements "come out in the wash" in actual observations. The observations are invariants, the simultaneity conventions are not.

I mean, Special Relativity is all about comparing two reference frames that are in relative motion to each other.Actually, that's really not what it's about, because you are basically talking about fairly arbitrary conventions (like global simultaneity). What special relativity, as a physical theory, is really about is its invariants. Yes the standard conventions are built into the common language of special relativity, but not into its testable predictions, which are the guts of any theory. I like to say that special relativity is actually less than most people think it is, because of the added untestable baggage that goes into its most common language usage.
We can have a third person, Carl, who is born at the same point in space-time as Ann's birth, but on a ship that is in relative motion to Ann and Bob. When Carl's ship reaches Bob, Carl will be younger than Bob. Isn't that effectively the "twin paradox," without any acceleration?No, it isn't. The crux of the twin paradox was summarized well:

1. All points of view are equal and it doesn't matter who is "really" faster - they all see each other's clock slower.

2. Bob ends up younger than Alice [unequivocally, and having started at the same age, unequivocally].
If you can think of way to get both points 1 and 2 without acceleration, by all means do so, but the Alice-Bob-Carl scenario (even your modification where Alice and Bob are born at different places) does not accomplish both 1 and 2 here. Neither time dilation, nor even time dilation plus an arbitrary global simultaneity convention applied to inertial frames, can do it, in terms of any unequivocal testable outcomes. You need to have an observer who, if he neglects his own acceleration, reaches a wrong conclusion because he expects a symmetric result between the twins that does not play out in the observed invariants. That's the twin paradox.

Carl will insist both he and Ann were born after Bob was. But it is a simultaneity issue with simple relative motion, not an issue with acceleration.True, but it's also not the twin paradox, by #1 and #2 above.

SeanF
2008-Nov-12, 02:35 AM
Ken, I see what you're saying.

But let me try something else to explain why I think pinning the twin paradox on "acceleration" is misleading, at best.

Consider three triplets, all born in the same reference frame at the same time. Ann stays behind, Bob and Carl are both accelerated away (identical accelerations). At some point, Bob decelerates back to the original reference frame but Carl continues "moving". Then, at some later time, Carl decelerates back to the original reference frame (same rate of deceleration as Bob).

Carl then accelerates back towards Bob (and, further in the distance, Ann). As Carl approaches Bob, Bob begins accelerating towards Ann (same rate of acceleration as Bob) so that he matches Bob's speed exactly as he and Bob come alongside each other.

They then continue together and undergo identical decelerations to meet up with Ann at the original starting point, original reference frame.

Ignore for the moment that Ann will be older than both Bob and Carl, and note that Bob will be older than Carl. But did they not experience identical accelerations? The only difference was the amount of time they spent in each inertial frame and the spatial distance between their respective "turning around" points. But the acceleration(s) themselves were identical.

And yet...Bob is older.

EDIT: Two predictions: 1) KenG will agree that Bob will be older than Carl. 2) Sam5 will be very disappointed when KenG acknowledges this.

Ken G
2008-Nov-12, 03:53 AM
But did they not experience identical accelerations? The only difference was the amount of time they spent in each inertial frame and the spatial distance between their respective "turning around" points. But the acceleration(s) themselves were identical.Yes that is what will happen, but all it says is that both acceleration, and time dilation, are essential aspects of the twin paradox. I agree with that. In a sense, the time dilation is what allows for the times to differ, but it is the acceleration that breaks the symmetry and allows Alice and Bob to agree on an invariant that would otherwise be in dispute. You cannot get a twin paradox with only one or the other, where the twin paradox is defined as an acceleration-blind expectation that is in contrast with a measured invariant. This is evidenced by the fact that as yet there are no examples of getting this without both acceleration and time dilation. No one describing an A-B-C scenario has been able to say "here are two twins that agree which one is older" without acceleration. But that's the twin paradox-- not that they disagree who is older, but that they agree, since that is non-symmetric.

pzkpfw
2008-Nov-12, 04:21 AM
This is evidenced by the fact that as yet there are no examples of getting this without both acceleration and time dilation.

Phew, 5 pm and things have moved on.

1. There's a clock on Earth. There's a sticker on it labelling it as "Alice".

2. A spaceship zooms by at constant velocity. When it passes Earth, a clock on board (labelled "Bob") is synchronised with the Earth clock*.

3. Later another spaceship zooms by the first, back in the direction of Earth. It is also not accelerating. It gets a clock (labelled "Clone of bob") synched to the first spaceships "Bob" clock.

4. When the second spaceship passes Earth, it's reading is compared to the "Alice" clock.

I'd expect the "Clone of bob" clock to have a lesser reading than the "Alice" clock, though none of the clocks were accelerated.

While it wasn't one physical clock that left and came back, why would this be an issue? The information left and came back... and experienced different frames.

* say, by a beam of light, which when received is corrected for known effects. (I'm trying to avoid the need for any concept of "simultaneous" in the syncing of the clocks)

Ken G
2008-Nov-12, 05:19 AM
3. Later another spaceship zooms by the first, back in the direction of Earth. It is also not accelerating. It gets a clock (labelled "Clone of bob") synched to the first spaceships "Bob" clock.You can call it a "clone" if you like, but Bob won't even think that clock stays synchronized with Bob! So why should Alice? There's no twin paradox there, as you defined it. Yes the clone of Bob will agree that Alice is older, but the "clone" is not Bob, nor is it synchronized with Bob, nor did it ever think it was as old as Alice ever since it synchronized to the young Bob.

I'd expect the "Clone of bob" clock to have a lesser reading than the "Alice" clock, though none of the clocks were accelerated.Of course you'd expect that-- it just comes from understanding time dilation. You cannot say the paradox was resolved when in fact it was never even encountered!

Let's look at the world according to each of A, B, and C:
A says: B is aging slowly, and so is C, so there's no surprise A is older than C.
B says: A is aging slowly, but C is aging really slowly, so there's no surprise that A is older than C.
C says: B is aging more slowly than A, so even though B started life at the same time as A, B is more time dilated than A. So when C synchronizes their clock to B, they are synchronizing to a clock that has elapsed less time than A. That lag persists even though A is being dilated as A approaches C. So again, C is not surprised that A is older than C.

So you see, with all inertial frames, it's all 100% pure time dilation, and no one reaches any contradictions using nothing other than time dilation. There's no twin paradox there.

But, let's say that, at the last minute, B decides to join C in the ride home. C will say "you do realize that you are already so much younger than A, you will not catch up to her on the way home?" And B will say "what do you mean, A is being time dilated, so has always been younger than me and should still be younger when I get back". To which C will say "look again, as soon as you joined my reference frame (by accelerating), A just got a whole lot older for you (I already thought she was older than we are, by the way)." That is the only way to encounter, and subsequently resolve, the paradox. Look again what happens if B says "in that case, I won't join you, I'll stay inertial". Then C says "OK, then I see Alice as older than us as she was less time dilated during your journey, but you still see her as younger than us as she was more time dilated. We just can't agree unless you accelerate into my reference frame, and if you don't then you will expect A to age more than I will during my return, so you won't be surprised when I show up and she's older than me, but younger than you." And in that lack of agreement, the paradox never appears.

While it wasn't one physical clock that left and came back, why would this be an issue? The information left and came back... and experienced different frames.Follow your own points #1 and #2 and tell me the two people who understand time dilation enough to expect to each be older than the other, yet find one is younger, in your scenario. You can't say C should expect to be younger than A, because as I said, C is synchronizing to B, who has always been more time dilated than A since birth, according to C.

The bottom line is, you just never get any twin paradox with all inertial observers. Such observers never need to undertand anything more than time dilation. It is only when you have acceleration that observers need to understand more than just time dilation to avoid contradictions, and that's why the twin paradox is so important to teach people who think everything is about time dilation in gravity-free relativity.

SeanF
2008-Nov-12, 12:26 PM
Yes that is what will happen, but all it says is that both acceleration, and time dilation, are essential aspects of the twin paradox. I agree with that. In a sense, the time dilation is what allows for the times to differ, but it is the acceleration that breaks the symmetry and allows Alice and Bob to agree on an invariant that would otherwise be in dispute. You cannot get a twin paradox with only one or the other, where the twin paradox is defined as an acceleration-blind expectation that is in contrast with a measured invariant.
You're missing my point, Ken G. People like Sam5 believe that Special Relativity is fundamentally flawed, that there is no time-dilation, and that General Relativity is talking about a physical effect that acceleration has an actual atomic clocks. When you insist that "acceleration causes the twin paradox," they see it as an agreement with that position.

You talk about an "acceleration-blind expectation." That doesn't necessarily mean no acceleration, it can mean "any accelerations cancel out," or "both observers expect the same acceleration effects." That's what I'm trying to provide with my latest thought experiment.

I know where symmetry breaks down in this last thought experiment, why the accelerations don't actually cancel out, and I'm sure you do, too, but it's got to be made clear that it's not acceleration making someone older (or younger). The symmetry is not broken by "one observer accelerated and the other didn't," nor "one observer accelerated more than the other did."

grav
2008-Nov-12, 01:17 PM
Consider three triplets, all born in the same reference frame at the same time. Ann stays behind, Bob and Carl are both accelerated away (identical accelerations). At some point, Bob decelerates back to the original reference frame but Carl continues "moving". Then, at some later time, Carl decelerates back to the original reference frame (same rate of deceleration as Bob).

Carl then accelerates back towards Bob (and, further in the distance, Ann). As Carl approaches Bob, Bob begins accelerating towards Ann (same rate of acceleration as Bob) so that he matches Bob's speed exactly as he and Bob come alongside each other.

They then continue together and undergo identical decelerations to meet up with Ann at the original starting point, original reference frame.

Ignore for the moment that Ann will be older than both Bob and Carl, and note that Bob will be older than Carl. But did they not experience identical accelerations? The only difference was the amount of time they spent in each inertial frame and the spatial distance between their respective "turning around" points. But the acceleration(s) themselves were identical.

And yet...Bob is older.Ahah, very good. I like your scenarios. They are breaking things down to what is really going on here. In another thread, I did something similar. I had identical relativity of speeds and of accelerations as you have done here, but still found an age difference, or something of that nature if I remember correctly. The only thing left, then, was a possible relativity of distances to explain the difference which I never see discussed. But simultaneity does just that. It is directly proportional to the distance between points in different frames of reference. So if Carl travels further than Bob at the same relative speed from Alice and turns around with the same acceleration applied, there will still be a greater simultaneity shift between Carl and Alice due to the larger distance between them.

I guess it could also be consider a relativity of time, though, since Carl travels away from Alice for a longer period, but it would be different from just time dilation, though it will figure into that as well as the simultaneity shift. Depending on whether we use a relativity of distance or time, then, the formula for the simultaneity shift will become either tl = 2 L d v / (c^2 - v^2) = 2 d (v/c) / L, or tl = 2 Z t v^2 / (c^2 - v^2) = 2 t (v/c)^2 / Z, where L and Z are the Lorentz contraction and time dilation, respectively, and d and t are the distance travelled and the time of travel according to the traveller.

dhd40
2008-Nov-12, 02:55 PM
Doppler effect depends on velocity of approach or separation, time dilation only depends on relative velocity.

Yes, a good example for this are geostationary (geosynchronous?)sattelites. No approach, no separation, still time dilation (ignoring gravitational effects)

If you mean you doubt whether either is younger than the other...

Well, this was actually meant to be a joke because of the "huge" time difference (7000+ ns/d) :)

dhd40
2008-Nov-12, 03:49 PM
why is it that a moving object which would have to be losing mass ...

There must be a misunderstanding. Why should a moving object lose mass? Do you think the Earth is permanently losing mass on its way around the sun???

... be creating more gravity than something that is standing still >.> That sounds weird to me.

A moving object is creating gravity?? Where did you get this from?
On the other hand, between "standing still" and "moving" there must have been some acceleration. And if you had done this with your eyes closed you wouldn´t be able to tell the difference between acceleration and gravity (greetings from Einstein´s elevator :))

Ken G
2008-Nov-12, 04:10 PM
When you insist that "acceleration causes the twin paradox," they see it as an agreement with that position.That is of no concern, I would not reject a fact simply because someone else could unite that fact with some other type of erroneous reasoning. What I have said is, in a world where acceleration is impossible, no one would have ever dreamed of a twin paradox. It simply would never come up, and to see that, note that such a world would be like my "world according to A, B, and C" above. All time dilation, no twin paradox, no breaking of any symmetry between observer's views. If a world where acceleration is impossible could never need to confront a twin paradox, then clearly acceleration is crucial to the twin paradox. That's all I said, yet it is being disputed, though no one has yet given an example of all-inertial observers who encounter a twin paradox.
I know where symmetry breaks down in this last thought experiment, why the accelerations don't actually cancel out, and I'm sure you do, too, but it's got to be made clear that it's not acceleration making someone older (or younger). If there's no acceleration, no one is unequivocally made younger! Both observers think they are older, it is simply a disputed issue. It is only with acceleration that anyone has to confront that one is really younger, that's the whole point. Draw whatever conclusions you will from that, it is nevertheless true.

The symmetry is not broken by "one observer accelerated and the other didn't," nor "one observer accelerated more than the other did."
That is precisely what breaks the symmetry-- give me an example of a case where a symmetry is broken without that. I already said above why none of the A-B-C scenarios break any symmetries, because in all cases, every age difference that is encountered in a face-to-face meeting always had that age relationship, the entire time. But the twin paradox contrast two separate age relationships between the same two people, once when they are the same (ergo, "twin"), and once when they are different in a non-symmetrical way. The latter simply never happens in any purely inertial scenario, and if anyone still thinks it does, why are there still zero examples of it?

SeanF
2008-Nov-12, 04:24 PM
The symmetry is not broken by "one observer accelerated and the other didn't," nor "one observer accelerated more than the other did."
That is precisely what breaks the symmetry-- give me an example of a case where a symmetry is broken without that.

1) Did Carl and Bob begin the experiment...
a) at the same point in space-time? Yes.
b) in the same reference frame? Yes.
c) at the same age? Yes.

2) During the duration of the experiment, did...
a) Carl accelerate more than Bob? No.
b) Bob accelerate more than Carl? No.

3) Did Carl and Bob end the experiment...
a) at the same point in space-time? Yes.
b) in the same reference frame? Yes.
c) at the same age? No.

In light of the "No" answers to 2a and 2b, what explains the "No" answer to 3c?

pzkpfw
2008-Nov-12, 08:08 PM
You can call it a "clone" if you like, but Bob won't even think that clock stays synchronized with Bob!

I agree, but I don't see why that's an issue..

(Say there are triplets, in the acceleration-included version: When Bob accelerates to trun back towards Alice, Craig, who was with Bob, is jettisoned into space and continues on the original path. Craig does not remain synchronised with Bob - but that does not change the result of the coming Alice-Bob comparison.)

So why should Alice?

Well, if she understands enough of relativity she won't; but the "paradox" is only a "paradox" when using an incomplete understanding - after all: no-one is saying it's an unsolved puzzle.

There's no twin paradox there, as you defined it.

I still think there is; clocks have been in relative motion. That's it. By equivalence, they should each have been slower than the other - but that's not what eventuates. The shifting of reference frames breaks the symmetry.

Yes the clone of Bob will agree that Alice is older, ...

The Clone bob clock might not have expected that, using only time dilation and the equivalence principle - that his view that he is stationary and the Alice is moving is equally valid. (This is point 1. of my description of the two "facts" in the "paradox" - as in the post of mine you quoted.)

Of course, this would have to be after the Clone clock made a similar assumption for the Bob clock that his setting was synched to. It's a bit contradictory that the Clone clock could assume the Bob clock is stationary and Alice clock moving; then follow that with his own clock stationary and Alice moving - but then, the "answer" to the "paradox" is the shifting of reference frames!

...but the "clone" is not Bob, nor is it synchronized with Bob, ...

I don't see why that's an issue.

nor did it ever think it was as old as Alice ever since it synchronized to the young Bob.

He might (think that), if he only uses partial knowledge of relativity. (Which is what allows it to be called a "paradox" in the first place.)

Of course you'd expect that-- it just comes from understanding time dilation. You cannot say the paradox was resolved when in fact it was never even encountered!

In contrast it seems to me that you are using more complete knowledge of relativity to say a paradox doesn't exist, when the paradox itself requires that incomplete knowledge.

Why couldn't I say in answer to your resolution of the paradox "Of course you'd expect that-- it just comes from understanding acceleration under GR. You cannot say the paradox was resolved when in fact it was never even encountered!".

I think we still disagree on what the "paradox" is.

(I've been Googling for the web page where I "learned" the no-acceleration-required resolution to the "paradox"; no luck yet. The text wasn't pink on a yellow background, in multiple fonts, and there were no exclamation marks or claims of suppression - so I think it wasn't ATM...)

Ken G
2008-Nov-12, 08:24 PM

1) Did Carl and Bob begin the experiment...
a) at the same point in space-time? Yes.
b) in the same reference frame? Yes.
c) at the same age? Yes.
Check, check, and check. But, now look at Carl's history prior to the beginning of the experiment. He sees the approaching Bob as more time dilated than the distant Alice, yes? So when he synchronizes his age to Bob, does he think he is synchronizing to an age less or more than Alice's? So why should he be surprised that Alice is still older when he later gets to Alice? That's a twin paradox? Are you saying Carl has some reason to think Alice and Bob have to be the same age to Carl? Not if he understands time dilation. But even if you understand that, you still get the real twin paradox.

3) Did Carl and Bob end the experiment...
a) at the same point in space-time? Yes.No, certainly not.

b) in the same reference frame? Yes.Again, no. Not in either version of the A-B-C scenarios we've seen. I think you may mean Carl and Alice here, but it doesn't matter-- either they began at the same place and time, or ended it there, but no pair started and ended it that way, as you claim here.

speedfreek
2008-Nov-12, 08:32 PM
In light of the "No" answers to 2a and 2b, what explains the "No" answer to 3c?

The distance at which the accelerations occur - the size of the "slice" of space-time involved. The further away an observer is, when they change their inertial frame relative to your own, the larger the shift in simultaneity, the larger the difference in your relative definitions of now.

SeanF
2008-Nov-12, 08:38 PM
Check, check, and check. But, now look at Carl's history prior to the beginning of the experiment. He sees the approaching Bob as more time dilated than the distant Alice, yes?
Approaching Bob? Distant Alice?

You're looking at the wrong experiment. Rather than linking, I'll cut and paste the experiment and the questions back together into this post.

The Experiment (I've changed my original 'Ann' to 'Alice' and corrected some typos in this! :doh:):

Consider three triplets, all born in the same reference frame at the same time. Alice stays behind, Bob and Carl are both accelerated away (identical accelerations). At some point, Bob decelerates back to the original reference frame but Carl continues "moving". Then, at some later time, Carl decelerates back to the original reference frame (same rate of deceleration as Bob).

Carl then accelerates back towards Bob (and, further in the distance, Alice). As Carl approaches Bob, Bob begins accelerating towards Alice (same rate of acceleration as Carl) so that he matches Carl's speed exactly as he and Carl come alongside each other.

They then continue together and undergo identical decelerations to meet up with Alice at the original starting point, original reference frame.

The Questions:

1) Did Carl and Bob begin the experiment...
a) at the same point in space-time? Yes.
b) in the same reference frame? Yes.
c) at the same age? Yes.

2) During the duration of the experiment, did...
a) Carl accelerate more than Bob? No.
b) Bob accelerate more than Carl? No.

3) Did Carl and Bob end the experiment...
a) at the same point in space-time? Yes.
b) in the same reference frame? Yes.
c) at the same age? No.

Ken G
2008-Nov-12, 08:46 PM
Approaching Bob? Distant Alice?

You're looking at the wrong experiment. What I was referring to as the general class of Alice-Bob-Carl experiments is that class in which all the observers are always inertial, dating back to hhEb09'1s link on the topic, and the erroneous arguments contained therein. You have been talking about one in which they are accelerated. That's not even relevant to my point, because what I have said is that if you never have any acceleration, you never have any twin paradox, and if you do have proper acceleration, you can have a twin "paradox". Ergo, acceleration is crucial to the twin paradox. That's just a logical conclusion.

Now, you are apparently talking about something different, which is a claim, that I haven't made and is not the A-B-C issue, that all that matters in the twin paradox is acceleration. So for example, you show that where the acceleration occurs does matter. But I know that where the acceleration occurs does matter, as pointed out by speedfreek as well. That was never the claim that is being discussed-- the claim being discussed is whether you can have a twin paradox in the absence of any accelerated observer. That was the whole point of the A-B-C formulations. I now see that you have been talking about something quite different, so we can put that to bed by saying, the twin paradox must always involve acceleration, and where the acceleration happens does matter to the outcome.

Ken G
2008-Nov-12, 09:08 PM
(Say there are triplets, in the acceleration-included version: When Bob accelerates to trun back towards Alice, Craig, who was with Bob, is jettisoned into space and continues on the original path. Craig does not remain synchronised with Bob - but that does not change the result of the coming Alice-Bob comparison.)This is a scenario that includes proper acceleration, so of course it leads to the twin paradox. The claim by many on this thread was, you do not need any proper acceleration (or gravity) to get the twin paradox. That is the false claim at issue.

I still think there is; clocks have been in relative motion. That's it. By equivalence, they should each have been slower than the other - but that's not what eventuates. The shifting of reference frames breaks the symmetry.To claim this, what you need to do is tell me a pair of twins or part of a triplet or quintuplets, whatever you like, that start out at the same age in the same place, and end up at unequivocally different ages, breaking the symmetry-- all without any proper acceleration. This is precisely what you have not done, because it is impossible to do. All you ever get with inertial observers is disputes about who is older, disputes that are governed entirely by time dilation, and are completely symmetric because each observer is in the same boat-- they all think time is always going slower for everyone else, period. There's no twin paradox until someone actually has to say "oh, I guess I can't argue with the fact that less time has passed for me than for you". That requires acceleration (or gravity), always.

The Clone bob clock might not have expected that, using only time dilation and the equivalence principle - that his view that he is stationary and the Alice is moving is equally valid.We are stipulating that the Clone understands time dilation. As such, the Clone will certainly know that when he synchronizes his age to Bob, he is synchronizing to an age younger than Alice, because Bob has always been more time dilated than Alice from the Clone's point of view. This is the crucial point. So the Clone starts out younger than Alice, and remains younger than Alice when they meet. That's all time dilation, and is all understood by the Clone, and there is absolutely no twin paradox there. As you said, to have the twin paradox you have to have someone using nothing but time dilation and reasoning to a contradiction. That's precisely what the twin paradox is, but it does not happen here-- time dilation works fine, no contradiction at all. You still have not suggested a reasoning process whereby the Clone should ever expect to be older than Alice, because there is none.

It sounds like the reasoning you are trying to say by the Clone is something like "I'm older than Bob, since we were at the same age but he's been time dilating ever since, and Bob is the same age as Alice because... oops, no, Bob is way younger than Alice due to all that time dilating he's been doing since they were born." And right there you have no twin paradox. Time dilation all by itself is all you have to go on, and it always works fine.

In contrast it seems to me that you are using more complete knowledge of relativity to say a paradox doesn't exist, when the paradox itself requires that incomplete knowledge.The twin paradox, as it is always defined, is a paradox stemming from incomplete knowledge of relativity. The knowledge that is assumed is an understanding of time dilation, and the knowledge that is missing is what happens when there is proper acceleration of an observer applying relativity. That's just always what the twin paradox is. If all observers are inertial, they always get the right answers knowing nothing more than time dilation, so you never get a twin paradox that way.
I think we still disagree on what the "paradox" is.Well, if you think it is something different from what I just said here, then you'd better tell me what you think it is-- and where you got that idea from.

(I've been Googling for the web page where I "learned" the no-acceleration-required resolution to the "paradox"; no luck yet. The text wasn't pink on a yellow background, in multiple fonts, and there were no exclamation marks or claims of suppression - so I think it wasn't ATM...)It was probably perfectly mainstream-- but wrong nevertheless. There are plenty of wrong things on mainstream websites, and there are countless other equally or more authoritative web references that will give you the true scoop. Sometimes, when a website claims "here's something everyone else missed", they are actually right, but far more often, it is they who are missing something. To establish the latter is what I've been trying to do, because I think it's important to stamp out this incorrect idea, else it tends to spread like wildfire.

DrRocket
2008-Nov-12, 09:13 PM
What I was referring to as the general class of Alice-Bob-Carl experiments is that class in which all the observers are always inertial, dating back to hhEb09'1s link on the topic, and the erroneous arguments contained therein. You are now talking about one in which they are accelerated. That's not even relevant to my point, because what I have said is that if you never have any acceleration, you never have any twin paradox, and if you do have proper acceleration, you can have a twin "paradox". Ergo, acceleration is crucial to the twin paradox. That's just a logical conclusion.

Now, you are apparently talking about something different, which is a claim, that I haven't made and is not the A-B-C issue, that all that matters in the twin paradox is acceleration. So for example, you show that where the acceleration occurs does matter. But I know that where the acceleration occurs does matter, as pointed out by speedfreek as well. That was never the claim that is being discussed-- the claim being discussed is whether you can have a twin paradox in the absence of any accelerated observer. That was the whole point of the A-B-C formulations. I now see that you have been talking about something quite different, so we can put that to bed by saying, the twin paradox must always involve acceleration, and where the acceleration happens does matter to the outcome.

I believe that I can and have agreed with all of your points regarding the so-called Twin "Paradox".

While I cannot quite bring myself to read each and every post in this thread, it seems to me that to keep arguing against points that you have made it is necessary to ignore all of the following:

1) Within special relativity the resolution follows immediately from the observation that an inertial reference frame is necessary to apply special relativity and there is only one intertial reference frame in evidence -- that of the twin that stayed behing. There is no paradox as one can apply special relativity only in an inertial reference frame. Arguing from the perspective of the accelerating reference frame is not allowed within special relativity. The traveling twin will be younger when the two meet at the end of the trip.

2) If you look at the problem with the tools of general relativity there is not even an apparent paradox and the twin that took the trip will be younger when the two meet at the end of the trip. The analysis can also be interpreted so as to understand the result in light of special relativity. http://en.wikipedia.org/wiki/Twin_paradox

3) The experiment has been performed using aircraft and atomic clocks. The traveling clock records less time than the "stationary" clock. Experiment supports the theoretical analysis and shows that there is no paradox. http://en.wikipedia.org/wiki/Time_dilation http://en.wikipedia.org/wiki/Hafele-Keating_experiment

Bottom line: There is no paradox. The question can be resolved through either the theory of special relativity or the theory of general relativity, properly applied. It can and has been resolved experimentally. Attempts to try to create a paradox are just word games, based on misapplication of the hypotheses of the basic theories. One can confuse oneself with word games relatively easily, but no word game is going to change the outcome of an experiment.

pzkpfw
2008-Nov-12, 10:11 PM
This is a scenario that includes proper acceleration, so of course it leads to the twin paradox. The claim by many on this thread was, you do not need any proper acceleration (or gravity) to get the twin paradox. That is the false claim at issue.

That comment (in which I specifically agreed I was using acceleration) I was simply responding to your particular objection that my Clone bob clock does not stay sycnhronised with my Bob clock. I don't see why that matters in either of our constructions of the paradox.

To claim this, what you need to do is tell me a pair of twins or part of a triplet or quintuplets, whatever you like, that start out at the same age in the same place, and end up at unequivocally different ages, breaking the symmetry-- all without any proper acceleration. This is precisely what you have not done, because it is impossible to do. All you ever get with inertial observers is disputes about who is older, disputes that are governed entirely by time dilation, and are completely symmetric because each observer is in the same boat-- they all think time is always going slower for everyone else, period. There's no twin paradox until someone actually has to say "oh, I guess I can't argue with the fact that less time has passed for me than for you". That requires acceleration (or gravity), always.

What makes it a paradox is one might expect (with incomplete knowledge of what's going on and how things work) a different result than actually occurs.

Using the messenger clocks, and no acceleration, one gets such a situation - no matter how easily or obviously it is resolved.

We are stipulating that the Clone understands time dilation. As such, the Clone will certainly know that when he synchronizes his age to Bob, he is synchronizing to an age younger than Alice, because Bob has always been more time dilated than Alice from the Clone's point of view.

Sure, because in my construction the relative speed between Alice-Clone is less than that between Bob-Clone.

(Though I don't see why the Clone clock understanding the "answer" makes it all less of a "paradox" in the first place.)

This is the crucial point. So the Clone starts out younger than Alice, and remains younger than Alice when they meet.

Sure.

That's all time dilation, and is all understood by the Clone,

Sure.

(But I don't see why being "just" time diklation of the Clone understanding it removes the "paradox".)

and there is absolutely no twin paradox there.

That's where I differ, and where I think we have a different idea on what the "paradox" is. See my "point 1" that you had quoted. Using that fact, one would naively think the clocks should all agree at the end. That's it. They don't. That we know why they don't resolves the apparent "paradox". But we still call it a paradox.

As you said, to have the twin paradox you have to have someone using nothing but time dilation and reasoning to a contradiction. That's precisely what the twin paradox is, but it does not happen here-- time dilation works fine, no contradiction at all.

You still have not suggested a reasoning process whereby the Clone should ever expect to be older than Alice, because there is none.

See my point 1 that you quoted.

The Clone bob clock has been travelling at a relative speed to Alice. It was also synced to another clock (Bob) that was travelling at a relative speed to Alice. Because any two observers in relative motion will see each others clock slower than their own, they (using just this fact) have no way to reason that one should be younger than the other.

It sounds like the reasoning you are trying to say by the Clone is something like "I'm older than Bob, since we were at the same age but he's been time dilating ever since, and Bob is the same age as Alice because... oops, no, Bob is way younger than Alice due to all that time dilating he's been doing since they were born." And right there you have no twin paradox. Time dilation all by itself is all you have to go on, and it always works fine.

Sorry. That threw me.

The twin paradox, as it is always defined, is a paradox stemming from incomplete knowledge of relativity.

Yes.

The knowledge that is assumed is an understanding of time dilation, and the knowledge that is missing is what happens when there is proper acceleration of an observer applying relativity.

That's where I differ. In my construct the knowledge that is missing, is the effect of changing reference frames. (Which I don't think, e.g. the messenger clock scenario, requires acceleration).

That's just always what the twin paradox is. If all observers are inertial, they always get the right answers knowing nothing more than time dilation, so you never get a twin paradox that way.Well, if you think it is something different from what I just said here, then you'd better tell me what you think it is-- and where you got that idea from.

See my points 1 and 2 that you quoted.

grav
2008-Nov-12, 10:27 PM
We can synchronize two clocks, A and B, as long as they are stationary relative to each other - even if they are spatially separated. We can have two people (Ann and Bob) who are born at the two clocks simultaneously, in that reference frame.

We can have a third person, Carl, who is born at the same point in space-time as Ann's birth, but on a ship that is in relative motion to Ann and Bob. When Carl's ship reaches Bob, Carl will be younger than Bob.I've suddenly noticed a couple of seemingly major problems with this scenario that I cannot determine how to resolve. The first is that although Carl would observe a simultaneity shift for Bob over the distance between them, being in different reference frames, and would not say they were born at the same time, so would Bob for Carl. So they would both observe the same time lag between their ages due to simultaneity and the same time dilation due to the relative speed between them, and would both observe the same age difference between themselves and the other when they meet up, both older or both younger or the same.

The second problem is that if Carl and Alice are both born in the same place at the same time, then their births will coincide in any frame. In other words, the light from both events would travel together as a single event in any direction and so reach Bob at the same time also. So Bob would say they were born at the same place simultaneously also, and that is what he would actually observe of the events. So if Bob says that Alice, being in the same reference frame, was born at the same time as himself, then so was Carl. Carl would also say the same thing if Danielle was born in the same place at the same time as Bob but in Carl's reference frame. So what just happened there? Where did the simultaneity shift go?

Ken G
2008-Nov-12, 10:39 PM
What makes it a paradox is one might expect (with incomplete knowledge of what's going on and how things work) a different result than actually occurs.

Using the messenger clocks, and no acceleration, one gets such a situation - no matter how easily or obviously it is resolved.Then you will have to tell me what different result someone would get if they only understood time dilation and nothing else. You still have not supplied me with an example of purely inertial observers, all who understand time dilation but nothing else, who reach any kind of contradiction. But as soon as you let me give an example where there is acceleration, I will instantly give you an example of an observer who understands nothing but time dilation who will reach a conclusion contradictory to the unequivocal reality of the situation. So I can can supply an example of reasoning to a contradiction if there is acceleration, you cannot supply an example where there is no acceleration. How does this not make it quite clear that the twin paradox requires an observer to accelerate, in order to encounter the apparent paradox?

Your argument, and that in hhEb09'1s link, amounts precisely to saying "but if there's no acceleration, then the paradox can be resolved". No, if there is no acceleration, there is no paradox in the first place. One cannot "resolve" paradoxes by simply limiting consideration to situations where the paradox never appears!

It sounds to me like all you are saying is that time dilation is strange. Yes, time dilation is strange, and yes, you can see that with purely inertial observers. But the twin paradox is what comes next, after you have already come to terms with time dilation strangeness and are ready to get knocked on your keester yet again. If you understand time dilation quite well, but only time dilation, you will still get the twin paradox wrong if you apply time dilation from two contrasting frames, if one is accelerating. That contradiction is what everyone always means by the twin paradox.

Sure, because in my construction the relative speed between Alice-Clone is less than that between Bob-Clone.

(Though I don't see why the Clone clock understanding the "answer" makes it all less of a "paradox" in the first place.)
Here's why: the twin paradox is the way you will get a wrong answer if you only understand time dilation and try to apply that understanding to an accelerated frame. The way the paradox plays out is that time dilation always makes each twin think they are the older one, and if that is always true for them (as it is in the A-B-C scenario), there's no paradox! If time dilation alone always gets the right answer, and if Alice and Bob don't even agree on which one is older, you have simply not met the twin paradox.

Let me put this differently. The twin paradox is a discrepancy between two calculations, one which is correct, and one which is incorrect. The correct calculation is the only one you have ever considered, it is the calculation that is done by inertial Alice, and it involves nothing but time dilation. Yes, Alice does not care if Bob comes back, or sends Carl back, because Alice does the right calculation whether Bob is accelerated or not. But Alice's calculation is not the twin paradox, because Alice's calculation was always the correct one in the first place.

The incorrect calculation at the heart of the twin paradox is the calculation by Bob, if Bob returns to Alice. If Bob does not return, of if Bob sends Carl, then Bob is never doing any calculation that can be contrasted with Alice's. Bob is never saying "I expected to be older than you, but oops, I'm younger". The incorrect calculation never happens, because Bob always correctly concludes he is older than Alice! How can you have a twin paradox if Bob is never demonstrated to be younger than Alice? What difference does it make that the inertial calculation of Carl's clock can be correctly handled by either Alice or Bob, when Alice always thinks Bob is younger and Bob thinks Alice is younger? That's not the twin paradox, it's just a calculation of how inertial clocks act. The paradox is when you think the calculation that works for inertial clocks also works for accelerated clocks (after all, you can always pretend you are stationary if all motion is relative, right?), and then you find to your surprise that it does not.

Ken G
2008-Nov-12, 10:57 PM
Bottom line: There is no paradox. The question can be resolved through either the theory of special relativity or the theory of general relativity, properly applied.Yes, I think the problem with this discussion is that I am saying:

"If you try to do special relativity, specifically time dilation, as if it applied to an accelerating clock, you get the wrong answer. That is called the twin paradox, though it's not a real paradox, and it never appears unless an observer tries to do special relativity as if it applied to an accelerating clock, so acceleration is crucial to the paradox. However, you can of course do the calculation correctly if you stick with inertial clocks, and never encounter any acceleration."

Others are saying:
"The paradox does not require acceleration because you can get the answer right if you never try to use any accelerating clocks."

But that stance misses the point from the very outset, because the point is not to avoid the paradox, it is to encounter the paradox, and that does require we consider the perspective of an accelerated observer who is using an accelerated clock.

pzkpfw
2008-Nov-12, 11:38 PM
If Bob does not return, of if Bob sends Carl, then Bob is never doing any calculation that can be contrasted with Alice's. Bob is never saying "I expected to be older than you, but oops, I'm younger".

But he is.

The whole time he's moving, he's thinking that Alice's clock is running slower (because both Alice and Bob see each others clock running slower than their own (due to equivalence of point of view)). Same for the Clone.

So on return the Clone bob clock might well be expecting to be older... but it turns out it isn't.

The incorrect calculation never happens, because Bob always correctly concludes he is older than Alice!

Well, yeah, if he knows "the answer".

How can you have a twin paradox if Bob is never demonstrated to be younger than Alice?

But he (or his clock) is.

What difference does it make that the inertial calculation of Carl's clock can be correctly handled by either Alice or Bob, when Alice always thinks Bob is younger and Bob thinks Alice is younger?

Isn't that paradoxical? They might both be expecting the other to be younger - but it turns out only one is younger than the other. That's point 2 or the paradox, as you quoted me writing.

That's not the twin paradox, it's just a calculation of how inertial clocks act.

You still seem to be saying, here, that it's not a paradox because we know the answer. But that applies to your version, too.

(And we still seem to be starting from a different idea of what the paradox is, even though your quoted my version and seemed to approve.)

... (after all, you can always pretend you are stationary if all motion is relative, right?), and then you find to your surprise that it does not.

That's pretty much what I'm saying I think the twins paradox is.

Given equivalence of point of view, the situation should be symetircal, but it turns out not to be (the answer being that it's due to changing of reference frame).

DrRocket
2008-Nov-13, 12:37 AM
...
Given equivalence of point of view, the situation should be symetircal, but it turns out not to be (the answer being that it's due to changing of reference frame).

The whole point is that you do NOT have equivalent points of view.

Special relativity applies in inertial reference frames and only in inertial reference frames. There is only one inertial reference frame in the Twin "Paradox". In the traveling twin's frame of reference he feels acceleration as he leaves, he feels it again when he slows down, he feels it when he turns, he feels it when he accelerates again and he feels it when he stops on return. His frame of reference is not inertial, and you cannot apply special relativity in that frame.

You can consider the effect on an accelerating body within an inertial reference frame -- see Wolfgang Rindler's Introduction to Special Relativity for a treatment of that. So you can analyze the problem correctly from the perspective of the twin that stays behind. But you cannot from the point of view of the traveling twin. The so-called paradox arises from performing an analysis that is explicitly forbidden by special relativity.

Not all reference frames are equivalent. Only inertial reference frames are allowed in special relativity.

SeanF
2008-Nov-13, 01:24 AM
You still have not supplied me with an example of purely inertial observers, all who understand time dilation but nothing else, who reach any kind of contradiction.
The standard non-accelerating A-B-C thought experiment does that. Unless there's an understanding of both time dilation and simultaneity difference, the final situation will not be what one of them expected.

If you try to do special relativity, specifically time dilation, as if it applied to an accelerating clock, you get the wrong answer.
I'm not sure I agree with this. Einstein pointed out the "twin paradox" (although he didn't call it that) in his original 1905 paper, using nothing but the Special Relativity math.

SeanF
2008-Nov-13, 01:29 AM
I've suddenly noticed a couple of seemingly major problems with this scenario that I cannot determine how to resolve. The first is that although Carl would observe a simultaneity shift for Bob over the distance between them, being in different reference frames, and would not say they were born at the same time, so would Bob for Carl.
You're misunderstanding the simultaneity issue here. The two events (Bob's birth and Carl's birth) are simultaneous in Bob's reference frame but non-simultaneous in Carl's reference frame. If you require that they be the same in both (either simultaneous in both or simultaneous in neither), then you're actually avoiding the effect.

pzkpfw
2008-Nov-13, 01:49 AM
The whole point is that you do NOT have equivalent points of view.

...

Not all reference frames are equivalent. Only inertial reference frames are allowed in special relativity.

Well, yes.

That's why the otherwise apparent "paradox" has an answer; and why I've pointed out that my understanding of it (the "solution") is the changing reference frames.

Then Ken says "but acceleration is needed to change reference frames".

Then I bring up the A-B-C thought experiment, where reference frames change without requiring acceleration.

Then Ken says "but that's just normal time dilation".

Then I say, "so what? why does that invalidate the result?".

Then it gets fuzzy, and the cycle begins afresh.

grav
2008-Nov-13, 02:34 AM
You're misunderstanding the simultaneity issue here. The two events (Bob's birth and Carl's birth) are simultaneous in Bob's reference frame but non-simultaneous in Carl's reference frame. If you require that they be the same in both (either simultaneous in both or simultaneous in neither), then you're actually avoiding the effect.That's why I added Danielle, to make things clearer. Carl says that he was born simultaneously with Alice. He also says he was born simultaneously with Danielle in the same frame as himself. Danielle's birth coincides with Bob at the same place when he is born, so Carl also says Bob's birth is simultaneous with Danielle's, whereas Danielle's is simultaneous with his own, so Bob's birth is also simultaneous with his own. They are all simultaneous in either frame to all observers? What am I missing here?

grav
2008-Nov-13, 03:00 AM
Okay, thank you very much SeanF. I think your scenario just helped prove the solution to that "rope-and-rockets" paradox thing I'd been working on in another thread. My stance is that the distance between the rockets will contract the same to a stationary observer as the rockets themselves, so a rope between them will not break. Others say that only rigid material can contract, not distances themselves. But the only way that I can see for the simultaneity effect to work in your example is if the distance between the observers in each frame is Lorentz contracted.

So let's say Alice and Bob observe that they, Carl, and Danielle were all born at the same time. That means that Alice and Bob measure the same distance between themselves as the distance between Carl and Danielle. Due to a simultaneity effect, Carl and Danielle cannot agree that all four were born simultaneously. That also means that Carl and Danielle cannot measure the same distance between Alice and Bob as themselves. So a length contraction must take place for the distance between observers in each frame. If Alice and Bob measure the same distance between observers in each frame, then Carl and Danielle must see their own distance greater and Alice's and Bob's as shorter. In that case, Carl would say that Danielle coincides with Bob first, so they are born at the same time and both older than himself, and then Alice and Carl coincide later.

SeanF
2008-Nov-13, 04:01 AM
That's why I added Danielle, to make things clearer. Carl says that he was born simultaneously with Alice. He also says he was born simultaneously with Danielle in the same frame as himself. Danielle's birth coincides with Bob at the same place when he is born, so Carl also says Bob's birth is simultaneous with Danielle's, whereas Danielle's is simultaneous with his own, so Bob's birth is also simultaneous with his own. They are all simultaneous in either frame to all observers? What am I missing here?

...Danielle was born in the same place at the same time as Bob but in Carl's reference frame.
Doesn't make sense. If Danielle's birth and Bob's birth occurred at the same place and the same time in any reference frame, then they occurred at the same place and the same time in all reference frames.

If I'm following what you're trying to say here, then Alice and Bob would say that all four were born at the same time. Carl would say that he and Alice were born at the same time. Carl would say that Bob and Danielle were born at the same time as each other, but at a different time than Alice and Carl.

What Danielle would say depends on her reference frame. If she's in the same reference frame as Alice and Bob, she'd agree that all four were born simultaneously. If not, she'd say that there were two different birth times - one for her and Bob and a different one for Alice and Carl. Whether or not she agrees with Carl on exactly when Alice/Carl were born and Bob/Danielle were born depends on whether or not she and Carl are in the same reference frame.

Okay, thank you very much SeanF. I think your scenario just helped prove the solution to that "rope-and-rockets" paradox thing I'd been working on in another thread. My stance is that the distance between the rockets will contract the same to a stationary observer as the rockets themselves, so a rope between them will not break. Others say that only rigid material can contract, not distances themselves. But the only way that I can see for the simultaneity effect to work in your example is if the distance between the observers in each frame is Lorentz contracted.
Close. It's a simultaneity difference.

If the rockets are accelerating equally in one reference frame, they will not be accelerating equally in another reference frame. So, yes, in the scenario you're describing, the two rockets get closer together. But they do so because the back rocket is accelerating faster and thus "catching up to" the front rocket, not because of Lorentz contraction.

Ken G
2008-Nov-13, 04:52 AM
The standard non-accelerating A-B-C thought experiment does that. Unless there's an understanding of both time dilation and simultaneity difference, the final situation will not be what one of them expected.No, that's simply not true. I explained above entirely how in the A-B-C scenario, no one needs anything but pure time dilation. I showed that explicitly, never a single reference to any global simultaneity conventions.

Since this approach is not getting anywhere, let me try another one. It is kind of tricky discussing what is the error that leads to a contradiction, when a correct analysis leads to no contradiction. So instead of "twin paradox", let me refer to the "twin strangeness". To wit, the twin strangeness is: you can have two twins born together who are later at the same place and time, and are not the same age. That is precisely what is always referred to in this twin issue, whether one calls it a paradox or just a strangeness.

Now, I assert with 100% confidence that in any situation where you find the "twin strangeness", you are absolutely guaranteed that acceleration (or gravity) has been experienced by one of the twins. Ergo, the twin strangeness requires acceleration, with no exceptions, no messenger clocks, nothing. This is another way to put what I am saying-- we absolutely see the effects of acceleration any time we encounter the twin strangeness, and none of the A-B-C scenarios contradict that assertion, which is in fact the only assertion I have been making all this time. The two inertial A-B-C scenarios never encounter the "twin strangeness", and your version is non-inertial, so of course it does.

I'm not sure I agree with this. Einstein pointed out the "twin paradox" (although he didn't call it that) in his original 1905 paper, using nothing but the Special Relativity math.Yes, exactly-- if you use nothing but time dilation, and try to apply it in an accelerating frame, you do get the twin paradox! That's exactly what I'm saying. If you use more generally correct treatments of accelerating frames (that account for more than just time dilation), all you get is the "twin strangeness", no longer the "twin paradox". But nevertheless, there still had to be proper accleration-- my assertion once again has always been: you never ever get the twin paradox, or the twin strangeness, unless an observer has undergone acceleration (or gravity). If you go back to hhEb09'1s original link way back in post #31 that claimed otherwise, you find the following patently false assertion:

"The three inertial frames are 1) at-home twin 2) the going-away twin and 3) the coming-back twin. It doesn't make any difference that the last two are physically the same twin--they still define different inertial frames.

Of course it makes a difference if the last two are physically the same twin. Not in the correct calculation of how much time elapses, that was always easily done in Alice's inertial frame, but in the analysis of what generates the twin strangeness. If they are the same twin, you have an observer in an accelerating reference frame, and if they are not, you never encounter the "twin strangeness" at all. The argument is simply wrong, all it does is provide a trivial way to calculate the time elapsed on an accelerating clock by staying in an inertial frame (it's pure time dilation). All the link does is calculate the answer from two different inertial frames, Alice and Carl, and gets the same answer. Of course it could introduce 97 other inertial frames, and also get the same answer. That is supposed to be relevant to the paradox? No, it isn't.

You see, we already knew we could calculate the time elapsed on an accelerating clock by staying in an inertial frame-- that's not the twin paradox. The twin paradox is, why do you have to stay in an inertial frame? If motion is relative, why can't everyone simply be considered at rest all the time? That's the paradox, and it absolutely requires that one analyze what happens to an accelerating observer. The answer is clear enough in general relativity: non-inertial frames are inherently local entities, so reasoning in terms of global connections (like the time dilation going on for some distant twin) in them will always have seemingly unphysical ramifications, and lead to perceived paradoxes.

By the way, my favorite example of such an unphysical result is that you can, right now, make time go backward in the Andromeda galaxy-- simply by starting a sprint in the opposite direction. It is customary to explain this as being due to the Einstein simultaneity convention, but since when do conventions dictate what is going on? Rather, time is simply not going backward in the Andromeda galaxy, no matter what the "convention" says-- because you can't make physically meaningful global assertions about how time is actually flowing at some distant place when you are in an accelerated frame. That is, above all, the true message of the twin paradox.

SeanF
2008-Nov-13, 09:53 AM
No, that's simply not true. I explained above entirely how in the A-B-C scenario, no one needs anything but pure time dilation. I showed that explicitly, never a single reference to any global simultaneity conventions.
No, I don't think so - unless we're again discussing two different scenarios. :)

We have two clocks motionless relative to each other and a third clock in motion relative to the first two. The third clock passes by the first and then later passes by the second. In order to accurately predict the outcome in both reference frames, you need to not only understand the time dilation, but also that the synchronicity of the two "motionless" clocks is different in the two reference frames. If you don't understand that synchronicity difference, your expected result in one reference frame will disagree with reality.

To wit, the twin strangeness is: you can have two twins born together who are later at the same place and time, and are not the same age. That is precisely what is always referred to in this twin issue, whether one calls it a paradox or just a strangeness.

Now, I assert with 100% confidence that in any situation where you find the "twin strangeness", you are absolutely guaranteed that acceleration (or gravity) has been experienced by one of the twins.
Well, sure, but that's axiomatic. Your definition of the "twin strangeness" includes one person being in one place, then a different place, then back in the first place. That's the definition of acceleration. All you're saying is that you don't believe in situations that include acceleration and don't include acceleration. It's meaningless.

Yes, exactly-- if you use nothing but time dilation, and try to apply it in an accelerating frame, you do get the twin paradox! That's exactly what I'm saying. If you use more generally correct treatments of accelerating frames (that account for more than just time dilation), all you get is the "twin strangeness", no longer the "twin paradox".
I love the choice of words! :)

Einstein called it "a peculiar consequence" (at least, in the English translation). In his original, SR-only formulation, it's not a paradox - it's just peculiar. Peculiar, as in strange.

But I think your mistake is in your first sentence here. "If you use nothing but time dilation" you are using only part of Special Relativity. You have to account for simultaneity as well. And if you do, you can deal with the "twin strangeness" - with one observer changing direction during the experiment - using only SR. Einstein did it, in 1905. You just have to use all of SR.

grant hutchison
2008-Nov-13, 11:37 AM
Close. It's a simultaneity difference.

If the rockets are accelerating equally in one reference frame, they will not be accelerating equally in another reference frame. So, yes, in the scenario you're describing, the two rockets get closer together. But they do so because the back rocket is accelerating faster and thus "catching up to" the front rocket, not because of Lorentz contraction.Grav is talking about the situation in which the rockets accelerate equally in the rest frame (and therefore don't share their own instantaneous inertial frames). They stay the same distance apart in the rest frame (and therefore break the Lorentz-contracting rope), while experiencing differential acceleration in their own frames (and therefore break the rope).

Grav, I suggest it might create (more!) confusion to revisit that complicated issue right slap bang in the middle of a thread dedicated to the twin "paradox". But I'm only a spectator, here.
And now I'm gone again ...

Grant Hutchison

grav
2008-Nov-13, 02:31 PM
Grav, I suggest it might create (more!) confusion to revisit that complicated issue right slap bang in the middle of a thread dedicated to the twin "paradox". But I'm only a spectator, here.
And now I'm gone again ...Yes, I'm sure you're right. I needed confirmation on the mechanism behind SeanF's example, but I guess I can pursue that in the other thread later on today.

SeanF
2008-Nov-13, 02:46 PM
Grav is talking about the situation in which the rockets accelerate equally in the rest frame (and therefore don't share their own instantaneous inertial frames). They stay the same distance apart in the rest frame (and therefore break the Lorentz-contracting rope), while experiencing differential acceleration in their own frames (and therefore break the rope).
Of course. mea culpa, Grav - Grant is correct. Either way, though, it's a simultaneity issue with the rockets' acceleration.

That being said, your comment about simple empty-space distances undergoing Lorentz contraction is correct. The distance between two clocks which are motionless relative to each other will be different depending on the observer's motion relative to those two clocks.

SeanF
2008-Nov-13, 02:52 PM
By the way, my favorite example of such an unphysical result is that you can, right now, make time go backward in the Andromeda galaxy-- simply by starting a sprint in the opposite direction. It is customary to explain this as being due to the Einstein simultaneity convention, but since when do conventions dictate what is going on? Rather, time is simply not going backward in the Andromeda galaxy, no matter what the "convention" says-- because you can't make physically meaningful global assertions about how time is actually flowing at some distant place when you are in an accelerated frame. That is, above all, the true message of the twin paradox.

If you have two observers passing each other and both tracking a distant clock, one of them will say, "That distant clock was at t=1000 when we passed," while the other will say, "That distant clock was at t=500 when we passed."

Are you suggesting that one - at least - of those measurements is not "real"?

Ken G
2008-Nov-13, 03:42 PM
We have two clocks motionless relative to each other and a third clock in motion relative to the first two. The third clock passes by the first and then later passes by the second. In order to accurately predict the outcome in both reference frames, you need to not only understand the time dilation, but also that the synchronicity of the two "motionless" clocks is different in the two reference frames.No, you only need to know what convention was used to synchronize those clocks. But that's perfectly obvious, there is zero physical content in that statement-- if I want to predict what my watch and my alarm clock read, I'll need to know how the two are set to each other. The point here is, if you tell me what you did to set those two clocks to each other, I will never need to include any "difference in synchronicity" in the moving inertial frame-- I will never need anything but time dilation, and the simple information of how you set those clocks.

If you don't understand that synchronicity difference, your expected result in one reference frame will disagree with reality.All I need is to understand how you set the clocks (which I would always need, even without relativity), and time dilation. That's all-- unless I'm accelerated.

Well, sure, but that's axiomatic. Your definition of the "twin strangeness" includes one person being in one place, then a different place, then back in the first place.But it's not "my" definition-- it's the definition. Just look up the twin paradox in any source you like, you will always find the situation I describe.
All you're saying is that you don't believe in situations that include acceleration and don't include acceleration. It's meaningless.What I'm saying is meaningful and simple: if two twins are born at the same place and time, and later are together but have different ages, then at least one of them must have experienced proper acceleration (or gravity). That is all I have ever said here-- the twin paradox (or strangeness) fundamentally requires proper acceleration. That statement is just plain true.

But I think your mistake is in your first sentence here. "If you use nothing but time dilation" you are using only part of Special Relativity. You have to account for simultaneity as well.Actually, this gets into very subtle terrain, but if you accept that the theory of special relativity is about predicting observations based on invariants, then you find that conventions are not part of that theory because they are not invariants. If we set clocks certain ways, we can hardly blame that on reality, and the theory does not predict how we set clocks-- that's our own choice. Thus, there is no simultaneity convention in the fundamental axiomatic structure of special relativity-- only in the standard way we teach it. In other words, the special relativity we teach is actually something more than a true physical theory.

And if you do, you can deal with the "twin strangeness" - with one observer changing direction during the experiment - using only SR. Einstein did it, in 1905. You just have to use all of SR.That's actually "too much" SR. But the real point is, you simply never encounter the twin strangeness unless there is proper acceleration somewhere, and I've demonstrated that explicitly in my above descriptions of the inertial A-B-C scenarios.

SeanF
2008-Nov-13, 05:13 PM
No, you only need to know what convention was used to synchronize those clocks. But that's perfectly obvious, there is zero physical content in that statement-- if I want to predict what my watch and my alarm clock read, I'll need to know how the two are set to each other. The point here is, if you tell me what you did to set those two clocks to each other, I will never need to include any "difference in synchronicity" in the moving inertial frame-- I will never need anything but time dilation, and the simple information of how you set those clocks.
Okay, fair enough.

That's actually "too much" SR. But the real point is, you simply never encounter the twin strangeness unless there is proper acceleration somewhere, and I've demonstrated that explicitly in my above descriptions of the inertial A-B-C scenarios.
No, it's not "too much" SR. It's the original 1905 transformation equations and nothing else:

Define an arbitrary point in spacetime, and call it Point A. Define an arbitrary inertial reference frame, and locate the point in spacetime that is, in that reference frame, 0 light-seconds distant from Point A but 10 seconds later than Point A. Call it Point B. Then locate one of the infinite points in spacetime that are both 5 seconds later than Point A and also 3 light-seconds distant from Point A. Call it Point C.

Now define a reference frame that is moving relative to the original arbitrary reference frame, with a velocity of 0.6c in the direction of A/B to C. The simple SR coordinate transformation equations tell us that in this second reference frame, points A and C are located 0 light-seconds apart (spatially) and 4 seconds apart (temporally).

Now define another reference frame that is moving relative to the original arbitrary reference frame, with a velocity of 0.6c in the direction of C to A/B. The simple SR coordinate transformation equations tell us that in this third reference frame, points C and B are located 0 light-seconds apart (spatially) and 4 seconds apart (temporally).

So, using nothing but the basic SR coordinate transformation equations for inertial frames, we can calculate that a clock which stays in the first inertial frame will "travel" from A to B in ten seconds.

We can also calculate that a clock which is in the second inertial frame long enough to "travel" from A to C and then instantaneously switches to the third inertial frame long enough to "travel" from C to B will take a total of 8 seconds to make the full trip from A to B, 4 seconds on each leg, and we don't have to even think about what happens to it during the actual inertial frame switch.

Did it switch inertial frames? Of course. But it was in inertial frames for the entire duration of the experiment, just not a single inertial frame. We need know nothing about SR except the coordinate transformations to deal with this "peculiar" and "strange" effect, nor to calculate the exact magnitude of it.

That's what Einstein did.

Ken G
2008-Nov-13, 06:18 PM
If you have two observers passing each other and both tracking a distant clock, one of them will say, "That distant clock was at t=1000 when we passed," while the other will say, "That distant clock was at t=500 when we passed."

Are you suggesting that one - at least - of those measurements is not "real"?I'm suggesting that neither clock reading you refer to is a measurement, they are both just conceptualizations of other measurements. The actual measurements are invariants, but the conceptualizations are not. The conceptualizations are only real in that someone is really conceptualizing that way.

Ken G
2008-Nov-13, 07:17 PM
No, it's not "too much" SR. It's the original 1905 transformation equations and nothing else:Yes, but that's "too much" SR. I'm claiming that Einstein's original formulation is really two things at once-- it is a physical theory, embedded in some conventional baggage (its simultaneity convention) that never plays any role in any measurable predictions. Certainly, Einstein was free to define a word like "simultaneous", and it is useful to have a convention for that, but it is neither a part of the theory nor a part of reality. That is because, we could just as easily choose other simultaneity conventions, transform all our predictions into that convention, and if clocks were set by that convention, the new predictions would be the applicable ones. And we would still never encounter any twin strangeness unless something was accelerated.

Now define a reference frame that is moving relative to the original arbitrary reference frame, with a velocity of 0.6c in the direction of A/B to C. The simple SR coordinate transformation equations tell us that in this second reference frame, points A and C are located 0 light-seconds apart (spatially) and 4 seconds apart (temporally).

Now define another reference frame that is moving relative to the original arbitrary reference frame, with a velocity of 0.6c in the direction of C to A/B. The simple SR coordinate transformation equations tell us that in this third reference frame, points C and B are located 0 light-seconds apart (spatially) and 4 seconds apart (temporally).That is true, but the only thing that is physical in all that is the invariant spacetime interval. Everything else is arbitrary convention, it's just a coordinatization.

It was general relativity that helped us understand this, even though general relativity was designed to treat gravity. What it also does is give us a healthy skepticism about the physical significance of a global coordinatization. It makes sense to go back and reframe special relativity in light of that insight, and then it's just general relativity with a zero stress-energy tensor-- and no reliance on inertial frames or global simultaneity conventions, just a prescription for identifying what is invariant to such frames and conventions.

So, using nothing but the basic SR coordinate transformation equations for inertial frames, we can calculate that a clock which stays in the first inertial frame will "travel" from A to B in ten seconds.That is an example of an invariant, yes. But it requires no global simultaneity convention. Any coordinatization that labels the events A and B in such a way as to preserve that 10 second interval in traveling between them would suffice equally well. A deeper question is, is it the events and the 10 seconds that tells us what the reference frame was, the events and the reference frame that tells us they are 10 proper seconds apart, or the reference frame and the 10 seconds of proper time that tell us what the events were? I'm not sure that one has an answer.

We can also calculate that a clock which is in the second inertial frame long enough to "travel" from A to C and then instantaneously switches to the third inertial frame long enough to "travel" from C to B will take a total of 8 seconds to make the full trip from A to B, 4 seconds on each leg, and we don't have to even think about what happens to it during the actual inertial frame switch.Of course, that is the correct half the calculation presented in the twin paradox, and that was never in dispute. Nevertheless, the clock did accelerate, and that will be quite important when you later hold it next to the clock it began next to, and get "the twin strangeness".

We need know nothing about SR except the coordinate transformations to deal with this "peculiar" and "strange" effect, nor to calculate the exact magnitude of it.But this is as irrelevant to the issue as the whole inertial A-B-C scenario always was. It was never disputed that an inertial reference frame can make correct calculations using SR. The question was always, what causes the strangeness of doing those same calculations in a frame that does not get the right answer? That's the twin paradox, and the answer is that you cannot do special relativity in an accelerated frame. Instead, you have to do it in an inertial frame, and then translate the result into the changing view from the accelerated frame.

What is going on here is, the physics of special relativity is actually a bit embedded in the baggage of global simultaneity conventions for inertial frames. That's what makes the inertial frames "special", that you can get away with doing that-- but is there any physics to it? If you single out inertial frames, and apply the Einstein global simultaneity convention, then the actual physics combines with all that to give you the Lorentz transformation. But that's what I mean by "too much" SR, because the real physics in there gets a bit lost in that extraneous baggage-- even though that is always the way we teach it. As such, we end up with making time go back and forth in Andromeda while we are doing wind sprints. It's unphysical; it's baggage. The twin paradox is our alert to this fact, but the inertial A-B-C scenarios obfuscate that message that we were supposed to be paying attention to by immersing only deeper into issues that are purely conventional-- and even farther from the true physics of the reality.

By the way, many of these ideas have been emerging in other threads, and my own recognition of these facts is evolving even in this very thread, so it shows why such discussions are valuable and why there is no shame in being "beguiled" by hhEb09'1s link. The swindle there is very subtle, and is of great value to identify.

SeanF
2008-Nov-13, 08:35 PM
Yes, but that's "too much" SR.
Blimey.

Two clocks. They use light pulses to verify their distance (three light-seconds, constant), and to synchronize themselves. A third clock passes by, at 0.6c relative to the first two clocks. The time displayed on the second clock at passing will be five seconds later than the time displayed on the first clock at passing. The time displayed on the third clock when it passes the second will be only four seconds later than the time displayed on the third clock when it passes the first.

Is that "too much" SR?

cjameshuff
2008-Nov-13, 08:37 PM
Saying "it's the acceleration" is technically true for the specific example of traveling twins, but a bit misleading and incomplete. The thought experiment can be framed in a way such that both twins experience exactly the same accelerations, yet still end up at different ages...say they both go off toward the same destination, but one turns back early and waits at the origin point for the other's return. And in the case of a clock setting being copied between passing spacecraft carrying identical clocks, no acceleration is necessarily involved. It is more accurate to say that it is the change in reference frames, and when those changes are made.

The biggest hangup here really seems to over something quite stupid and irrelevant...the fact that it's called a paradox. It's not a true paradox, because it *is* resolvable within SR. It is only an illustration of something that may initially go against intuition.

Ken G
2008-Nov-13, 10:02 PM
Two clocks. They use light pulses to verify their distance (three light-seconds, constant), and to synchronize themselves.You are forgetting something important-- they are using light signals and an instruction manual (an arbitrary, albeit reasonable, simultaneity convention) to synchronize themselves. This is my point-- there is zero physics in synchronization, though SR is normally taught that there is. The latter approach leads to all kinds of conceptual handicaps that later are very difficult to relax when learning general relativity. Not that I've every really "learned" general relativity, but I think I see the salient features-- syncronization is nothing but coordinatization (as long as you don't reverse any causality connections).

Is that "too much" SR?Yes, if you think the comparison of times on two separated clocks is a physical comparison, independently of the convention used to set them.

Ken G
2008-Nov-13, 10:17 PM
Saying "it's the acceleration" is technically true for the specific example of traveling twins, but a bit misleading and incomplete.But no one has made the claim on this thread that the acceleration is all you need to know about, that would overlook time dilation. Instead, the claim made is that acceleration is essential.

SeanF
2008-Nov-13, 10:34 PM
Yes, if you think the comparison of times on two separated clocks is a physical comparison, independently of the convention used to set them.
But not two non-separated clocks?

So the comparison between clocks 1 and 3 at the moment they pass is valid, as is the comparison between clocks 2 and 3 at the moment they pass?

And also a single clock, so the comparison of clock 3 (at the moment it passes clock 1) with (clock 3 at the moment it passes clock 2) is also valid?

And not "too much" SR?

DrRocket
2008-Nov-13, 10:36 PM
But no one has made the claim on this thread that the acceleration is all you need to know about, that would overlook time dilation. Instead, the claim made is that acceleration is essential.

Yes. And this results very directly from the basic assumptions of special relativity.

Special relativity applies in inertial reference frames, and only in inertial reference frames.

If you have one inertial reference frame, all other inertial reference frames move at constant velocity with respect to that frame. So non-inertial reference frames are distinguished by something other than moving at constant velocity with respect to one, hence all, inertial reference frames. Moving at something other than constant velocity is, by definition, accelerating.

The twin paradox is resolved by noting that only one of the reference frames in the problem as stated is inertial.

Formulations in which both twins accelerate with respect to some inertial reference frame are not paradoxes at all, and in fact can be pretty hard to analyze correctly at all.

The other common set of "paradoxes" arises from misusing simultaneity.

There are no real paradoxes in special relativity, just some confusing word games. The problem is not really physics, but abuse of language and of hypotheses. If you start out by violating the basic premises of special relativity, then apply the formalisms of SR anyway, you should not be surprised when the results are confusing.

Ken G
2008-Nov-13, 11:34 PM
But not two non-separated clocks?Correct. Or would you claim there is no physical difference between separated and non-separated clocks? The difference is, the more separated, the wider the spread in the possible simultaneity conventions that do not reverse causality.

So the comparison between clocks 1 and 3 at the moment they pass is valid, as is the comparison between clocks 2 and 3 at the moment they pass?Yes, locality is a hugely important physical invariant. That hardly seems controversial.

And also a single clock, so the comparison of clock 3 (at the moment it passes clock 1) with (clock 3 at the moment it passes clock 2) is also valid?
Yes, the difference between a single clock and multiple clocks is the whole need for the concept of simultaneity. Again, that's not controversial.

pzkpfw
2008-Nov-13, 11:41 PM
The twin paradox is resolved by noting that only one of the reference frames in the problem as stated is inertial.

In the messenger-clock-no-acceleration thought experiment, the reference frames are all intertial, the resolution is that one of the clocks (or it's setting...) is not in a single reference frame during the experiment.

I can only agree that an actual twin travelling would have to undergo acceleration to change reference frame (go away and come back); but in the messenger-clock-no-acceleration formulation.....?

The other common set of "paradoxes" arises from misusing simultaneity.

Are you implying that there is no way to synchronise clocks?

(Which I think is what I need in the messenger-clock-no-acceleration thought experiment.)

Ken G
2008-Nov-13, 11:42 PM
If you start out by violating the basic premises of special relativity, then apply the formalisms of SR anyway, you should not be surprised when the results are confusing.Right. Indeed, I would argue that the basic premise of special relativity (the existence of global inertial reference frames) was always kind of a fiction. Yes, the existence of gravity makes it only approximately true in appropriately small regions, but I think even in the absence of any gravity, it would still be a philosophical fiction. Such global descriptions are simply a useful construct that, like many other constructs of our intellect, should never be taken too seriously. Reality is actually a very local enterprise, but in some situations we can commonly get away with imagining that it has globally describable properties. The twin paradox is not one of those situations, nor is considering what is happening in Andromeda while you are doing wind sprints.

publius
2008-Nov-14, 12:08 AM
Hmmph. I missed another interesting discussion (I'm worried about "dilation" of things other than time, like the value of some of my investments, and the "event horizon" of economic collapse. :lol:).

While I skimmed over the brunt of it, let me say I think I pretty much agree with Ken. To get the "twin strangeness" as Ken puts it, one twin has to got to "see" (plot in his coordinates) that the other twin's clock is *running faster* than his own for some part of his own proper time/world line. That will happen only in non-inertial frames or with gravity, with path curvature , invariant space-time curvature, or both.

If you stick to comparisons between inertial frames in flat space-time, no clocks are ever moving faster than your own. Any differences when two clocks get to the same event is always explaine by time dilation, one clock running slower than the other, and/or difference in synchronization. Two distant clocks stationary in one frame are not properly synchronized according to other frames.

Distant clocks are running slow or out of whack with each other, and that explains it to every inertial observer. No one ever sees a clock "speed up".

Now, with curvature, path or space-time, you can "see" clocks speed up.

-Richard

Ken G
2008-Nov-14, 03:26 AM
Yes, I think a good way to sum this up is that the Einstein simultaneity convention is a global convention, not a local one. Also, it is not a set of simultaneous events, rather, it is a set of instructions for an observer to use, like "go forward three steps". As such, if different observers use it, they may arrive at a different result (the so-called simultaneity shifts, but those shifts are not real, they are simply the result of applying the same instructions by different observers).

But what is even more significant is that the instructions require doing things, like sending out light beams. Since the convention is global, it means you have to wait for the beams to get out there, and come back. This also means that the past history of the observer is relevant to their result when they use the instructions-- so to get the intended result, the observer has to have been moving the same way for all of past history. That's why no acceleration is permitted-- an inertial frame is not a description of the instantaneous motion of the observer, it has to encompass all of his past and future to avoid aphysical results (like time going backward in Andromeda). Global reference frames are inertial, expressly because they have to be constant for all time-- there is nothing else "magical" about inertial frames.

In short, it is unphysical to imagine that a global simultaneity convention can mean something in the context of instantaneous motion. That is the moral of the twin paradox-- when physics takes as input the instantaneous conditions, then its only meaningful output is purely local.

DrRocket
2008-Nov-14, 03:37 AM
Are you implying that there is no way to synchronise clocks?

(Which I think is what I need in the messenger-clock-no-acceleration thought experiment.)

No. I was making a general statement to the effect that the usual set of "paradoxes" that arise in discussions of special relativity are not paradoxes at all, and was alluding here to things like the train-in-the-tunnel "paradox" that is resolved by looking closely at the issue of the relativity of simultaneity.

I have not paid attention to the messenger-clock-no-acceleratin thought experiment and was not commenting on it.

DrRocket
2008-Nov-14, 03:43 AM
Hmmph. I missed another interesting discussion (I'm worried about "dilation" of things other than time, like the value of some of my investments, and the "event horizon" of economic collapse. :lol:). ...-Richard

If your investments have dilated, then you are unique. Mine have only experienced contraction, and the contraction is pretty breath-taking (I could live quite comfortably for a considerable period of time on this year's losses, and last month was really spectacular).

Fortunately, today's market action indicates that we may not actually reach the event horizon. I hope. But there does seem to be a singularity in operation somewhere.

The real problem is that things are not just relatively bad. They are absolutely horrific.

doc33
2008-Nov-14, 03:45 AM
Time dilation is independent of direction.

DrRocket
2008-Nov-14, 03:51 AM
Right. Indeed, I would argue that the basic premise of special relativity (the existence of global inertial reference frames) was always kind of a fiction. Yes, the existence of gravity makes it only approximately true in appropriately small regions, but I think even in the absence of any gravity, it would still be a philosophical fiction. Such global descriptions are simply a useful construct that, like many other constructs of our intellect, should never be taken too seriously. Reality is actually a very local enterprise, but in some situations we can commonly get away with imagining that it has globally describable properties. The twin paradox is not one of those situations, nor is considering what is happening in Andromeda while you are doing wind sprints.

I agree and that is why I phrased my post carefully. I personally don't think that a truly inertial reference frame exists. I certainly don't know of one. It is not the Earth which is rotating and revolving around the sun. It is not the sun which is revolving around the center of the galaxy. It is not the center of the galaxy with is rotating around the cg of the local group. etc, etc, etc.

There are some good approximations to an inertial reference frame, and they work pretty well in practice. But I don't think there is one that is truly inertial.

But to treat SR as a mathematical theory, you must start with an inertial reference frame somewhere, only by postulate perhaps. But once you have one, the others are all in uniform motion with respect to it. And you can only apply the theory in one of those reference frames.

And you are right, if you are doing wind sprints and I am watching from the bleachers our ideas of what is "now" in Andromeda might be off by a couple of weeks. So one had better be careful about that "reality" thing. Better to stick to what one can conclude from a purely mathematical evaluation of special relativity. It is a solid mathematical theory even if ultimately divorced from "reality" -- whatever that is. That is in fact the perspective that Rindler takes in his book.

publius
2008-Nov-14, 04:02 AM
If your investments have dilated, then you are unique. Mine have only experienced contraction, and the contraction is pretty breath-taking (I could live quite comfortably for a considerable period of time on this year's losses, and last month was really spectacular).

Yep, I should have said contraction. Dilation can indeed imply "stretching". Well, I feel the need to try to stretch what few dollars I have left as much as possible:)

Fortunately, today's market action indicates that we may not actually reach the event horizon. I hope. But there does seem to be a singularity in operation somewhere.

Don't let a little sunshine interrupt the rain on your parade. Bear rallies happen all the time. Sustained trend is down, with wild swings that produce little rallies as goes in the crapper. Volatility is the hallmark of bear markets, and you better believe things are volatile (swing was over 800 points today). And looking at the other indicators, this is going to be another "b-word" of a bear. But this ain't the thread for that -- see the "Is today Black Monday" thread in OTB where I've become Dr. Doom.

There's an old saying that the bear is dead until the last bull is dead. The global bottom doesn't happen until *everybody* has given up all hope. Be optimistic only after the last optimist has jumped out the window.

-Richard

publius
2008-Nov-14, 04:08 AM
I agree and that is why I phrased my post carefully. I personally don't think that a truly inertial reference frame exists. I certainly don't know of one.

What you mean is a *global* inertial frame doesn't exist. In GR, any "free fall" (or free float it's sometimes called) frame is inertial. It is following a force free geodesic path. But that frame is of course not a global inertial frame in the sense of SR. Minkowski doesn't apply globally, only in a local neighborhood where tides(curvature) are insignificant.

-Richard

DrRocket
2008-Nov-14, 04:51 AM
What you mean is a *global* inertial frame doesn't exist. In GR, any "free fall" (or free float it's sometimes called) frame is inertial. It is following a force free geodesic path. But that frame is of course not a global inertial frame in the sense of SR. Minkowski doesn't apply globally, only in a local neighborhood where tides(curvature) are insignificant.

-Richard

Agreed. I was speaking in terms of an inertial reference frame for either special relativity or Newtonian mechanics, where the stage is a global set of coordinates. GR has the luxury of operatinn on a manifold in which there are no global coordinates, only coordinate patches.

dhd40
2008-Nov-14, 10:28 AM
Yep, I should have said contraction. Dilation can indeed imply "stretching". Well, I feel the need to try to stretch what few dollars I have left as much as possible:)

-Richard

Now here comes the really bad news of relativity: While the value of my investments contracted by only 50%, I now need a dilation of 100% to get back where I came from.

I hate relativity in this field of reality :mad:

SeanF
2008-Nov-14, 03:08 PM
Correct.
Okay, but see, then I don't get where your ultimate objection is coming from.

In the Alice-Bob-Carl scenario, it's strictly local comparisons of inertially moving clocks. You object to that on the grounds that Bob and Carl are not the same person.

But I don't see why you insist that changing it from "Alice stays put, Bob goes out, Carl comes back" to "Alice stays put, Bob goes out, Bob comes back" is so significant. It's still local comparisons of inertially moving clocks.

Now, before you object, yes, Bob "turns around" and SR doesn't tell us what happens while he turns around. But SR does tell us the difference between "Bob before he turns around" and "Bob after he turns around" - it's the exact same as the difference between Bob and Carl in the first scenario.

And since, in the A-B-C scenario, that difference is sufficient to produce a total-time discrepancy, then in the A-B-B scenario it should sufficient to explain the total-time discrepancy.

The official "twin paradox" needs two specific aspects at its end: first, that the moving twin is back where he started; and second, that the moving twin is younger. "Acceleration" is necessary to obtain the first aspect, but I don't see why it's needed to explain the second.

Ken G
2008-Nov-14, 05:49 PM
In the Alice-Bob-Carl scenario, it's strictly local comparisons of inertially moving clocks. You object to that on the grounds that Bob and Carl are not the same person.I don't object to them being different people, I object to claiming one has a twin paradox if Carl goes back and meets Alice for the first time in his life, as opposed to Bob going back and meeting her for the second time. Only the latter brings one into contact with the twin paradox, only because there was acceleration. In other words, you can never get it if all observers cling to their same global simulataneity conventions (as happens in the inertial A-B-C scenario).

You need to have one observer who actually switches simultaneity convention, and that can only happen if that observer accelerates. You can use Carl to calculate what the new simultaneity convention needs to be, but you cannot escape the need to switch conventions by an observer only when that observer accelerates. If no observer needs to switch conventions, the problem can be done entirely with each observer's concept of time dilation, and no paradox appears because all observers have their own concept of everyone else's age.

The official "twin paradox" needs two specific aspects at its end: first, that the moving twin is back where he started; and second, that the moving twin is younger. "Acceleration" is necessary to obtain the first aspect, but I don't see why it's needed to explain the second.There is no need to "explain" what is never "obtained".

SeanF
2008-Nov-14, 06:03 PM
But you don't need acceleration to have a difference in simultaneity convention, you only need two different inertial frames.

The difference in simultaneity convention between Bob and Carl in the A-B-C scenario is in no substantial way distinct from the difference in simultaneity convention between Bob-before-he-turns and Bob-after-he-turns in the A-B-B scenario.

You earlier mentioned a hypothetical universe in which there was relative motion but no acceleration. Differences in simultaneity convention still exist in that universe, so they are not created by or a product of acceleration.

The fact that you need acceleration in order for a single observer to experience two different simultaneity conventions is, to coin a phrase, a difference that makes no difference. It does not create the effect, it only allows an individual to directly observe it.

There is no need to "explain" what is never "obtained".
In the A-B-B scenario it is obtained, but acceleration is not necessary to explain it.

Ken G
2008-Nov-14, 07:18 PM
But you don't need acceleration to have a difference in simultaneity convention, you only need two different inertial frames.I agree-- the point is, the "twin paradox" (or the "twin strangeness") is not just a difference in simultaneity conventions, it is a real physical effect. In other words, I am free to structure a physical theory that uses any simultaneity convention I like, and as long as it does not reverse causality connections, it will work just fine as a physical theory. Differences in convention, even between reference frames, are never an "explanation" of anything.

But even this is more that I was saying-- I was simply saying that to encounter the twin strangeness, you need acceleration, so acceleration is essential to that strangeness. You are talking about explaining the answer to the twin strangeness, which, given that you have acceleration, you might imagine you can explain the strangeness (that is encountered due to acceleration) by asking the accelerated observer what simultaneity convention they are adopting, and they can point to inertial simultaneity conventions in their answer. That approach gets us into even murkier water-- the issue of "what constitues an explanation".

I maintain that even if you take that stance (which is indeed the stance you are taking, and hhEb09'1s link did too), it is still quite lacking as an explanation-- because it implies that agreed-on conventions about how to set clocks can somehow cause people to age differently. Such explanations are missing something quite important, which is all about actual acceleration and would be there for any chosen simultaneity convention (being a result that is invariant to coordinatizations).

The difference in simultaneity convention between Bob and Carl in the A-B-C scenario is in no substantial way distinct from the difference in simultaneity convention between Bob-before-he-turns and Bob-after-he-turns in the A-B-B scenario.That is quite true, but also unresponsive to the point I have been making.

You earlier mentioned a hypothetical universe in which there was relative motion but no acceleration. Differences in simultaneity convention still exist in that universe, so they are not created by or a product of acceleration.Also true, and also unresponsive for two reasons: (1) such a universe never has any twin strangenesses in it, so has nothing to explain in that regard, and (2) an explanation that cites only a convention is not an explanation of anything, it is just instructions for doing a calculation a particular way, like a particular recipe for chocolate cake that tells us nothing fundamental about chocolate cakes.

I can sum it all up by pointing out that all inertial A-B-C scenarios amount to is saying, "Alice can get an answer in her inertial frame that is correct. Or, we can use any number of other inertial frames and also get the right answer." But that adds nothing-- we already did the calculation in one inertial frame, why should splicing in a few more add anything new? The twin paradox is all about the perceptions of the accelerated twin, and why those perceptions will get the wrong answer if the frame of the accelerated twin applies the same rules that inertial frames are allowed to employ.

"What is different about an accelerated frame, relative to an inertial frame, that allows the rules of inertial frames to get the right answer, and applying those same rules in an accelerated frame gets the wrong answer?"
Yes we can get the right answer by replacing the accelerated frame with connected inertial frames, but that only ducks the question. What is the physical source of the disconnect? If relativity means the rules are the same for all observers, why do they have to be inertial? The twin paradox raises this challenge, and accepting the challenge teaches us something important about reality that sticking to connected inertial frames simply does not tell us, because it is just following a recipe. That's the flaw in the claim that the A-B-C formulation "resolves" the paradox-- it ducks the paradox, and its physical ramifications.

It does not create the effect, it only allows an individual to directly observe it.As physics is an empirical science, allowing an individual to directly observe something is exactly the same thing as creating the effect.

speedfreek
2008-Nov-14, 08:15 PM
I need to get a few things straight here, as I think I am getting a little confused. Please confirm or refute these statements so I know where I am!

Clocks can always be considered to tick at 1 second per second, in their local frame of reference.

For observers in inertial motion, moving at speed relative to each other, one will always see the others clock running at a different rate to their own. Both will see the others clock as different by the same amount. Time-dilation is symmetrical between observers in inertial frames of reference.

So, there is a shift in the simultaneity between inertial frames which are moving relative to each other. Each sees the other shift in simultaneity by the same amount as this is essentially saying the same thing as the paragraph above.

Both observers are correct. The other is ageing at a different rate, relatively. They are both ageing differently in a symmetrical way, so if one sees the other ageing at half the rate of himself, he can consider it to be true, and it is true both ways - both are ageing at half the rate of the other, if you get my meaning. But locally to each observer, time always passes at 1 second per second.

Only if one changes frames and returns to the other, will the shift in simultaneity be realised, be "encountered", and in doing so you have to break the symmetry of the shift in simultaneity, unless both change frames symmetrically.

So, if a spaceship coasts past the Earth at 86.6% of c, we see the ships clock ticking at half the rate of our clocks. The occupants of the ship see clocks on Earth ticking at half the rate of the ships clock. Both are correct.

Have I got any of this right? Or should I be saying that we cannot consider anyone to be ageing at a different rate until they come back and prove it?

SeanF
2008-Nov-14, 09:54 PM
"What is different about an accelerated frame, relative to an inertial frame, that allows the rules of inertial frames to get the right answer, and applying those same rules in an accelerated frame gets the wrong answer?"
But that's just the point. If you want to consider that the traveling twin was in a single frame during the experiment, than you have to use acceleration - it's an accelerated frame. And if you try and apply the inertial frame rules to that single frame, you'll get the wrong answer.

But what hhEb09'1's link is intended to demonstrate (and what I've been trying to demonstrate) is that you don't have to consider the traveling twin to spend the entire experiment in one, single accelerated frame. You can consider him to be in multiple, distinct inertial frames. And if you apply the inertial frame rules to those distinct frames, you will get the right answer.

And it doesn't "duck the question" about the "disconnect," it just gives a different formulation of the answer. Rather than "an inertial frame vs. an accelerated frame," it's "one inertial frame vs. multiple inertial frames."

dhd40
2008-Nov-14, 10:22 PM
I need to get a few things straight here, as I think I am getting a little confused. Please confirm or refute these statements so I know where I am!

I will give my view of this just to see if I understood correctly the discussions on this extremely interesting thread. So, please, don´t look at my answers as being correct

Clocks can always be considered to tick at 1 second per second, in their local frame of reference.

Yes

For observers in inertial motion, moving at speed relative to each other, one will always see the others clock running at a different rate to their own. Both will see the others clock as different by the same amount. Time-dilation is symmetrical between observers in inertial frames of reference.

Yes, because they don´t accelerate relative to eachother (you don´t "feel" velocity, but you feel acceleration)

So, there is a shift in the simultaneity between inertial frames which are moving relative to each other. Each sees the other shift in simultaneity by the same amount as this is essentially saying the same thing as the paragraph above .

No comment, because I´m still not completely understanding the meaning of simultaneity

... so if one sees the other ageing at half the rate of himself, he can consider it to be true, and it is true both ways - both are ageing at half the rate of the other ...

Wrong. Only the one who is/was accelerating ages less

Only if one changes frames and returns to the other, will the shift in simultaneity be realised, be "encountered", and in doing so you have to break the symmetry of the shift in simultaneity ...

Yes, because "changing frames" always means acceleration (or decelaration?)

So, if a spaceship coasts past the Earth at 86.6% of c, we see the ships clock ticking at half the rate of our clocks. The occupants of the ship see clocks on Earth ticking at half the rate of the ships clock. Both are correct.

Yes, because there is no acceleration between them (unless they moved on curved trajectories)

I wonder which of these I got right

Ken G
2008-Nov-15, 01:16 AM
Clocks can always be considered to tick at 1 second per second, in their local frame of reference.Yes.

For observers in inertial motion, moving at speed relative to each other, one will always see the others clock running at a different rate to their own. Both will see the others clock as different by the same amount. Time-dilation is symmetrical between observers in inertial frames of reference.
Yes, if you have adopted a symmetrical simultaneity convention, like Einstein's. This is certainly a reasonable thing to do if you want to end up with a theory that is symmetrical for inertial observers, as is very much the intention of special relativity. But why single out inertial observers to be the ones who receive this symmetrical treatment? I could as easily choose a convention that singles out observers who are accelerating at g, and equip all such observers with a symmetrical simultaneity convention. I agree g=0 is the only non-arbitrary value, but it's still a choice.

So, there is a shift in the simultaneity between inertial frames which are moving relative to each other. Each sees the other shift in simultaneity by the same amount as this is essentially saying the same thing as the paragraph above.Yes. But the expression you likely have in mind for that simultaneity shift (the Lorentz transformation) only applies for inertial motion-- you have singled out that type of motion to get the agreement to which you refer. That's also the Einstein simultaneity convention, it is the symmetrical convention that singles out inertial motion. But the only observable is the history of clock readings and redshifts one clock will get from light signals from the other, and that can reconstruct the simultaneity shift, but only if it is a function of the precise history of the motion of the receding clock. That is not a global simultaneity convention, however, because it is not just a function of the distance and the instantaneous clock speed-- it is an integral over the motion of that clock. You only get a global convention if you single out the inertial clocks, which is why it is a convention, not an invariant simultaneity description. In general, the details of the motion are key-- that's why acceleration is key to the twin paradox.

Only if one changes frames and returns to the other, will the shift in simultaneity be realised, be "encountered", and in doing so you have to break the symmetry of the shift in simultaneity, unless both change frames symmetrically.Yes, that's how I see the key issue here, and note that if you do it symmetrically, you get no paradox.
Or should I be saying that we cannot consider anyone to be ageing at a different rate until they come back and prove it?That's a profound question. It has to do if we can really assume the speed of light is the same in all directions, and this is actually debated. My take on it is, yes, you'd really have to wait for them to come back and prove how they've been aging, because you can never measure the speed of light in only one direction-- it has to be a round trip. However, it would be a travesty to Occam to assume the speed of light was not isotropic if you had no reason to suspect anything but that it was isotropic.

The point of note is, the symmetry of time dilation comes from assuming a symmetry in the speed of light, so we built that symmetry right into time dilation based on our expectations about symmetries that reality ought to express. Normally, I'm uncomfortable telling reality what it ought to do, but symmetries may be a special case where we can get away with that, as they are so fundamental to how we think.

grav
2008-Nov-15, 02:54 AM
To me, for my way of thinking anyway, the key mechanisms of the twin paradox would just be that which leads to the correct resulting time lag between observers mathematically. The time dilation, of course, is one of those, although once we move past that part of the "paradox" from where the twins should be the same age when they meet back up to where each sees the other as younger, the paradox still persists, so there is something else required.

Now sure, acceleration is required for one of the twins to move away from the other and physically move back again, but it is not a key mathematical mechanism. That is, as SeanF is also saying, it is not the part of the solution to the paradox that gives the correct mathematical result for the overall time lag. It does add to the time lag, but only as an integrated form of the original time dilation of SR, so it is the same as the first mechanism for the time dilation that has already been covered. Ironically even, the more acceleration that is applied to achieve a change of frames to some other relative speed, the less the acceleration applies to the resulting time lag. That is because, since there is only a time dilation applied over the time of acceleration, integrated over the instantaneous speeds during the acceleration, then the greater the acceleration that is applied, the less becomes the time of acceleration, and so the less becomes the time lag resulting from the time dilation over that time of acceleration.

That is why I like to use an instant acceleration, leaving no time of acceleration to figure into the resulting time lag. An instant acceleration is really an infinite acceleration, but ironically doesn't figure into the time lag at all because there is no time of acceleration to dilate. I say "ironically" because while it might originally seem that it is the acceleration that makes the difference, the time lag due to acceleration might actually even barely figure into the resulting time lag mathematically, if at all, depending upon the time of acceleration, which is then just integrated over the time of integration using SR the same as the time dilation over constant speed, which still says each observer should see a lesser time on the other's clock in the same way anyway, so gets us no further in solving the paradox.

What does solve the paradox directly and mathematically is a shift in simultaneity, either sudden or gradual, same as Ken was saying earlier, and gradual if acceleration is applied over a long period of time, yes, but not at all due to the acceleration mathematically. That is, although acceleration is required to employ the twin paradox in the way that KenG insists upon doing, comparing the ages of the same two physical observers, it does not explain the resulting time lag mathematically, simultaneity does.

Ken G
2008-Nov-15, 03:10 AM
But what hhEb09'1's link is intended to demonstrate (and what I've been trying to demonstrate) is that you don't have to consider the traveling twin to spend the entire experiment in one, single accelerated frame.It was never disputed that one can do a calculation from a series of inertial frames and get the right answer for the elapsed time. As I explained above, if you do that, you never need anything but time dilation. But we already had an inertial frame in which to do that calculation-- Alice's. Adding Carl's frame is pointless, we already knew how to get the right answer.

The simple reason that adding Carl does not in any way alleviate the crucial presence of acceleration any time a twin strangeness is encountered is straightforward: if Bob hands his watch to Carl, the watch accelerates, and that is the physical cause of why it ultimately reads less than Alice's. If Bob does not hand his watch to carl, his watch does not accelerate, but it also never reads less time than Alice's-- not from the perspective of Bob's watch. Ergo, the acceleration is indeed the crucial ingredient here, though that of course does not imply that the location of the acceleration is not also important.

And it doesn't "duck the question" about the "disconnect," it just gives a different formulation of the answer. Rather than "an inertial frame vs. an accelerated frame," it's "one inertial frame vs. multiple inertial frames."Multiple inertial frames is simply not sufficient to describe the paradoxical result-- the watch must physically pass between those multiple frames. If it does not, there's never any twin issue, and if it does, then it physically accelerates. Introducing Carl is utterly irrelevant to those facts.

speedfreek
2008-Nov-15, 02:34 PM
So if there is symmetry between the shift in simultaneity for inertial frames in relative motion, surely that means all observers are correct in their assumptions about the other frame during the period they are monitoring it (after calculating out things like light travel time)?

On the outward leg of his coasting journey at 86.6% of c my twin and I age at half the rate of each other, on the return leg we age at twice the rate of each other, and only during the accelerations at the beginning, halfway point and end of his journey does the symmetry break (with most of the difference occurring at turnaround)? Does that sound absurd or is that the nature of space-time?

If he decides to coast away forever instead of turning around, can he consider the people on Earth (after calculating out the difference caused by his initial acceleration) to be now ageing at half the rate that he is whilst acknowledging that if he did turn around the situation would not only be reversed, but the act of his turning around would swing our respective notions of simultaneity in wildly different directions?

Ken G
2008-Nov-15, 03:05 PM
So if there is symmetry between the shift in simultaneity of inertial frames in relative motion, surely that means all observers are correct in their assumptions about the other frame during the period they are monitoring it (and calculating out things like light travel time)?Yes, special relativity equips each inertial observer with equal right to assert what is really happening. That's the beginning of its quintessentially local character. When accelerated observers (or gravity) enter the mix, general relativity affords them with similar status, at which point even the whole concept of a 'reference frame" becomes a local entity. That all this works so well in practice suggests there is something about observers' interaction with spacetime that is fundamentally local as well. The idea that we can seamlessly extend our local perceptions of how space and time work into a globally unified reference frame (that could encompass, for example, distant twins) is the "fiction" I was referring to above. In fact, the importance of acceleration comes in the form of the fact that the way space and time are globally perceived depends on the motion of the observer over her entire history. That was also true for inertial motion, but that recognition is hidden in the fact that the assertion of inertial motion implicitly specifies all that history. That is the main difference between uniformly inertial and momentarily accelerated motion.

On the outward leg of his coasting journey at 86.6% of c my twin and I age at half the rate of each other, on the return leg we age at twice the rate of each other, and only during the accelerations at the beginning, halfway point and end of his journey does the symmetry break (with most of the difference occurring at turnaround)? Does that sound absurd or is that the nature of space-time?Perhaps the former, but apparently the latter as well. But note, you and your twin always age at half the rate as each other, never twice.

If he decides to coast away forever instead of turning around, can he consider the people on Earth (after calculating out the difference caused by his initial acceleration) to be now ageing at half the rate that he is whilst acknowledging that if he did turn around the situation would not only be reversed, but the act of his turning around would swing our respective notions of simultaneity in wildly different directions?Yes, although I think the turn around wouldn't reverse the aging rate situation, it would only cause the swing in the Einstein simultaneity convention. In that motion, any valid simultaneity conventions (that preserve causality) will be the same at the start and at the finish, but will separate in between in ways that depend explicitly on the integrated motion, but integrate ultimately to the same invariant aging. That's what I mean about the real physics being "less than" special relativity, as it is generally taught.

ETA: All this makes me see better now what is flawed in the inertial A-B-C logic. If you analyze it carefully, it makes an assumption pretending to be a physical statement but which is in fact pure arbitrary convention. It asserts that if B returns in C's reference frame, then B must by all rights use C's simultaneity convention. But now we see that any extension of a reference frame globally has an arbitrary character, and so it is only by using an inertially-based convention that we say B must adopt C's convention, rather than simply having two different conventions for B and C. Anyone who thinks that B and C must use the same convention shuld note that A and B do not have the the same convention as each other at the end of the journey, as A thinks the "now" of B's return comes many years later than B thinks the "now" of his return comes. They have acquired a different sense of how to coordinatize that "now", even though it is the same now for them at that point, so they are in fact in the same reference frame but using different simultaneity conventions. As such, it is clear that B's acceleration puts the lie to the A-B-C scenario's unstated assumption that any two observers moving instantaneously the same must necessarily have the same simultaneity convention.

speedfreek
2008-Nov-15, 09:23 PM
But note, you and your twin always age at half the rate as each other, never twice.

Of course - :doh: I don't quite know where I got that idea from.

DrRocket
2008-Nov-15, 10:21 PM
So if there is symmetry between the shift in simultaneity for inertial frames in relative motion, surely that means all observers are correct in their assumptions about the other frame during the period they are monitoring it (after calculating out things like light travel time)?

On the outward leg of his coasting journey at 86.6% of c my twin and I age at half the rate of each other, on the return leg we age at twice the rate of each other, and only during the accelerations at the beginning, halfway point and end of his journey does the symmetry break (with most of the difference occurring at turnaround)? Does that sound absurd or is that the nature of space-time?

If he decides to coast away forever instead of turning around, can he consider the people on Earth (after calculating out the difference caused by his initial acceleration) to be now ageing at half the rate that he is whilst acknowledging that if he did turn around the situation would not only be reversed, but the act of his turning around would swing our respective notions of simultaneity in wildly different directions?

Look at the resolutions via special relativity and via general relativity in this Wiki article. I think they will be interesting to you.

grav
2008-Nov-16, 02:05 AM
Of course - :doh: I don't quite know where I got that idea from.After looking at the link DrRocket linked to, I'd say you were probably thinking about Relativistic Doppler for what is actually observed including flight of light effects, where the observed time dilation for observers travelling toward each other would be the inverse of that for travelling away at the same relative speed.

sirius0
2008-Nov-16, 02:17 AM
This thread is really starting to annoy me. :)
I may have to unsubscribe for a period. :lol:
I am trying to revise classical mechanics so that I can revise/learn properly SR so that I can (mostly for the first time) learn GR. This thread is too interesting and a big distraction!

I don't think the twins are a paradox, I think they sort of prove the paradox but I don't think they are the paradox. I think the paradox is actually in inertial observers observing each other to have slowed clocks even though the clocks may be identical, but this can never be established mutually between the observers. I think there is some value in talk of acceleration Ken, but grav has a point too. I started thinking about energy in my last post and I am going to unsubscribe whilst I have a look at E=gamma mc^2 already I can see acceleration lurking in there between the Kg.m.m.s^-2. Just have to focus this lazy brain. My agenda will be to show that both the inertial case and the twin case have a delta Energy involved. The inertial case is due to the mutually observed kinetic energy. The non-inertial case is due to one of the twins consuming or utilising energy that both can agree to (being the reason I don't see the paradox for this case). If I am wrong I will try to tell you all before you do :)

kjavds
2008-Nov-16, 04:08 PM
I want to use only most fundamental theories and get rid of all redundancy. Since such thing as SR really mess up everything they give good results but they destroy logic.

:shifty:

Ken G
2008-Nov-16, 06:53 PM
That's the A-B-C argument of the thread, and it is irrelevant for all the same reasons. In a nutshell, the argument says that you can use two inertial frames, instead of one (Alice's), and get the right answer. That is not suprising-- you can use 97 inertial frames, cobbled together any way you like, and also get the right answer. None of it is the twin paradox, because every single observer in every one of those frames thinks they themselves always have time passing more quickly than Alice, so they all think they are always younger than Alice if they were all born at the same time as Alice (by their own reckoning). That means that no twin paradox is ever encountered, it is a resolution of nothing other than how to calculate the times that other passing clocks will elapse under purely inertial conditions.

The twin paradox is about why physics in noninertial frames must be treated differently or you do get the wrong answer. Most generally, the key lesson of all this is that any physically meaningful (as opposed to purely conventional) global sense of "now" is a function of the complete history of motion of the observer in question, and inertial motion is merely the subclass where you can specify that entire history with a single vector, the current velocity. Because "resolutions" like the above completely miss that lesson, they do not involve the physics of the twin paradox.

pzkpfw
2008-Nov-16, 07:40 PM
...because every single observer in every one of those frames thinks they themselves always have time passing more quickly than Alice, so they all think they are always younger than Alice if they were all born at the same time as Alice...

I was going to have one more go at explaining why some of us still don't see why the A-B-C experiment is "wrong" or whatever, but the above struck me. Could you clarify?

(If they think their clocks are quicker than Alice's wouldn't they think they are older?)

kjavds
2008-Nov-16, 09:50 PM
That's the A-B-C argument of the thread, and it is irrelevant ...
The twin paradox is about why physics in noninertial frames must be treated differently or you do get the wrong answer. Most generally, the key lesson of all this is that any physically meaningful (as opposed to purely conventional) global sense of "now" is a function of the complete history of motion of the observer in question

Obviously I dissent from that, for starters because it says that my essay is wrong. Okay, maybe I could concede that the utmost crux of the twin paradox would involve accelerations and real bodies wearing real wristwatches. But I also find my simple SR treatment without acceleration to be analogous, perfectly on point and 100% valid.

And...
Physical or conventional, there clearly is no global (cosmos-wide) sense of "now". And I differ with any assertion that the history of a body says something about a time continuum. The subject body's own native time continuum proceeds uniformly without even the tiniest variation, regardless of that body's circumstances (to wit relative speed, or actual acceleration or proximity to gravity). These factors only play into how observers stationed on that body must reckon distant/alien time continua.
:exclaim:

Ken G
2008-Nov-16, 10:15 PM
If they think their clocks are quicker than Alice's wouldn't they think they are older?Yeah, that's a typo-- I meant older!

Ken G
2008-Nov-16, 11:24 PM
Obviously I dissent from that, for starters because it says that my essay is wrong. Okay, maybe I could concede that the utmost crux of the twin paradox would involve accelerations and real bodies wearing real wristwatches. But I also find my simple SR treatment without acceleration to be analogous, perfectly on point and 100% valid.
The essay is not wrong in that it presents how we actually do time-elapse calculations using inertial frames in special relativity. The question is-- what do you think doing all the time-elapse calculations from the point of view of inertial frames actually demonstrates? That we can get the right answer from inertial frames? We know we get the right answer for any clock behavior using inertial frames, that's not the twin paradox. There is nothing in that argument but time dilation in inertial frames that are instantaneously tangential to the motion of any clock. So what the argument does is simply look for inertial frames that are instantaneously comoving with any accelerating clock, and using special relativity (with nothing but time dilation) to determine how long the next "tick" will take, relative to Alice (or Stella). That's all the exercise does, it's exactly how Stella does the calculation of the time on Terra's clock (if Terra turns around). So you are not comparing two ways of doing the calculation there, you are only comparing one way to do a calculation applied to one clock that is not time dilated to one that is. That calculation is an assumed precursor to the twin paradox-- the teacher makes sure the student knows how to do that calculation prior to introducing the twin paradox. Just as with the A-B-C argument, it is an illusion that this is actually resolving anything, it is simply not encountering the problem.

The real aspect of the twin paradox that needs to be "resolved" is that meaningful global concepts of "now" are functions of the history of the observer making that determination. Special relatlvity uses a poor global simultaneity convention-- a convention dictated by the instantaneous motion of the observer relative to that global reference frame (which is, no motion at all, instantaneously). That's why it only works for inertial frames, because the physics is already using the fact that inertial frames have a history that is determined by their instantaneous motion.

Physical or conventional, there clearly is no global (cosmos-wide) sense of "now". That is false, of course there is a conventional global sense of now, it's used in cosmology all the time (comoving age is the most common one). It is a function of the complete history of the motion of the universe, as I've claimed. What there is not is a global Minkowski coordinatization-- if you insist on Minkowski geometry, then you need to use tangent spaces to get a global coordinatization, which is what the A-B-C argument is doing. It is just doing what needs to be done, with no recognition or exploration of why that needs to be done, or what other options are imaginable (like trying to do time dilation from an accelerated frame on the grounds that "all motion is relative").

And I differ with any assertion that the history of a body says something about a time continuum. The subject body's own native time continuum proceeds uniformly without even the tiniest variation, regardless of that body's circumstances (to wit relative speed, or actual acceleration or proximity to gravity).By it "own native time continuum", I gather you mean only its local sense of now. Certainly, the local sense of now does not require the object's history-- that's the whole point.

These factors only play into how observers stationed on that body must reckon distant/alien time continua.Precisely-- the global concept of "now", just as I've been saying.

kjavds
2008-Nov-17, 12:17 AM
The essay is not wrong in that it...
... So you are not comparing two ways of doing the calculation there, you are only comparing one way to do a calculation applied to one clock that is not time dilated to one that is.
... The real aspect of the twin paradox that needs to be "resolved" is that meaningful global concepts of "now" are functions of the history of the observer making that determination. Special relatlvity uses a poor global simultaneity convention
... of course there is a conventional global sense of now, it's used in cosmology all the time
... Precisely-- the global concept of "now", just as I've been saying.

Okay, there is the conceived global sense of now with which I'm vaguely familiar that is a rough set of guideposts following the course of the Big Bang and what all has ensued. Sure, and that measure has very real value to cosmological theorists. Other than that I cannot quite connect with your complex of sentiments above. Theorists use a concocted measure that can apply viable attributes and serve expedience. That system of Time need not bear on the pristine purity of physics and its attendant relativistic formulations. And I certainly did NOT as you seemed to infer use ONLY time dilation or ONLY from one perspective. Yes I used only one method (SR), and it was applied with total equanimity to both (all 3) frames according to Lorentz; but I can't imagine why you'd yearn for a mixture of methodologies :doh:. Remember the post to which I 1st replied?
I want to use only most fundamental theories and get rid of all redundancy.
Truthfully, I wish you'd supply a specific link to this "A-B-C scenario" from which you keep distancing yourself

Aw hell

pzkpfw
2008-Nov-17, 12:17 AM
Yeah, that's a typo-- I meant older!

Thanks.

No fingers pointed, by the way. I'm a programmer: you should be very happy I don't program nuclear power plants or medical equipment... I'm the guy who'd "-" instead of "+"; or mix units...

-----

In post #96 Durakken made the useful observation:

A paradox is two opposite things being held as being true when there is no possible way for it to be.

So I clarified again, in post #97, what I thought the twins paradox is:

1. All points of view are equal and it doesn't matter who is "really" faster - they all see each others clock slower.

2. Bob ends up younger than Alice.

You seemed to agree with that, because you quoted it in post #105, saying:

The crux of the twin paradox was summarized well:

The issue, for me, is that I just don't understand your objections to the A-B-C messenger clock situation; why it doesn't essentially meet the conditions listed above . They (the objections) seem to boil down to two things:

(I apologise if I've misreported these.)

Objection (1): for Bob to leave and come back, he must experience acceleration.

My reply (1): sure, for any real Bob, yes. I agree, and in such a case fully accept that acceleration/GR/... must be used to calculate what happens. But in the messenger clock example, nothing is accelerating but the same "paradoxical" result applies - everyone (by application of equivalence) could expect the other to be younger, but at the end one is.

Objection (2): it's (i) "just" application of time dilation, and (ii) everyone knows about that, anyway.

My reply (2.i): I don't understand why "it's just application of time dilation" is any worse then "it's just application of acceleration under GR". Under the terms of the "paradox", the "strangeness" occurs; in either variation of the experiment.

My reply (2.ii): How's that different to the acceleration case? If they are all GR experts does that make it any less of a seeming "paradox"?

I'll try again to map out what I think the A-B-C experiment is, and why it's a "paradox" (for which we know the answer):

1. There's a clock on Earth labelled "Alice".

2. A spaceship zooms by Earth. A clock labelled "Bob" is synchronised to the "Alice" clock.

3. The operators on Earth say "that spaceship is moving very fast relative to us; it's clock must be slower than ours".

4. The spaceship crew say "Earth is moving very fast relative to us, as we may consider ourselves still and it moving. So it's clocks must be running slower than ours".

5. That spaceship laters passes another going back towards Earth.

6. The "Bob" clock is synchronised to the 2nd ships' "Clone of Bob" clock.

7. With the synchronisation signal comes a message from the first spaceship "hey, watch out, our clock must be ahead of the "Alice" clock as Earth has been moving very fast relative to us". So the 2nd ship knows their "Clone" clock must be starting out "ahead" of the "Alice" clock.

8. The 2nd ship zooms back towards Earth.

9. The 2nd ship says "any clock on Earth must be running slower than ours, as Earth is moving fast, relative to us".

10. The "Alice" operators see the ship approaching and say "wow that's fast, their clocks must be slower than ours".

11. As the 2nd ship passes Earth, the "Clone" clock reading is sent to Earth, along with a message that reads "hey, this clock reading is probably ahead of yours, as your clock has been slower than ours (and the 1st ship we set our clock to) this whole time".

12. The "Alice" clock watchers find that the "Clone" clock reading is LESS than the "Alice" clock. They were expecting this, as the ships were moving fast, but are puzzled by the message received from the 2nd ship.

That's it.

I don't see why it's not "valid". Yes, if the crews all knew SR and GR they'd have not made the mistake, but full knowledge is not assumed in the set-up of either version of the "paradox".

Due to lack of simulataenity I don't think this is specifically relevant or "real", because there is no "when" at which to compare the clocks (as they are distant at that time) but I don't see why that's any different to the acceleration experiment.

kjavds
2008-Nov-17, 12:28 AM
... That's it.

I don't see why it's not "valid".

Sure you see why it's not valid. You stated in your footnote why it's not valid. It's not valid because step #7 is fallacious. The ship carrying the Bob-clone clock can only adopt the Bob clock reading, but it can NOT adopt the passing ship's assessment of Earthbound clocks. That's a no-no. Differently moving observers don't reckon distant clock readings the same.

Ken G
2008-Nov-17, 06:30 AM

The answer appears in general relativity: what is special about special relativity is pure convention, it's coordinatization not physics, but to see this one needs a better understanding of the limitations of global simultaneity conventions, and that is the true lesson of the twin paradox. There simply is no point in ever introducing the twin paradox if this lesson is going to be swept under the rug.

Truthfully, I wish you'd supply a specific link to this "A-B-C scenario" from which you keep distancing yourself
It appeared earlier in the thread, but you don't need a reference, because it was virtually identical in every detail with your essay. There is nothing wrong with either of them-- other than the interpretation of what they tell you. What they tell you is that Stella can do the calculaton of Terra's elaped time using nothing but time dilation, so it's nice to verify that rather than just know it to be the case in special relativity, but it still has nothing to do with the physical cause of the twin paradox: the role of acceleration, or more generally, the connection between global simultaneity and the history of motion of an observer.

Ken G
2008-Nov-17, 07:08 AM
The issue, for me, is that I just don't understand your objections to the A-B-C messenger clock situation; why it doesn't essentially meet the conditions listed above . They (the objections) seem to boil down to two things:

(I apologise if I've misreported these.)

Objection (1): for Bob to leave and come back, he must experience acceleration.

My reply (1): sure, for any real Bob, yes. I agree, and in such a case fully accept that acceleration/GR/... must be used to calculate what happens. Another way to say this is, if you view the twin paradox as simply a kind of practice application of the Lorentz transformation from B to C, then you can use the A-B-C scenario to show that the Lorentz transformation does indeed give what A would also get. But you can do that already in greater generality just by deriving the Lorentz transformation directly from the postulates of special relativity, and it follows that it will give the same answer the B-C way as it would the A way of calculating the clock results. We know this as soon as we derive the Lorentz transformation from the postulates of special relativity. The point of the twin paradox is not a specific concrete example of this general proof, it is to pose a philosophical question: what is special about acceleration?

Perhaps if I put this a different way. Let's imagine that no one ever talked about a twin paradox, and the A-B-C scenario was what was pointed out first. C sets his watch to B, zooms to A, and has a result younger than A, in exactly the way A would get with nothing but pure time dilation (since that's all the physics that's in there, it's what goes into the Lorentz transformation). No paradox, it's all just an exercise in applying the Lorentz transformation, like a practice problem.

But then, one day, you ask yourself-- wait a minute, what if, instead of C setting his watch to B, B actually hands his watch physically to C? Surely this will give the same result, but now we have a watch that actually reads less time than another watch that was in motion relative to it. What gives? I thought moving watches were supposed to run slower, how can A's watch run faster than B? The paradox would then be seen to start where the A-B-C scenario leaves off, which is the proper way to interpret the nature of this paradox. What is special about acceleration that allows ** watch to run slower than A's, when B's watch perceives itself as always being stationary, and A's as always being time dilated? At what point in B's motion did A's watch gain all that time? Using one convention, you could say it all happened during that brief acceleration, but why? What was the physical cause of that happening in that brief time?

There is not an answer to that because it is purely conventional when that time advance happened-- there is nothing physical about claiming that it happened during the acceleration. When it happened is not an invariant, it is purely a matter of coordinatization. So the bottom line is, above all the "twin paradox" is a lesson about the physical difference between an observable invariant and a matter of arbitrary coordinatization. It is the point of introduction of general relativity notions, even though one does not need general relativity to get the answer right-- in the absence of gravity, inertial frames and special relativity can always be used, if you don't mind missing the lesson involved in the twin paradox.

b]But[/b] in the messenger clock example, nothing is accelerating but the same "paradoxical" result applies - everyone (by application of equivalence) could expect the other to be younger, but at the end one is.But that is precisely what does not happen in the A-B-C scenario. I explained that earlier-- there is no reason at all for C to expect to be older than A, because C thinks he is synchronizing to someone (B) who is more time dilated than A, so of course C is setting his watch to a point earlier than A's watch reads. Some of that gap is made up by A's dilation while C approaches A, but not all of it, so A ends up older. There would never be any reason for C to expect otherwise-- that's always how it works out if you use purely inertial frames, time dilation is the only physics you ever need to understand to get clocks right from purely inertial frames, once you prescribe how you are setting them to begin with.

7. With the synchronisation signal comes a message from the first spaceship "hey, watch out, our clock must be ahead of the "Alice" clock as Earth has been moving very fast relative to us".But that's your problem right there-- C will not pay any attention to that nonsensical message. C will say, "no, you are moving much faster than A, so your clock is well behind A by now, not ahead of it". It's pure time dilation, which we do not consider a paradox here-- we know that different people will not agree on how much time dilation is going on, so we take their claims with a grain of salt and do not call them paradoxical, just inapplicable to our own inertial frame of reference. That's what C would do also, with B's message. It does not create any paradoxes for C, because C expects B to be mistaken about that message, from C's point of view. That's what I meant by "it's all just time dilaton" there.

kjavds
2008-Nov-17, 11:30 AM
Another way to say this is, ...
... That's what I meant by "it's all just time dilaton" there.

Thanks(?) for uh clarifying(?).
You sure can talk up a storm, Ken!

And of course you're correct that the twin paradox scenario resolved with inertial frames alone is no particular leap once the transform is derived by Lorentz and found (by Einstein et al) to apply.

But I still think there is no difference between the A-B-C scenario resolved by Lorentz Transform alone, and the scenario that incorporates actual accelerations. When you apply calculus (eg integration) to the LT, it will handle accelerations just fine without resorting to GR. And of course the end result is resolution of the scenario without any paradox (ie contradiction). It's the combination of time dilation, length contraction and clock dissynchronicity that resolves it all quite nicely. This is true whether you cobble together 3 inertial frames for simplicity (as in the A-B-C or my treatment here (http://placido.u21.0web-hosting.com/kavs/kjs/addend4.html)), or whether you employ accelerations and use integrated variants of the LT!

I'm suspecting that Ken's balk is all about the inability of fundamental relativity to connect with the holy grail of cosmology, that cosmos-wide comoving Time progression that has been concocted/conceived and was mentioned in a post or two here.

:wall:

Ken G
2008-Nov-17, 05:37 PM
But I still think there is no difference between the A-B-C scenario resolved by Lorentz Transform alone, and the scenario that incorporates actual accelerations. When you apply calculus (eg integration) to the LT, it will handle accelerations just fine without resorting to GR.That's a different issue-- that's the issue of, do you need general relativity to do calculations that involve acceleration. The answer to that is no-- you only need general relativity to do calculations involving gravity. The issue about general relativity in the absence of gravity is only that it allows you to do correct calculations from any type of reference frame, inertial frames are not seen as special. This is what I've been saying-- not that we need GR to figure out how much time will elapse on B's clock, that can be done in special relativity-- but that's only half the twin paradox.

What makes it a paradox is why you need to do that calculation using inertial frames, and why you get the wrong answer if you don't. You can just say "in SR I need to use inertial frames", but why? The lesson of the paradox answers the why question, it's because SR implicitly specifies the complete history and future of an observer, even as it pretends to apply only to the observer's instantaneous condition. That's the "little lie" of SR, whenever one treats the Einstein simultaneity convention as part of the physics of that theory (as you do when you talk about synchronization shifts)-- it makes one imagine that the Einstein simultaneity convention is something physically meaningful, when in general it is purely an arbitrary way to achieve a global coordinatization. This should be called the "twin lesson", not the "twin paradox", because the latter sounds like what is at issue is getting the answer right, but that was never at issue given the postulates of SR as seen from inertial frames.

kjavds
2008-Nov-17, 06:50 PM
That's a different issue-- that's the issue of, do you need general relativity to do...
... SR implicitly specifies the complete history and future of an observer
... it makes one imagine that the Einstein simultaneity convention is something physically meaningful, when in general it is purely an arbitrary way to achieve a global coordinatization. This should be called the "twin lesson", not the "twin paradox"

Yea, the twin lesson then.

Relativity purists don't ask for or expect global coordinatization.
I wish you'd quit using the word "global" when you obviously mean "cosmic".
I wish you'd quit using the word "coordinatization" when you obviously
mean system of time/space measure ie "metric".
Relativity purists don't ask for or expect any master cosmic metric.

And about the history of a body or particle: there are a potential infinity of alien frames that will be reckoned differently by that body based on its history, and each of those infinity will be skewed in a slightly different manner and extent. That's a rather enormous potential for skews and variances but NEVER ANY to the observer body/station ITSELF. So WHY the huge hang-up on history at all?
:question:

cjameshuff
2008-Nov-17, 09:39 PM
This should be called the "twin lesson", not the "twin paradox", because the latter sounds like what is at issue is getting the answer right, but that was never at issue given the postulates of SR as seen from inertial frames.

I like "twin conundrum". Seems to carry the implication that despite an apparent problem, there is an answer that can be reached with further inspection. Much better than calling it a "paradox".

Ken G
2008-Nov-17, 10:31 PM
Relativity purists don't ask for or expect global coordinatization.But that's because they've learned the "twin lesson"! In special relativity, where all observers are inertial, there is no reason at all to balk at the Einstein global simultaneity convention, it works perfectly well. It is only when observers can accelerate that it becomes unphysical (and downright meaningless if there is gravity, but we are never talking about gravity here). Your Alf-Terra-Stella scenario uses only inertial observers, so there's no problem in using global simultaneity conventions, and indeed they are often used to explain what happens for Stella during her acceleration if she does in fact return. That's the part that I'm saying is unphysical-- the physical solution is simply that accelerations mess up the meaning of the global convention. That's the role of acceleration in the twin paradox/lesson, and that's why acceleration is so crucial in encountering the lesson. If you scenario really alleviated the problem, there would never be any reason to abandon global simultaneity conventions, as there is not a reason to abandon them in your scenario.

I wish you'd quit using the word "global" when you obviously mean "cosmic".I mean no such thing. Nothing that I'm talking about has anything to do with the cosmos, I have not even included gravity in the argument in any way. Accelerating observers suffice.

I wish you'd quit using the word "coordinatization" when you obviously
mean system of time/space measure ie "metric".The metric is determined by the physics and the coordinatization, but has invariant properties that do not depend at all on the coordinatization. So no, I am not talking about the metric, I'm talking about the coordinatization.

So WHY the huge hang-up on history at all?The history is related to the instructions for composing a global coordinatization, like the Einstein simultaneity convention. Since the history of the motion determines the time difference between Terra and Stella (if she returns), that's why if you want to do the problem from the point of view of a global coordinatization (which your scenario does, that's what comes out of Stella's conceptualization of how old Terra is at every point along the way), you have to include the actual motion of Stella, accounting for the role of her acceleration in its integrated effect. That's the "twin lesson". All the Alf-Stella-Terra scenario does is let you calculate in the Stella-Alf combined frame the time elapsed if Stella returns, but you can already do that in Terra's frame. What does more inertial frames add if you can already get the answer in just one frame? The paradox is why Stella cannot do the exact same calculation by conceptualizing Terra's motion relative to Stella. So, why can't she? If you say "because she's not inertial", I'll say, exactly-- that's the crucial role of her acceleration that I'm talking about! That is also what DrRocket said above.

kjavds
2008-Nov-18, 01:16 AM
I checked a score of dictionaries and there's NO SUCH WORD as coordinatization. Global means pertaining to our globe, The Earth. YOU MISUSE WORDS. There is also no such thing as your "Einstein simultaneity convention". You're lost, a goner, and I am done trying to dignify your flailing. :harumph:

01101001
2008-Nov-18, 01:43 AM
I checked a score of dictionaries and there's NO SUCH WORD as coordinatization.

Try the Web.

Results 1 - 100 of about 29,100 for coordinatization

grant hutchison
2008-Nov-18, 02:18 AM
And I shudder to think that there are twenty dictionaries out there that don't offer "pertaining to a totality" (or something similar) as a meaning for "global".
Kjavds, you need a score of better dictionaries. :)

You also need to check Einstein's original 1905 paper (http://www.fourmilab.ch/etexts/einstein/specrel/www/), in which he set forth, up front, Section 1, his conventional definition of simultaneity.

Grant Hutchison

Ken G
2008-Nov-18, 03:24 AM
I'm sort of glad that's over.

sirius0
2008-Nov-18, 06:02 AM
Maybe a paradox can be defined as a long argument between people with a different point of view :)

By the way I will be back with that math soon. I don't think anyone will appreciate it but it is proving a good way for me to learn.

publius
2008-Nov-18, 06:56 AM
Relativity purists don't ask for or expect global coordinatization.
I wish you'd quit using the word "global" when you obviously mean "cosmic".
I wish you'd quit using the word "coordinatization" when you obviously
mean system of time/space measure ie "metric".
Relativity purists don't ask for or expect any master cosmic metric.

Ken is using his terms quite correctly as used and understood by those with any training and background in physics and relativity. Local vs. global is a ubiquitous dicotomy, an important distinction in many fields of physics. It's a biggy in General Relativity.

Coordinatization means just that, a choice of coordinates to map the space-time. One can use cartesians to coordinatize the Euclidean plane. One can use polar coordinates. One can use ellipitical coordinates. One can use an infinite number of possible coordinate systems to map that invariant "manifold". Note how very different curves of constant x or y are from curves of constant 'r' and 'theta'.

One's choice of coordinates has everything to do with one's notion of simultaneity, where things are "now". It has everything to do with what distant clocks are doing relative to your own at any point along your world line.

-Richard

Ken G
2008-Nov-18, 07:36 AM
Yes, and it's the pesky invariants that must correspond to the actual physics, but they are always getting confused with the coordinates. I think special relativity goes a long way to cement that confusion, and I can't help wondering if there is not a better way to teach all this without using the postulates of special relativity. It's not like they are all that intuitively clear, anyway! And doesn't the Lorentz transformation mix what is physical with what is purely part of a conventional coordinatization in a maddeningly unclear way? Yes it's great for getting the right answer from an inertial frame, but what is it really saying physically? It seems to me it says more than it has a right to, it is "too much" SR.

kjavds
2008-Nov-18, 09:27 AM
... but they are always getting confused
... goes a long way to cement that confusion
... It's not like they are all that intuitively clear, anyway!
... in a maddeningly unclear way?
... but what is it really saying physically?
... it is "too much" SR

Ah, it's all just too much, and confusion grips. My sympathies.

What is it saying physically?? It's saying that EM signals can do what mortals will never comprehend: they propagate predictably thru any observer's 3D space, and they will behave with such perfect grace to a multitude of disparate onlookers simultaneously! Regardless of vantage, each observer witnesses the light beam to move at constant speed c with perfect straightness through his personal simple space, yet curved and/or frequency-shifted if gravity tugs or if the observer should accelerate.

But that much was clear from the get-go I suppose.

How I love these threads -- so warm, so cuddly

Ken G
2008-Nov-18, 10:10 PM
Regardless of vantage, each observer witnesses the light beam to move at constant speed c with perfect straightness through his personal simple space, yet curved and/or frequency-shifted if gravity tugs or if the observer should accelerate.Ah, but there is an important lesson even in that observation. Why do inertial observers see light as moving straight (if no gravity), and accelerated observers see it is as curved? Is it something special about inertial observers? No! The lesson is, it is something special about the implicit choice of coordinates you must be using to claim that light is straight. The observation is entirely circular, because all it says is that if we choose global coordinates such that inertial observers will see light as propagating in straight lines, then such observers will, using that coordinate system, interpret light as propagating in straight lines. That's exactly what I mean by "too much SR"-- not too much for me to understand, too much to be making a valid physical argument.

kjavds
2008-Nov-19, 12:01 PM
...Why do inertial observers see light as moving straight (if no gravity), and accelerated observers see it is as curved? Is it something special about inertial observers? No! The lesson is, it is something special about the implicit choice of coordinates you must be using to claim that light is straight. The observation is entirely circular...

Total crap from you! If you're accelerating, then obviously a beam of light crossing your path will appear (to you) to be curved. And a non-accelerating observer finds light to move straight. These empirical observations have ZERO to do with the schema of some 'coordinatizers' -- uh, get real

SeanF
2008-Nov-19, 03:14 PM
Ken, I'm getting a better understanding of what your objection is, but I still think it's misplaced.

It was never disputed that one can do a calculation from a series of inertial frames and get the right answer for the elapsed time.
Oh, yes, it most certainly is disputed, just not by you. There are those (on this board - posting in this very thread) who would claim that were the A-B-C experiment conducted in real life, B's time plus C's time would exactly equal A's time.

They go on to claim that if you were to do a real-life "twin paradox" experiment, you would find the traveling twin's atomic clock to end up behind the stay-at-home twin, but the two twins themselves would still be identically aged.

They say this because they are under the mistaken impression that General Relativity postulates an actual, physical effect that the stresses of acceleration have on the mechanics of atomic clocks, not any different than the physical effect gravity has on pendulum clocks. They do not accept that there is anything regarding time itself here.

The page that hhEb09'1 linked to is intended for those people, to show them that you can, as you've admitted, "get the right answer" - and a non-contradictory answer - using just inertial frames. No acceleration.

For that page to claim that physical acceleration is in any way necessary would undermine that lesson.

hhEb09'1
2008-Nov-19, 10:06 PM
They say this because they are under the mistaken impression that General Relativity postulates an actual, physical effect that the stresses of acceleration have on the mechanics of atomic clocks, not any different than the physical effect gravity has on pendulum clocks. They do not accept that there is anything regarding time itself here.

The page that hhEb09'1 linked to is intended for those people, to show them that you can, as you've admitted, "get the right answer" - and a non-contradictory answer - using just inertial frames. No acceleration.

For that page to claim that physical acceleration is in any way necessary would undermine that lesson.That page (http://mentock.home.mindspring.com/twins.htm) was written years ago in response to just that sort of claim. Because of personal distractions, it has taken me until Sunday, a week after my last post, to get back to this thread with time to digest all that has been said. It has taken me since Sunday to do that! I've read the material three times, and diagrammed out the arguments.

Ken G has mentioned (http://www.bautforum.com/1361453-post40.html) that the math is correct in that page, so we don't have to belabor that. I've looked at all Ken G's objections and I think I have found a formulation that answers them.

Twins (as we are using "twins") are clones, and their similarity is what makes them appropriate in the "twin paradox", because we expect them to age similarly. I mentioned our current time standard of cesium clocks in post 35 (http://www.bautforum.com/questions-answers/81067-twin-paradox-relativity-2.html#post1361420)--the clocks serve a similar function in that their results are expected to also reproduce each others aging process, and they're even more aptly clones, or twins, of each other. Sometimes, two or more such clocks are used as checks against each other, to maintain a reliable timekeeping function, but all-in-all they're more accurate than the average human body, as timekeeping devices.

So, let Alice, Bob, and Carl procede as before, where Alice stays home, Bob moves off (instead of "rockets off" because of some objections that "rockets off" implies some sort of acceleration on his part after leaving Alice) and meets Carl, who returns to Alice, all in uniform motion. If Alice maintains two cesium clocks, and Bob leaves with two cesium clocks, and meets Carl who also has two cesium clocks, and they exchange one clock, then the result is that all joined pairs of clocks at all points of space and time that they occupy show the same time. And, they show an elapsed time that corresponds to the elapsed time that not only Carl observes, but also the time that Bob would have observed, had he returned with Carl. The elapsed time that we expect does not require any physical handoff at the turn around point--because the clocks are not only identical, but indistinguishable, to the accuracy of what we are trying to measure.

Any errors in judgement regarding the physical world can be applied to any clock, human or not. I'm starting to wonder why the paradox should depend upon a particular point of view rather than another point of view if both are wrong--why value one over the other! :)

By the way, many of these ideas have been emerging in other threads, and my own recognition of these facts is evolving even in this very thread, so it shows why such discussions are valuable and why there is no shame in being "beguiled" by hhEb09'1s link. The swindle there is very subtle, and is of great value to identify.This follow up page (http://mentock.home.mindspring.com/twin2.htm) addresses some of the concerns you have about it being a "swindle" (it treats the notion that Bob can consider himself to be unmoving the entire time). Another one (http://http://mentock.home.mindspring.com/twinrdux.htm) mentions five posters specifically in the acknowledgements, SeanF being one of them, as well as the BABB/BAUT community as a whole. I just wanted to repeat that.

Sam5
2008-Nov-20, 12:59 AM
That page (http://mentock.home.mindspring.com/twins.htm) was written years ago in response to just that sort of claim.

So, let Alice, Bob, and Carl procede as before, where Alice stays home, Bob moves off (instead of "rockets off" because of some objections that "rockets off" implies some sort of acceleration on his part

Yes, someone pointed that out to you 7 or 8 years ago. The term, “rockets off”, certainly implies using a “rocket”.

But Einstein never specified how we “impart” a “constant velocity v” to the k system in his 1905 thought experiments in Sections 3 and 4. There are two well know ways to do it: (1) Using a “rocket” was not as well known in 1905, but it would have “imparted” the motion only to the k system, and of course it would have accelerated it. (2) However, he often used “trains” for his various thought experiments, and by using a train we would be using “traction” to “push off” the k system from the K system, which, under Newton’s 3rd Law, would “impart” an equal acceleration and motion to both the K and k systems: ”To every action there is always opposed an equal reaction; or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.”

But Einstein didn’t specify which method to use to “impart” the motion, since acceleration is totally disregarded in the thought experiments, as Wolfgang Pauli pointed out in his 1925 book, “Theory of Relativity”, and Einstein was only interested in what he called the “kinematical” effect of relative motion on his “balance wheel” clock.

That’s what led to the paradox, and that’s why the “clock paradox” is still being debated more than 100 years later.

What Einstein considers in that thought experiment in the 1905 paper is “relative motion” only and a ”constant velocity v.

He did not add acceleration or gravity or atomic clocks to the 1905 thought experiments until his “Dialogue” article of 1918, as published in Die Naturwissenschaften, 29 November 1918:

Someone brought that article to your attention shortly after it was first published in English in 2002.

In that article, he used gravity to get rid of the clock paradox. I.E., in his 1918 paper, one of two systems exists under strong gravity longer than the other system, and, therefore, the atomic clock of the system that experienced more gravity lags behind the clock of the other system. Pauli also pointed that out in his 1925 book:

http://i34.tinypic.com/zj9ldj.jpg

hhEb09'1
2008-Nov-20, 05:14 AM
Yes, someone pointed that out to you 7 or 8 years ago. The term, “rockets off”, certainly implies using a “rocket”.That was indeed for your benefit. :)

sirius0
2008-Nov-20, 06:50 AM
Maybe a paradox can be defined as a long argument between people with a different point of view :)

By the way I will be back with that math soon. I don't think anyone will appreciate it but it is proving a good way for me to learn.

I got to this via dE/dv but finished with effectively dE/dt

I am short on time and will explain myself more later.

dE=a'.dt.1/(1-(v^2/c^2)).m.v The acceleration element will be contentious as it is popping out in the "non-paradox" case but i will explain.

sirius0
2008-Nov-20, 01:18 PM
Quite a few steps behind what I got to there. And I know it is all fairly basic, just a de with some algebra. And I am not to sure of some of the conclusions I make or the legitimacy of what I set out to do.

Firstly I thought that seeing my twin wizz past could be considered a change in energy, in the sense that given he has the same (rest) mass as me he has actually gained some mass (being relativistic mass in total). The difference in energy being the relativistic kinetic energy. The result I came up with is similar to KE but was arrived at by differentiating dE/dv from the E=1/((1-(v^2/c^2))^0.5)mc^2.

dE=a'.dt.1/(1-(v^2/c^2)).m.v

The a' is a debatable pseudo acceleration. It is not reduced back to velocity by the dt because dt is from my frame not his. The a' comes from placing the dv over the dt' the time increments observed from our frame on his clock. The dv fits my understanding of the situation, being that as we observe the other we assign all the velocity difference to the twin. This is what I mean by psuedo acceleration because we observe a difference in velocity and a resultant difference in the clocks we get an inference of acceleration (dv/dt'). We look at the twin, we see an energy difference relative to us. He looks at me and sees the same difference but assigns it to me, hence he sees me with a slower clock. the a' comes about because there is an energy difference and closing this difference would require acceleration but in a sense we are closing it by making the observation and this brings about a' due to our mental efforts to mesh two inertial frames.

In the paradox case, where the twin returns to the frame we are observing from, the acceleration becomes "real" in every sense. dv becomes increments above or below initial observed velocity and both twins are able to agree to the fact that the returned one is younger, that he was non-inertial for part of the trip and that the twin used fuel or had some utilization of a potential. My point here is that in either case it is a difference in energy that causes both cases of time dilation and it is bringing home the energy difference that allows the effect to be agreed on meeting up.

As I said earlier though I am just learning this SR. What still puzzles me is similar to the ancient Greeks idea of a falling beam that can never touch the ground paradox that proved atoms. Is that for the whole trip the twin will observe us to be having a slower clock, even though the twin, if at all competent, will know when he is in a non-inertial frame, our clock will continue to seem slower to him. At what point will our clock, from his perspective, catch up and over run his? No clock of course is observed to be running faster so it is this 'catch up' point that really goes to the paradox in my view. Well where have I gone wrong, I expect I have somewhere. But I am very pleased with how much I seem to be understanding.

kjavds
2008-Nov-20, 03:05 PM
... for the whole trip the twin will observe us to be having a slower clock
Actually, the word "observe" is less-than-ideal there. Relativistic distortions are things that are attributed or perhaps reckoned, though not always immediately observed.

... even though the twin ..will know when he is in a non-inertial frame, our clock will continue to seem slower to him. At what point will our clock, from his perspective, catch up and over run his? No clock of course is observed to be running faster so it is this 'catch up' point that really goes to the paradox in my view. Well where have I gone wrong, I expect I have somewhere.
You say, "no clock is observed to be running faster". Again, put the word "observe" to bed and go with "reckon", okay? So long as there is any relative motion, the astronaut twin must (1) ascribe time dilation to the other. But there certainly comes a period when the astronaut must (2) reckons the other's clock to be running faster and that is based on the acceleration of reversing direction ('not sure how that bears on the energy picture). The astronaut twin need simply add the two effects together to arrive at the net distortion, and so with some fairly simple math the point of overtaking can readily be pinpointed.

Ken G
2008-Nov-20, 09:40 PM
Oh, yes, it most certainly is disputed, just not by you.But those who dispute that are simply mistaken, as this is testable by experiment. I'm actually not interested in opinions that are contradicted by measured invariants, my comments are directed to those who do understand what measurements give, and are interested in how best to explain those results.

They go on to claim that if you were to do a real-life "twin paradox" experiment, you would find the traveling twin's atomic clock to end up behind the stay-at-home twin, but the two twins themselves would still be identically aged.Well, that's their mistake, but neither my explanation nor yours is liable to deter them, so it is irrelevant to the issue of "what is the twin paradox/strangeness/lesson".

They say this because they are under the mistaken impression that General Relativity postulates an actual, physical effect that the stresses of acceleration have on the mechanics of atomic clocks, not any different than the physical effect gravity has on pendulum clocks. They do not accept that there is anything regarding time itself here.I'm not sure how one distinguishes something happening to time from something physically happening to a clock. It's all the same to me.

The page that hhEb09'1 linked to is intended for those people, to show them that you can, as you've admitted, "get the right answer" - and a non-contradictory answer - using just inertial frames. No acceleration.
I think it is actually intended for a different audience, those who claim that acceleration does have physical effects on a clock. Not the silly effects you are arguing against, but the actual physical effects that it really does have. In other words, there is less time elapsed between two events if the events are connected by an accelerated path rather than an inertial one. That is a physical effect, and is the subject of the twin paradox/strangeness/lesson. One can derive the answer in a single inertial frame (Alice's), or any number of cobbled together inertial frames, and it simply doesn't address the issue of why the time elapsed is different along an accelerated path. That is a physical effect that must be recognized.

For that page to claim that physical acceleration is in any way necessary would undermine that lesson.Physical acceleration is necessary, that's the source of the differing elapsed times. That you can correctly calculate the elapsed times in an inertial frame doesn't contradict that-- indeed, you only need Alice's frame to get the calculation right. It is an elementary result of the axioms of special relativity, axioms that the A-B-C calculation uses, that they must get the same answer as A alone, so actually doing that calculation does not say anything other than that mathematics is axiomatic. The physical statement is coming from the acceleration.

Ken G
2008-Nov-20, 09:51 PM
This follow up page (http://mentock.home.mindspring.com/twin2.htm) addresses some of the concerns you have about it being a "swindle" (it treats the notion that Bob can consider himself to be unmoving the entire time).Before I look at how that argument plays out, let me ask you, is it going to address the mathematical truth that the axioms of special relativity guarantee that all inertial frames must always calculate the same measured invariants, given any other measured invariants necessary to do the calculation? If we can all agree that this is the very mathematical structure of the special relativity axioms, then we have no need to do any A-B-C calculations, we can just do it in A's frame, and as long as we insure that the required invariants in all other frames agree (which is what you do with the clock-exchanging business), then we are guaranteed from the mathematical structure of special relativity that we will always get the same answer in the A-B-C system as we do in the A system alone. The point is, that is pure mathematics-- not one ounce of physics in it, if we accept that special relativity does indeed work for inertial observers.

So where's the physics? The physics asks, how do you get two different elapsed times connecting the same two events? The physical answer to that is, you must have acceleration of one of the observers. That is all that is meant when someone says "the resolution of the twin paradox/strangeness/lesson is intimately and inseparably connected with the acceleration of an observer". That statement is still completely true when one lays out the inertial A-B-C scenario-- all the inertial A-B-C scenario is is an unnecessary check of the mathematical self-consistency of the axiomatic structure of special relativity. As a mathematician, you can see that.

Ken G
2008-Nov-20, 10:08 PM
If you're accelerating, then obviously a beam of light crossing your path will appear (to you) to be curved. And a non-accelerating observer finds light to move straight. You have simply fallen into the exact circular argument I mentioned above. If we let the inertial observers do the coordinatizing, then you are correct, and if we let observers who are accelerating, say at g in some direction, do it, then you are quite mistaken. Going with what seems "obvious", i.e., only considering straightness as it relates to a path in space alone, you get the wrong answer as to which one is "straight", and going with the infinitely more subtle concepts of geometry by Riemann, you find they are all straight (in spacetime), if there is no gravity.

kjavds
2008-Nov-20, 10:38 PM
... and going with the infinitely more subtle concepts of geometry by Riemann, you find they are all straight (in spacetime), if there is no gravity.

Yo but curved in plain-jane space, to the eyes of an accelerating observer who staunchly considers himself to be at rest.

In context (http://www.bautforum.com/questions-answers/81067-twin-paradox-relativity-7.html#post1368582), I was expressly emphasizing the empirical when I posted the quoted passage; it's about what the presumed-still observer would see in his own very-local "simple" space, ie 3-D space.

SeanF
2008-Nov-20, 10:51 PM
I'm not sure how one distinguishes something happening to time from something physically happening to a clock. It's all the same to me.
You believe that the effect gravity has on a pendulum is the same as its effect on time?

I think it is actually intended for a different audience, those who claim that acceleration does have physical effects on a clock. Not the silly effects you are arguing against, but the actual physical effects that it really does have.
The author of the page had the opportunity to disagree with my interpretation of his intent, and he chose to acknowledge it, instead. I'll take his opinion over yours. :)

In other words, there is less time elapsed between two events if the events are connected by an accelerated path rather than an inertial one. That is a physical effect, and is the subject of the twin paradox/strangeness/lesson.
But you yourself have admitted the importance of the distance at which the acceleration takes place. If it's a physical effect on the accelerating clock, how can the distance to the non-accelerating clock be a contributing factor? Especially when you consider that there may be multiple non-accelerating clocks, at different distances?

sirius0
2008-Nov-20, 11:01 PM
E=(delta t/delta t')*mc^2
What I am saying here is that i agree with the essentials of acceleration but I think it is the energy difference that "causes" the dilation. Equivalently it is also a mass difference, but my self study is not ready for this just yet.

kjavds i have noted your semantics as they may have value later but I learn SR now andt me learnt enGlish lateA :)

hhEb09'1
2008-Nov-20, 11:23 PM
So where's the physics? The physics asks, how do you get two different elapsed times connecting the same two events? The physical answer to that is, you must have acceleration of one of the observers. That is all that is meant when someone says "the resolution of the twin paradox/strangeness/lesson is intimately and inseparably connected with the acceleration of an observer". That statement is still completely true when one lays out the inertial A-B-C scenario-- all the inertial A-B-C scenario is is an unnecessary check of the mathematical self-consistency of the axiomatic structure of special relativity. As a mathematician, you can see that.I think the "pairs of cesium clocks" example above shows that the elapsed time measured does not depend upon the acceleration of an observer. No observer has to be accelerated in order for us to measure two different elapsed times connecting "the same two events".

I think it is actually intended for a different audience, those who claim that acceleration does have physical effects on a clock. Not the silly effects you are arguing against, but the actual physical effects that it really does have.
The author of the page had the opportunity to disagree with my interpretation of his intent, and he chose to acknowledge it, instead. I'll take his opinion over yours. :)Before I disagree with Ken G's interpretation, I want more explanation of his interpretation, whether his statement implies something broader. It was intended for his audience as well. All audiences, actually. :)

Ken G
2008-Nov-21, 12:13 AM
Yo but curved in plain-jane space, to the eyes of an accelerating observer who staunchly considers himself to be at rest. Which brings us to the lesson you are so far not getting-- even an accelerated observer "considers himself to be at rest". That is basically what I have been saying here.

Ken G
2008-Nov-21, 12:20 AM
You believe that the effect gravity has on a pendulum is the same as its effect on time?
Certainly, to the extent that a pendulum is a good clock. That is the point of clocks-- they are all physically "plugged in" to the same time, regardless of how the clock actually works.

The author of the page had the opportunity to disagree with my interpretation of his intent, and he chose to acknowledge it, instead. I'll take his opinion over yours. So you are claiming that site did not say that acceleration was not the fundamental physical source of the shortened time in the twin paradox? If they are not making that claim, then I would have no disagreement with them. I thought I recalled words precisely to that effect.

But you yourself have admitted the importance of the distance at which the acceleration takes place. If it's a physical effect on the accelerating clock, how can the distance to the non-accelerating clock be a contributing factor? It could be, because it is. Why should it not be? It seems you are indeed claiming just what I suggested was being claimed, that acceleration is not the physical cause. But no other cause has been suggested, or is possible to suggest.

Especially when you consider that there may be multiple non-accelerating clocks, at different distances?This just says the physical reality is complicated, it does not say there's anything wrong with it.

Ken G
2008-Nov-21, 12:30 AM
I think the "pairs of cesium clocks" example above shows that the elapsed time measured does not depend upon the acceleration of an observer. No observer has to be accelerated in order for us to measure two different elapsed times connecting "the same two events".That is where you are mistaken. If you look carefully at the meaning of the word "measure" using a clock, you will certainly note that the clock must be in the possession of the observer at all times, for it must be "the observer's clock". In special relativity, because you can treat inertial observers in a special way, you can (carefully) get away with extending that to clocks not in your possession but in your global "inertial reference frame". However, you certainly cannot claim to be making a "measurement" using a clock in a different frame, as you are now doing. That is simply not the meaning of a measurement-- if I can use any clock I like, then I can get any result I like-- some "measurement" that. So if we stick with the standard meaning of measurement, then yes, you must have an accelerated observer to get two different measured times connecting two events. That is precisely "the twin lesson".

hhEb09'1
2008-Nov-21, 01:42 AM
That is where you are mistaken. If you look carefully at the meaning of the word "measure" using a clock, you will certainly note that the clock must be in the possession of the observer at all times, for it must be "the observer's clock". In special relativity, because you can treat inertial observers in a special way, you can (carefully) get away with extending that to clocks not in your possession but in your global "inertial reference frame". However, you certainly cannot claim to be making a "measurement" using a clock in a different frame, as you are now doing. That is simply not the meaning of a measurement-- if I can use any clock I like, then I can get any result I like-- some "measurement" that. So if we stick with the standard meaning of measurement, then yes, you must have an accelerated observer to get two different measured times connecting two events. That is precisely "the twin lesson".I disagree. The clock's do not have to be in the possession of a single observer, in that sense. I think you should agree.

Why do I say that? Because otherwise your own words are meaningless:

So where's the physics? The physics asks, how do you get two different elapsed times connecting the same two events? The physical answer to that is, you must have acceleration of one of the observers.In that question of yours that I quote, you have two observers. But you end up with two different elapsed times.

The difference between those two elapsed times is exactly the issue that we are discussing. It is impossible to observe, even in your approach, without the use of more than one observer, in the sense that you are using "observer".

Beyond that, in the paired cesium clocks example I gave above, it is impossible for anybody to tell one of the pair of clocks from the other of the pair, therefore the distinction that you are making is not physically relevant.

ETA: We, you and I both, are using more than one clock to measure a difference, a physically real and physically interesting difference. There is nothing wrong with that, anymore than using one clock for a while, then using a second clock. At the level of reliability of the instruments.

Ken G
2008-Nov-21, 03:42 AM
I disagree. The clock's do not have to be in the possession of a single observer, in that sense. I think you should agree.The history of the clock is irrelevant to my point, I am saying that the clock you have in your hand is the only one that can give you a time measurement. In other words, it has to be in your possession for the duration of whatever you are calling a time measurement. If you doubt that, you are going to have to tell me what you think a measurement using a clock is, if that clock need not be in your possession or even in your reference frame.

In that question of yours that I quote, you have two observers. But you end up with two different elapsed times.
Precisely-- two observers, two different clocks, two different elapsed times, two different spacetime paths. Where do you see a problem there? I see perfect consistency.

It is impossible to observe, even in your approach, without the use of more than one observer, in the sense that you are using "observer".Yes, you need two observers to get two times, again perfect consistency.

Beyond that, in the paired cesium clocks example I gave above, it is impossible for anybody to tell one of the pair of clocks from the other of the pair, therefore the distinction that you are making is not physically relevant.Of course the clocks are identical, that matters not. What matters is that an observer must have a clock in his/her possession to make a time measurement. This is quite fundamental to the whole concept of measurement, and empirical objective science for that matter.

ETA: We, you and I both, are using more than one clock to measure a difference, a physically real and physically interesting difference. Certainly. What I'm saying is that those are two measurements, by two observers, using their own clocks, just the way the term measurement is intended to be used in physics. Unless an observer is accelerated, they cannot get two different measured elapsed times between the same two events.

There is an important point here. Physics measurements are entirely local to an observer. Even if light is used, one can send out light, with a locally held laser, and detect the return, with a locally held detector. Whatever happens in between is pure conceptualization. The measurements are unique and invariant, the conceptualizations are generally neither. Confusing a conceptualization with a measurement is a Bad Idea, if one wants to think physics is an empirical science.

hhEb09'1
2008-Nov-21, 04:31 AM
The history of the clock is irrelevant to my point, I am saying that the clock you have in your hand is the only one that can give you a time measurement. In other words, it has to be in your possession for the duration of whatever you are calling a time measurement. If you doubt that, you are going to have to tell me what you think a measurement using a clock is, if that clock need not be in your possession or even in your reference frame.Ann uses two different clocks, with two different readings, to come to a conclusion about the way the world works. In order to even test that, she needs at least two clocks, one of which is not in her possession.

Precisely-- two observers, two different clocks, two different elapsed times, two different spacetime paths. Where do you see a problem there? I see perfect consistency.No problem as far as I can see!
What matters is that an observer must have a clock in his/her possession to make a time measurement. This is quite fundamental to the whole concept of measurement, and empirical objective science for that matter.We use probes all the time. We've made measurements on Mars.
Unless an observer is accelerated, they cannot get two different measured elapsed times between the same two events.I've shown that the unaccelerated observers get the same measurements as the accelerated observers.

You move back and forth in your claim. You say an observer can only get one measurement, but then you say they get two. That's inconsistent.

There is an important point here. Physics measurements are entirely local to an observer. Even if light is used, one can send out light, with a locally held laser, and detect the return, with a locally held detector. Whatever happens in between is pure conceptualization. The measurements are unique and invariant, the conceptualizations are generally neither. Confusing a conceptualization with a measurement is a Bad Idea, if one wants to think physics is an empirical science.Which do you think is a Worse Idea, measuring the passage of time using a human pulse, or that of a cesium clock?

SeanF
2008-Nov-21, 02:39 PM
But you yourself have admitted the importance of the distance at which the acceleration takes place. If it's a physical effect on the accelerating clock, how can the distance to the non-accelerating clock be a contributing factor?
It could be, because it is. Why should it not be?
Consider the case of three clocks, A-B-C, some distance apart but motionless relative to each other and unaccelerated.

Now accelerate clock B.

You are claiming a physical effect on clock B, but saying that the magnitude (not to mention direction) of that effect is different when measured against clock A than it is when measured against clock C.

First, that contradicts your other assertion that no physical reality can be ascribed to measurements between distant clocks.

Second, it is self-contradictory in that you get from A=B=C to A>B>C (which means A>C) without ascribing any physical effects to either A or C.

Ken G
2008-Nov-21, 03:17 PM
Ann uses two different clocks, with two different readings, to come to a conclusion about the way the world works.No-- no observer ever uses two different clocks to get two different readings. If you even think that makes any sense, you have lost contact with the single most important principle of empirical science-- the property of objectively repeatable observations. (As well as with the ancient Chinese proverb, "a man with one clock knows what time it is, a man with two is never sure".) When two measurements of the same thing by the same observer give different results, it's goodbye physics. Fortunately, that never ever happens. You are mistaken about the meaning of the word "measurement". Is it any surprise people get confused about the differences between science, mathematics, and non-science?

You move back and forth in your claim. You say an observer can only get one measurement, but then you say they get two. That's inconsistent.Again you are mistaken, my position is not only consistent, it is science. One observer, one measurement. If you ever saw me refer to any other measurement, you can be absolutely sure I was talking about a measurement by a different observer, or a calculation by the same observer. Never two measurements.

Which do you think is a Worse Idea, measuring the passage of time using a human pulse, or that of a cesium clock?Completely irrelevant to the issue here, when both the heart and the cesium clock are in the possession of the observer. That irrelevance is what gives us the very concept of time.

SeanF
2008-Nov-21, 03:27 PM
If you ever saw me refer to any other measurement, you can be absolutely sure I was talking about a measurement by a different observer, or a calculation by the same observer. Never two measurements.

Unless an observer is accelerated, they cannot get two different measured elapsed times between the same two events.
Which, read normally, would make "an observer" the antecedent of "they."

Next time, try "Unless one of the two observers is accelerated, they..." to make it at least arguable that "they" refers to two observers instead of one.

Ken G
2008-Nov-21, 03:33 PM
You are claiming a physical effect on clock B, but saying that the magnitude (not to mention direction) of that effect is different when measured against clock A than it is when measured against clock C.I'm not saying it, reality is. But I think your confusion here is that you think the two simultaneity comparisons you are making are somehow physically "real". Simultaneity conventions are just that-- conventions. If you want something real, you have to compare two invariant measurements. What are the invariant measurements that you are claiming are "different" here? You don't get them until you have connected the two events in question, and at that point you cannot say "when" the physical effect was manifest. It just is. This is quite common in relativity-- one cannot say when something happened, the thing that happened is a kind of integrated effect of choosing two meaningful points of comparison. (Example: when we observe a blueshift of a spectral line from a star that is moving toward us, when did that blueshift happen?)

Second, it is self-contradictory in that you get from A=B=C to A>B>C (which means A>C) without ascribing any physical effects to either A or C.I'm afraid I have no idea what this is supposed to mean.

Ken G
2008-Nov-21, 03:36 PM
Which, read normally, would make "an observer" the antecedent of "they."I think if you take the time to check the context of that remark, you will see that the full quote was:

What I'm saying is that those are two measurements, by two observers, using their own clocks, just the way the term measurement is intended to be used in physics. Unless an observer is accelerated, they cannot get two different measured elapsed times between the same two events.Now, seriously, is it not perfectly obvious from the full quote that the "they" refers to "two measurements, by two observers"?

SeanF
2008-Nov-21, 03:59 PM
Now, seriously, is it not perfectly obvious from the full quote that the "they" refers to "two measurements, by two observers"?
Seriously, no, it is not. In fact, your posts on this thread, in entirety, have not been "perfectly obvious" at all.

1) acceleration
2) non-accelerated "motion"
3) deacceleration/reacceleration
4) non-accelerated "motion"
5) deacceleration

Is it your assertion that Bob ends up younger than Alice because of physical effects of segments 1, 3, and 5?

Solely, primarily, or partially?

Do you agree or disagree that there are any contributing physical effects of segments 2 and 4 at all?

Ken G
2008-Nov-21, 04:11 PM
Seriously, no, it is not. In fact, your posts on this thread, in entirety, have not been "perfectly obvious" at all.
Well, I wager that the lurkers had no trouble understanding what the two sentences I quoted above meant, and neither did you-- as your "corrected grammar" clearly demonstrated. How can you correct the grammar and at the same time claim you didn't understand what I meant? Bizarre.

1) acceleration
2) non-accelerated "motion"
3) deacceleration/reacceleration
4) non-accelerated "motion"
5) deacceleration

Is it your assertion that Bob ends up younger than Alice because of physical effects of segments 1, 3, and 5?As I thought I said above, also quite clearly, you cannot associate physical meaning to when the acceleration had its "physical effect" on the elapsed time (which is what I presume you are doing when you use the term de-acceleration), it depends on how you are coordinatizing things-- except for the obvious statement that acceleration that extends for zero time is no acceleration at all. The physical statement is this: the proper time (measured time by an observer) elapsed between two events depends on the spacetime path taken by that observer. End of story, that's the physics. You can calculate the answer in various coordinatizations, and each coordinatization affords you with a different interpretation of what happened and when it happened, but answers to those questions are not physical invariants-- neither solely, primarily, nor partially.

SeanF
2008-Nov-21, 04:59 PM
Well, I wager that the lurkers had no trouble understanding what the two sentences I quoted above meant, and neither did you-- as your "corrected grammar" clearly demonstrated. How can you correct the grammar and at the same time claim you didn't understand what I meant? Bizarre.
The first time I read that post, I read what you wrote. So did hhEb09'1. When he referred to what you wrote, and you basically said,
"I've never written that, only this," I went back and reread it, to see if I misread it the first time.

I didn't. You did, in fact, write what hhEb09'1 and I thought you wrote. But, since the second time I had knowledge not only of what you wrote but also what you meant to write, I could see (and point out) the difference between what you wrote and what you meant.

Not bizarre at all. Happens all the time, to me, too. :)

As I thought I said above, also quite clearly, you cannot associate physical meaning to when the acceleration had its "physical effect" on the elapsed time (which is what I presume you are doing when you use the term de-acceleration)
I probably should've just used the word "acceleration" in all four segments, since it's "acceleration" whether you're "speeding up" or "slowing down" (see, sometimes I don't exactly write what I mean, either).

At any rate, no, I'm not asking nor wondering about "when" the effect happened, merely "what" caused it. Did segments 2 and 4 cause any physical effect at all?

Ken G
2008-Nov-21, 05:19 PM
Not bizarre at all. Happens all the time, to me, too. Well, I hope the situation is clear enough now, that's all that really matters. I suppose I cannot hold you responsible to correctly interpret what I'm saying, but if you do that, you will find that it is all perfectly consistent, and indeed it says something important about relativity-- and empirical science. That is what we are trying to get at here, and yes, your paraphrase is exactly the point I intended to convey.

At any rate, no, I'm not asking nor wondering about "when" the effect happened, merely "what" caused it. Did segments 2 and 4 cause any physical effect at all?Everything that participates in determining the path taken by the observer between the two events participates in how long it takes to get there. If you walk a mile east, and a mile north, instead of 1.4 miles northeast, then why did you cover 2 miles instead of 1.4? Was it the walking east, the walking north, or the left turn that is responsible for the difference?

SeanF
2008-Nov-21, 07:33 PM
Everything that participates in determining the path taken by the observer between the two events participates in how long it takes to get there. If you walk a mile east, and a mile north, instead of 1.4 miles northeast, then why did you cover 2 miles instead of 1.4? Was it the walking east, the walking north, or the left turn that is responsible for the difference?
The walking east and the walking north. After all, if you have one person walking east and a separate person walking north who simply pass each other at the appropriate point, you still get two miles total - one east, and one north. You neither gain nor lose any distance in the physical act of turning.

:)

Ken G
2008-Nov-21, 08:55 PM
The walking east and the walking north.By saying those, you would seem to have intentionally left out the "turning left" step. So you will now have to explain to me how you can walk east, and north, without turning left. I, on the other hand, would say the turning left is the crucial fact that allowed you to walk east and north in the same walk. I believe we have come to the very heart of the issue here, all the A-B-C debate comes right down to this.

After all, if you have one person walking east and a separate person walking north who simply pass each other at the appropriate point, you still get two miles total - one east, and one north. Certainly-- but it's just a number, it doesn't mean squat. Specifically, it is not a measurement, in the same sense of the term in my sidebar with hhEb09'1 just above. I can get all kinds of numbers by adding distances of all kinds of things-- we are talking about the reason why two paths taken by two travellers connecting the same two points can require a different distance (that is the precise analog of the "twin strangeness" here). There is no possible way you can get that if you force travellers to walk in straight lines. I would without hesitation state that the ability to turn is the exact physical reason why two different travellers can cover two different distances between the same two points-- in exact analogy with the crucial role of acceleration in the twin problem.

You neither gain nor lose any distance in the physical act of turning.
Of course not-- but you make the non-straight path possible in the first place, which is precisely the crucial role of acceleration in the twin paradox. Indeed, the analogy is extremely close: I could equally say there is a "walking time paradox", whereby two walkers, walking at exactly the same speed, can take two different times to walk between the same two points. Indeed, each can think the other is "falling behind them", in some arbitrary coordinatization (such as extending their arms outward to each side and noting how the other walker falls behind the indicated line). It is the turning that allows the difference-- one who turns will always take longer to get there than one who does not turn, and just "when" they fell behind is not a physically invariant truth of the situation, because the turner (with his arms out sideways) could say "I was ahead of you before I turned, and I caught up on you after I turned, but I just lost so much distance in the turning that I was not able to make it up". The analogy is virtually exact, except the turner takes more time not less. You would apparently say he will "neither gain nor lose any distance in the physical act of turning", but to him, in arm-coordinates, that was exactly the crucial moment when he lost the race (imagine, for example, the "walkers" are in empty space with no other points of reference but their own arms). It's all a question of coordinates-- explanations are not unique, but the need for turning is.

dhd40
2008-Nov-21, 09:14 PM
Which brings us to the lesson you are so far not getting-- even an accelerated observer "considers himself to be at rest".

I´m surprised. I always thought that it is acceleration (not speed/velocity) which tells you that you´re not at rest.:confused:

SeanF
2008-Nov-21, 09:30 PM
The walking east and the walking north.
By saying those, you would seem to have intentionally left out the "turning left" step.
You did not ask me to list all the steps in following the path. You asked me, "why did you cover 2 miles instead of 1.4?" or, to paraphrase, "Why are the two paths different lengths?"

And the path is independent of the observer following the path. Whether one person walks both legs of the path or a different person walks each leg, the path is the same.

It's all a question of coordinates-- explanations are not unique, but the need for turning is.
But, unless there's been another miscommunication, your entire basis for rejecting A-B-C and insisting on acceleration has been that A-B-C is merely coordinization whereas acceleration produces a real, physical effect. But now it appears that that "real physical effect" is nothing but a change in coordinization (am I spelling that word right?). What the A-B-C scenario allows us to do is have that coordinization change without actually accelerating an observer. But the effect - the change in coordinization - is exactly the same.

m74z00219
2008-Nov-21, 09:54 PM
The twin paradox, of course, is really not a paradox at all. It can easily be resolved using the lorentz transformations properly.

The key point is frame changing. Imagine a rocket ship passes by the earth and at that instance they synch their clocks... so t' = t = 0.

If the rocket ship is flying by at a constant velocity from the earth (and never slows to stop), then the clock ticking on the spaceship will indeed tick slower relative to the clocks on earth. At the same time though, the clocks on earth will tick slower relative to the spaceship.

When the space ship stops at its destination the problem is no longer symmetrical. It is the spaceship that is changing frames. Relative to the space ship, it is during the time in which it changes frames that the earth's clocks will rapidly tick faster such as to make it older relative to the spaceship.

Hope this helps.

mugaliens
2008-Nov-21, 10:08 PM
Was it the walking east, the walking north, or the left turn that is responsible for the difference?

It's the vector summation of each mile walked that transforms 2 miles walked into 1.41 miles distance since the last point.

Naturally, this depends on where you are, however. If you begin this journey 1 mile south of the north pole, you'll travel two miles and wind up just one mile from your initial position. ;)

Ken G
2008-Nov-21, 10:11 PM
I´m surprised. I always thought that it is acceleration (not speed/velocity) which tells you that you´re not at rest.It depends on what you think of as "at rest". If you have lived your entire existence in the presence of a certain acceleration (which, by the way, you have), then it would be perfectly natural for you to consider to be at rest everything that also has that same acceleration (which, by the way, you do).

Ken G
2008-Nov-21, 10:32 PM
And the path is independent of the observer following the path. Whether one person walks both legs of the path or a different person walks each leg, the path is the same.I think we can summarize what we've learned, as this analogy is so close to the twin paradox and yet so much more clear. We can both agree that two different paths will give different lengths, and we can also agree that the key difference in the paths are their straightness versus jaggedness. I further point out that the whole reason a path can be jagged is because a walker can turn, and you are saying that multiple walkers could successfully combine their measurements into a calculation of the length of such a path without any of them actually turning. Nevertheless, the key issue is the jaggedness of the path, and jaggedness is about the turning of the path. In the analogy, turning maps into acceleration if one is talking about a single person following the path, and the twin paradox is about a twin following a path. Ergo, the twin paradox is about the acceleration of the twins, just as the length of a path is about how it turns.

But, unless there's been another miscommunication, your entire basis for rejecting A-B-C and insisting on acceleration has been that A-B-C is merely coordinization whereas acceleration produces a real, physical effect. That's not how I put it, my objection to the A-B-C explanation is that it is simply not the twin paradox, it is nothing more than an unnecessary mathematical check of an elementary consequence of the structure of special relativity, that all inertial frames make the same calculations for elapsed times along a given path. The crucial new element of the twin paradox is expressly that you have a single observer, who thinks he/she can apply the same instructions for measuring time as their symmetric twin, yet not get a symmetric result.

So the nontrivial question is, what breaks the symmetry? The answer is, acceleration. This is exactly analogous to asking, what breaks the symmetry in the lengths of various paths that connect two points, and the answer is, jaggedness. To miss that is to miss something geometrically important about paths, which we all learn as babies-- walk the straight line.

But now it appears that that "real physical effect" is nothing but a change in coordinization.Heavens no, the whole point is that no "physical effects" are ever dependent on a coordinatization. That's what "covariance" means. I brought in the coordinatization to show the error in attributing physical significance to it.

SeanF
2008-Nov-22, 05:24 AM
The crucial new element of the twin paradox is expressly that you have a single observer, who thinks he/she can apply the same instructions for measuring time as their symmetric twin, yet not get a symmetric result.
Why would he think that?

01101001
2008-Nov-22, 06:03 AM
Why would he think that?

'Cause the observer didn't read this topic and is overlooking something.

Ken G
2008-Nov-22, 02:46 PM
Why would he think that?
That isn't the question, the question is, why shouldn't he? Well? The answer is the whole point of the "twin lesson."

SeanF
2008-Nov-22, 08:04 PM
That isn't the question, the question is, why shouldn't he?
No, the question is, why would he? Special Relativity doesn't predict symmetry there.

dhd40
2008-Nov-22, 08:13 PM
It depends on what you think of as "at rest". If you have lived your entire existence in the presence of a certain acceleration (which, by the way, you have), then it would be perfectly natural for you to consider to be at rest everything that also has that same acceleration (which, by the way, you do).

(Hopefully, this is not too much off-topic)
How I see it: I was born in an Earth-centered, rotating frame. And right now, I´m sitting on my chair in front of my PC. I´m still in the same Earth-centered, rotating frame. I can´t "see" any acceleration (dv/dt), unless I start to move, of course. Everything around me has the same velocity v=0, the floor, the ceiling, the walls, .... in my frame. Which acceleration am I experiencing, sitting on my chair?

Where´s the error in my reasoning?

Ken G
2008-Nov-22, 08:33 PM
No, the question is, why would he? Special Relativity doesn't predict symmetry there.And why do you claim that? Could it be that the symmetry is broken by proper acceleration? Yes, I think so-- that is precisely what I have been saying all along, and what DrRocket said on page 3.

ETA: we were making progress a moment ago. What we established is that acceleration breaks the symmetry of two observers, and allows a different time to be elapsed between two common events for those observers, in almost exactly the same way that a walker who turns will cover a different distance than a walker who takes a straight path. In other words, the answer to why two walkers can cover a different distance is, "the walker can turn", and the answer to the twin paradox is, "the observer can accelerate".

Ken G
2008-Nov-22, 08:39 PM
Which acceleration am I experiencing, sitting on my chair?
Where´s the error in my reasoning?I don't think there is any error-- I brought up the acceleration you are experiencing, but not noticing, precisely to show the importance of an arbitrary coordinate system. Special relativity picks out inertial observers, but this is an arbitrary choice that is not even consistent with the coordinates we all use every day. One could build a theory exactly like special relativity based on a particular accelerated frame, instead of inertial frames, and one would get a different explanation for why everything happens-- but all the same measured invariants.

grav
2008-Nov-22, 09:46 PM
Are you guys tiring out? The posts don't seem quite so long anymore. Take an energy booster. :) Matter of fact, now that I think about it, I might need one too. :o Probably not a good idea, though.