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uncommonsense
2010-Mar-19, 06:53 PM
As I further self study relativity, I repeatedly wonder: "by what mechanism do clocks described in relativity slow". Not looking for another explanation of relativity, but an explanation of the physical characteristics that are caused by relativistic traits,i.e. the internal workings that describe in a mechanical sense why clocks slow. Furthermore, a physiological description of how a biological entity would age more slowely.
I do not accept that time has any inherrent attributes.Rather, tiome is simply a "report" of distance and motion. Therefore, to simply conclude that "clocks run slow because time slows" makes no sense to me. Anyone?

I suspect it does not matter, but TR is taught using examples of comparing clocks that slow as compared to others, so I am looking for the connection or disconnect as to whether it matters exactly how.

ShinAce
2010-Mar-19, 07:08 PM
For a clock to be measured running at half the rate of yours, then distances for that clock's world are also halved.

We love to think that a meter is a meter, but the truth is that the nearest star is only 4 light years away at slow travel speeds. Find a ship that can really zip and the odometer will read less for the same trip.

It's not time by itself that is changing, it's all measured quantities that are changing.

The question I always ask myself is "How does the universe make it so that the speed of light is always measured to be the same?" It makes me want to say "Who is coaxing light to trick me?".

uncommonsense
2010-Mar-19, 07:13 PM
For a clock to be measured running at half the rate of yours, then distances for that clock's world are also halved.

We love to think that a meter is a meter, but the truth is that the nearest star is only 4 light years away at slow travel speeds. Find a ship that can really zip and the odometer will read less for the same trip.

It's not time by itself that is changing, it's all measured quantities that are changing.

The question I always ask myself is "How does the universe make it so that the speed of light is always measured to be the same?" It makes me want to say "Who is coaxing light to trick me?".

Yes. But a clock is a 3 dimentional device, yet distance contraction occcures along only one of those 3 axis????

Argos
2010-Mar-19, 07:21 PM
[SIZE=2]As I further self study relativity, I repeatedly wonder: "by what mechanism do clocks described in relativity slow". Not looking for another explanation of relativity, but an explanation of the physical characteristics that are caused by relativistic traits,i.e. the internal workings that describe in a mechanical sense why clocks slow. Furthermore, a physiological description of how a biological entity would age more slowely.

Lets start by saying that Relativity has no bearing on the internal workings of clocks and organisms.

I do not accept that time has any inherrent attributes.Rather, tiome is simply a "report" of distance and motion.

That 'report' on the status of the motion must be coveyed by light. Light has a finite speed, and hereīs where relativity begins. Because light has a finite speed it takes some time to reach the observers. Depending on the position and motion of the observers they may not agree on the timing of the events. It is necessary to employ mathematical [geometric] transformations. It is in these mathematical transformations that time gets dilated.

Now lets wait for the other members to contribute, and let the fun begin. :)

Kwalish Kid
2010-Mar-19, 07:37 PM
Indeed, relativity theory is about what it means to say things about the times of things that are separated by distances.

uncommonsense
2010-Mar-19, 07:43 PM
So the twin thing - returning younger - is not accepted?

Argos
2010-Mar-19, 08:01 PM
So the twin thing - returning younger - is not accepted?

It is a real phenomenon. Maybe I havenīt made myself clear, but the geometric transformations I mentioned enable us to understand this real phenomenon. It is counter-intuitive, but it is real. The Universe is relativistic.

uncommonsense
2010-Mar-19, 08:19 PM
I am trying to understand the mechanics, if that's the right word. If a clock or twin returned age retarded, then, the rate of change of distance of the clock works or atoms of the twin s body were affected by the high speed motion. Otherewise the conclusion would be that the slowed age result was simply a result of the observations. That sounds more like quantum theory.

Am I way off base? To me, theory should have logical manifestations in the real world. If a clock returns from a near light speed trip with a slower time, then there was a physical, mechanical occurance that caused this. Thats what I am looking for.

Argos
2010-Mar-19, 08:35 PM
I am trying to understand the mechanics, if that's the right word. If a clock or twin returned age retarded, then, the rate of change of distance of the clock works or atoms of the twin s body were affected by the high speed motion.

In fact, if Bob sets out to travel near the speed of light, leaving Alice at home, upon return Bob will be younger, because the speed he traveled affected his path in relation to Aliceīs position [and Alice is able to calculate Bobīs status using the suitable geometric transformations of coordinates]. In their own positions [or 'frames'] they do not perceive any change.

uncommonsense
2010-Mar-19, 08:46 PM
In fact, if Bob sets out to travel near the speed of light, leaving Alice at home, upon return Bob will be younger, because the speed he traveled affected his path in relation to Aliceīs position [and Alice is able to calculate Bobīs status using the suitable geometric transformations of coordinates]. In their own positions [or 'frames'] they do not perceive any change.

Thank you, but that is an aspect of TR results, not an answer to how or why. Sure, whatever mechanical process is happening to Bob is happening to his entire frame, so of course he would not notice it.

But once he returns to Alice's frame, some mechanical explanations are begged. What are they. How did his path in relation to alice result in time dialation, mechanically? Because that is what we are left with. TR gives us accurate results, but what are the mechanical hows and whys.

ShinAce
2010-Mar-19, 08:51 PM
I am trying to understand the mechanics, if that's the right word. If a clock or twin returned age retarded, then, the rate of change of distance of the clock works or atoms of the twin s body were affected by the high speed motion. Otherewise the conclusion would be that the slowed age result was simply a result of the observations. That sounds more like quantum theory.

Am I way off base? To me, theory should have logical manifestations in the real world. If a clock returns from a near light speed trip with a slower time, then there was a physical, mechanical occurance that caused this. Thats what I am looking for.

Are you confused about why the shipbound person is younger even though relativity says they both have the right to claim they are at rest?

The resolution is simple. On the way out, they do in fact each think the other is going to be younger. But then when Bob turns around, this leaves a permanent effect on his measurements. If it weren't for the turnaround, BOTH Bob and Alice could claim the other's clock is running slow, and each would be right. For me, that's the real paradox. There is no universe where Alice is younger than her twin Bob AND Bob is younger than Alice. That is a coordinate(reference frame) issue.

edit: I'm slow today...but what is TR?

forrest noble
2010-Mar-19, 08:51 PM
uncommonsense,

As I further self study relativity, I repeatedly wonder: "by what mechanism do clocks described in relativity slow". Not looking for another explanation of relativity, but "physical characteristc" explanations that are caused by relativistic traits, i.e. the internal workings that describe in a mechanical sense why clocks slow. Furthermore, a physiological description of why a biological entity would age more slowly. I do not accept that time has any inherent attributes. Rather, time is simply a "report" of distance and motion. Therefore, to simply conclude that "clocks run slow because time slows" makes no sense to me. Anyone?

I suspect it does not matter, but TR is taught using examples of comparing clocks that slow as compared to others, so I am looking for the connection or disconnect as to whether it matters exactly how.

My recollection of reading such explanations involves the mechanics of an atom. Whatever the interpretation/ hypothesis concerning the actual mechanics of an atom as proposed today, the physical motion accordingly would slow in accord with the physics which describes it (SR/GR/LT)?. Describing the mechanics: Since relative motion would accordingly increase internal atomic velocities in the direction of the relative motion, limiting the fastest speeds within the atoms to the speed of light or to the same speeds that existed in its rest frame, would accordingly result in the atom's slowed rate of change and therefore the related passing of time from the perspective within that time frame. Such examples would be the physical rotation of the nucleus of atoms or the physical orbital rotation of electrons or whatever the process actually is; controlling the fastest speeds to a constant (regardless of the the frames relative motion) would influence the rate of all the other internal related motions because of the interactions between atomic factions.

Simply put, from the perspective of an outside observer, time progression of the processes within the effected atoms would accordingly move at a slower rate than those atoms/ molecules outside strong gravitational influences and without relative motion to the controlling gravitational source(s). This of course would accordingly explain why clocks and biology would progress more slowly time wise. Whether this is presently the preferred explanation I do not know.

If one is fond of preferred reference frames just for the sake that all time dilation would extend time and not be negative numbers, then your chosen reference frame would be the one with the fastest progression of time relative to all others within the same primary gravitational field such as the orbital distance of about 100 to maybe 30,000 miles above the Earth, for instance, with little if any orbital or escape velocity.

http://www.statemaster.com/encyclopedia/Time-dilation

Argos
2010-Mar-19, 08:56 PM
But once he returns to Alice's frame, some mechanical explanations are begged. What are they. How did his path in relation to alice result in time dialation, mechanically? Because that is what we are left with. TR gives us accurate results, but what are the mechanical hows and whys.

I think the word that defines relativity is Dynamics and not Mechanics. Thereīs no mechanical transformation involved. The transformations derive from the dynamics.

Check out this wiki (http://en.wikipedia.org/wiki/Special_relativity#References) about SR, and take a look at the graphs. They may clear out some aspects. We can continue later.

WaxRubiks
2010-Mar-19, 09:13 PM

well that's how I see it.....matter as a bunch of information traveling at c, back and forth.

Digix
2010-Mar-19, 09:16 PM
As I further self study relativity, I repeatedly wonder: "by what mechanism do clocks described in relativity slow". Not looking for another explanation of relativity, but an explanation of the physical characteristics that are caused by relativistic traits,i.e. the internal workings that describe in a mechanical sense why clocks slow. Furthermore, a physiological description of how a biological entity would age more slowely.
I do not accept that time has any inherrent attributes.Rather, tiome is simply a "report" of distance and motion. Therefore, to simply conclude that "clocks run slow because time slows" makes no sense to me. Anyone?

I suspect it does not matter, but TR is taught using examples of comparing clocks that slow as compared to others, so I am looking for the connection or disconnect as to whether it matters exactly how.

Not sure if that is not ATM(everything is supposed to be same as mainstream), but mechanical reason will be, that clock parts get additional mass.

Assume that you have spring and ball that system oscillates, if ball becomes heavier, your clock become slower.

Once you accelerate something that object gains mass proportional to its kinetic energy, so it appears that mass is also relative.
But to avoid that GR chooses to mangle space-time instead of readjusting mass-energy of every object and recalculating every clock.

I would like to remap all GR into mass-energy instead of space-time since this it more intuitive if we keep space time absolute and change everything else instead.

Argos
2010-Mar-19, 09:43 PM
Not sure if that is not ATM(everything is supposed to be same as mainstream), but mechanical reason will be, that clock parts get additional mass.

I donīt think it is useful to introduce these concepts [namely Relativistic Mass] at this point. It can only distract uncommonsense, and weīd be doing him a disservice. As I said, thereīs no mechanical alteration or transformation when bodies travel close to c.

uncommonsense
2010-Mar-19, 09:49 PM
I am digesting. It's all so beuatiful and elegant. Yes, I am a dork.

Strange
2010-Mar-19, 09:49 PM
I don't think you can think of it in mechanical terms because it is real effect on time, not the clock. The same time dialtion effect is seen in things like the decay rates of fundamental particles which have no "mechanics" involved.

geonuc
2010-Mar-19, 09:52 PM
edit: I'm slow today...but what is TR?
I believe the OP is using TR to stand for the Theory of Relativity.

cjl
2010-Mar-19, 09:54 PM
Not sure if that is not ATM(everything is supposed to be same as mainstream), but mechanical reason will be, that clock parts get additional mass.

Assume that you have spring and ball that system oscillates, if ball becomes heavier, your clock become slower.

Once you accelerate something that object gains mass proportional to its kinetic energy, so it appears that mass is also relative.
But to avoid that GR chooses to mangle space-time instead of readjusting mass-energy of every object and recalculating every clock.

I would like to remap all GR into mass-energy instead of space-time since this it more intuitive if we keep space time absolute and change everything else instead.
Not really. In the object's rest frame, it will gain no mass, despite the high relativistic velocity relative to some other frame. Therefore, as viewed from the object, the period will be the same. In addition, completely mass-independent processes slow down at exactly the same rate as mass-dependent processes, which makes this explanation misleading at best.

uncommonsense
2010-Mar-19, 09:59 PM
I don't think you can think of it in mechanical terms because it is real effect on time, not the clock. The same time dialtion effect is seen in things like the decay rates of fundamental particles which have no "mechanics" involved.

But time is a man made unit to measure a rate of distance and motion and therefore those parameters are the ones that are relative.

uncommonsense
2010-Mar-19, 10:00 PM
I believe the OP is using TR to stand for the Theory of Relativity.

Correct

DrRocket
2010-Mar-19, 10:01 PM
Lets start by saying that Relativity has no bearing on the internal workings of clocks and organisms.

I think I know what you mean, but I disagree with this characterization.

Relativity does indeed govern the behavior of clocks, organisms n(rate of cell division for instance) and even the decay of elementary particles. The dynamics involved follow relativistic dynamics.

What is true is that the difference in time intervals measured by two clocks (atomic, battery-powered, or wind-up) is not due to some change in the internal configuration or design principles of the devices, but due to the fact that time itself is an observer-dependent quantity.

Relativity is at the most fundamental level a revolutionary theory of the very nature of space and time. Indeed, it tells us that there the issue is not space and time at all. There is really no such thing as time and no such thing as space but only spacetime. Space and time are observer-dependent artifacts of coordinate systems.

We get confused by our language which was developed to describe a Newtonian perception of the world.

Digix
2010-Mar-19, 10:37 PM
I donīt think it is useful to introduce these concepts [namely Relativistic Mass] at this point. It can only distract uncommonsense, and weīd be doing him a disservice. As I said, thereīs no mechanical alteration or transformation when bodies travel close to c.
Problem with usual explanation is that it is purely mathematical representation without any material reasoning. it is impossible to understand why space or time is contracting if we have no material and imaginable representation of space and time you cannot imagine space or time. so if we replace world "time" with "clock" and space with some reference cube it becomes much simpler.

Not really. In the object's rest frame, it will gain no mass, despite the high relativistic velocity relative to some other frame. Therefore, as viewed from the object, the period will be the same. In addition, completely mass-independent processes slow down at exactly the same rate as mass-dependent processes, which makes this explanation misleading at best.

That is why i said that mass itself can be viewed as relative value.
just instead of time dilation we can recalculate everything to mass increase.

And it does not matter if clock is pendulum based or particle decay. since we can assume that particles have also some oscillations too.
I think that is only way to imagine all reactivity process mechanically.

01101001
2010-Mar-20, 01:58 AM
Just think of some of those nice circular clock gears becoming ellipsoids with speed.

Small wonder the clock runs slow!

(No. As a matter of fact I am not serious.)

Jeff Root
2010-Mar-20, 02:21 AM
I'd say that time dilation and length contraction are physical, but not
mechanical. Instead, they are geometric. It isn't possible to have time
dilation without length contraction, and it isn't possible to have length
contraction without time dilation. They are two different aspects of the
same phenomenon: Geometric distortion of spacetime.

One clock undergoes time dilation and length contraction relative to
another clock when it is accelerated so that it has a different speed for
a while. In order to compare the two clocks it is necessary to accelerate
the first clock a second time, to bring it back to the unaccelerated clock.

I look up and see the tip of the antenna on the Empire State Building.
It is at an angle of 50 degrees up from the horizontal. My friend, talking
with me on his cell phone, says that he, too, is looking up at the tip of the
Empire State Building's antenna, but that it is at an angle of 70 degrees up
from the horizontal. The difference between what I see and what he sees
is not a change in the Empire State Building, nor is it a difference between
he and I, but it is a difference between my geometric relationship with the
ESB and his geometric relationship with the ESB. Different measurements
of time due to time dilation works very similarly.

-- Jeff, in Minneapolis

Jeff Root
2010-Mar-20, 02:35 AM
Time is a dimension, or quantity, rather than a unit. Just as length is a
dimension or quantity. Or mass, or electric charge, or temperature. Time
is no more manmade than are length, mass, electric charge, or temperature.
They all equally exist whether anyone is around to know it or not.

-- Jeff, in Minneapolis

Ken G
2010-Mar-20, 05:49 AM
[SIZE=2]As I further self study relativity, I repeatedly wonder: "by what mechanism do clocks described in relativity slow".

A good example of how that works is called a "light clock", which is two mirrors with a rigid rod fixing the (local) distance between them, and a beam of light bouncing back and forth ("ticking") between them. This device can tell you everything that relativity does with time, as long as you avow that it is indeed a good clock, and use the postulates of relativity about the speed of light being (locally) the same in all frames. Such a device can be used to derive time dilation, and you can use it to answer the OP-- it's a mechanism by which a moving clock appears to tick slowly, given the symmetry principle that says if such clocks in arbitrary motion look and function the same for an observer moving with said clock.

Argos
2010-Mar-20, 02:58 PM
Argos said: Lets start by saying that Relativity has no bearing on the internal workings of clocks and organisms.

DrRocket replied: I think I know what you mean, but I disagree with this characterization. Relativity does indeed govern the behavior of clocks, organisms n(rate of cell division for instance) and even the decay of elementary particles. The dynamics involved follow relativistic dynamics.

I was trying to keep the explanation simple. Of course Relativity governs the most basic aspects of reality, l but was trying to deal with more basic misconceptions.

uncommonsense
2010-Mar-22, 03:40 AM
Thank you for the replies but I am still confused because:

- math does not act upon matter and so it can not slow a clock or cause a person to age more slowly.

-By way of analogy, if you expose one twin to massive radiation, then later compare changes in that twin's body to the other twin, the results are not a "dynamic", they are physical, the cause was physical or "mechanical".

- I cannot use the workings of a light clock to understand the slowing of other types of clocks nor the slowing of biological process.

Bottom line is at the end of classic twins example, the body of one is younger, and his/her wrist watch (not a light clock) has a different time. Math did not cause this - unless it was a result of quantum math in that all states of existance are probabilities and traveling at near light speed increases probability of returning home in an age retarded condition - but that's not TR and it's certainly not what a am suggesting. I want to know how TR explains it.

Whatever the cause, it effects every thing, not just light clocks - but all particles, or atoms, or elements. Don't all elements have to maintain certain characteristics in order to remain that element? What adjustments are required to maintain it's physical state when the element is accellerated? Do the various forms of energy of the element require redistribution? Am I an idiot?

uncommonsense
2010-Mar-22, 05:18 AM
I'd say that time dilation and length contraction are physical, but not
mechanical. Instead, they are geometric. It isn't possible to have time
dilation without length contraction, and it isn't possible to have length
contraction without time dilation. They are two different aspects of the
same phenomenon: Geometric distortion of spacetime.

One clock undergoes time dilation and length contraction relative to
another clock when it is accelerated so that it has a different speed for
a while. In order to compare the two clocks it is necessary to accelerate
the first clock a second time, to bring it back to the unaccelerated clock.

I look up and see the tip of the antenna on the Empire State Building.
It is at an angle of 50 degrees up from the horizontal. My friend, talking
with me on his cell phone, says that he, too, is looking up at the tip of the
Empire State Building's antenna, but that it is at an angle of 70 degrees up
from the horizontal. The difference between what I see and what he sees
is not a change in the Empire State Building, nor is it a difference between
he and I, but it is a difference between my geometric relationship with the
ESB and his geometric relationship with the ESB. Different measurements
of time due to time dilation works very similarly.

-- Jeff, in Minneapolis

Jeff,

I feel I must humbly suggest that this answer is a non-answer to my querry. I understand time is simply a ratio, and leangth is a parameter thereof.

Further, my feeble mind cannot find any meaning in comparing the two returned twins in the classic example to the antenna in your example. What have I missed? It wouldn't be the first time I have been confused.

Celestial Mechanic
2010-Mar-22, 05:22 AM
Thank you for the replies but I am still confused because: {Snip!}

Whatever the cause, it effects every thing, not just light clocks -- but all particles, or atoms, or elements. Don't all elements have to maintain certain characteristics in order to remain that element? What adjustments are required to maintain its physical state when the element is accelerated? Do the various forms of energy of the element require redistribution?
Please read the dialog I wrote here (http://www.bautforum.com/science-technology/40149-relativistic-ramblings.html#post718941) entitled "Relativistic Ramblings, Part Two -- There is Nothing Wrong With Your Clock". In essence all properly constructed clocks measure what is called "proper time" and if two clocks are later compared and found to differ it is because they have experienced and measured different amounts of proper time.

Am I an idiot?
No. A lot of people have had problems understanding Special Relativity over the last century, even people like Dingle mentioned in the link above, who actually wrote a book on SR before turning against it.

loglo
2010-Mar-22, 05:48 AM
Uncommonsense,
Your question, at its heart, assumes a preferred reference frame. The physical effect is caused by the twins/clocks travelling different paths through spacetime.

uncommonsense
2010-Mar-22, 08:14 AM
Uncommonsense,
Your question, at its heart, assumes a preferred reference frame. The physical effect is caused by the twins/clocks travelling different paths through spacetime.

Strange
2010-Mar-22, 09:01 AM
But time is a man made unit to measure a rate of distance and motion and therefore those parameters are the ones that are relative.

I'm not quite sure I underestand this. You seem to be saying that it is not the particle decay rate that changes but just what we measure? Is that different? If particles of a given type take a known time to decay at rest, but at near light speed take significantly longer, then it is reasonable to deduce that time is passing slower for those particles.

uncommonsense
2010-Mar-22, 09:20 AM
I'm not quite sure I underestand this. You seem to be saying that it is not the particle decay rate that changes but just what we measure? Is that different? If particles of a given type take a known time to decay at rest, but at near light speed take significantly longer, then it is reasonable to deduce that time is passing slower for those particles.

Well, start by considering just what is an hour - an hour is NOTHING more than the standardized syncronization of the earth's rotation and a machine / device, (clock), 24 of which represent one full rotation of the earth. So when a clock MOVES 1 hour, the earth MOVES 1/24 rotation.

Time is simply a comparison of motion of different objects. Thats it.

So, to say time slowed, is really saying motion of one thing changed in relation to another thing. That's it.

To say time slows is actually saying motion or distance decreased. It's that simple.

Strange
2010-Mar-22, 09:27 AM
- math does not act upon matter and so it can not slow a clock or cause a person to age more slowly.

True. Math simply describes (more accurately than words) what happens.

- I cannot use the workings of a light clock to understand the slowing of other types of clocks nor the slowing of biological process.

Why not? How is that different? What about atomic clocks, which have been used to make very precise measurements of the effects of relativity? They are not mechanical" in the sense they have no moving parts.

I want to know how TR explains it.

One analogy is that when you travel through spacetime, if you move in a "space" dimension then you are not moving as fast through the time dimension.

Whatever the cause, it effects every thing, not just light clocks - but all particles, or atoms, or elements.

Doesn't that contradict what you said earlier about light clocks and mechanical clocks being different? The important point is that it does affect everything - it isn't that the mechanics of the clock are slowed, it is time (which the clock is measuring) that is slowed.

Am I an idiot?

I think the fact that you are asking the questions demonstrates you are not an idiot. On the other hand, the fact you are struggling with the answers ... just kidding ;) ... I don't understand all of this myself (and certainly don't understand all the math behind it).

uncommonsense
2010-Mar-22, 09:38 AM
"Why not? How is that different? What about atomic clocks, which have been used to make very precise measurements of the effects of relativity? They are not mechanical" in the sense they have no moving parts."

I guess I'm hung up on leangth contraction only occures in diection of travel, so in one dimention. So if "slowing" of clock is tied to leangth contraction, then the clock would need to be juxtaposed accordingly in order to be slowed - but TR does not demand this condition.

Strange
2010-Mar-22, 09:55 AM
Well, start by considering just what is an hour - an hour is NOTHING more than the standardized syncronization of the earth's rotation and a machine / device, (clock), 24 of which represent one full rotation of the earth. So when a clock MOVES 1 hour, the earth MOVES 1/24 rotation.

But the way the second is defined involves no moving parts.

Time is simply a comparison of motion of different objects. Thats it.

So, to say time slowed, is really saying motion of one thing changed in relation to another thing. That's it.

To say time slows is actually saying motion or distance decreased. It's that simple.

And in the case of particle decay, there are no moving parts.

uncommonsense
2010-Mar-22, 10:33 AM
But the way the second is defined involves no moving parts.

Huh? Every unit of time we use is related to the MOTION of the earth. A minute is 1/60 of hour and a second is 1/60 of a minute.

And in the case of particle decay, there are no moving parts.

There are no continuously moving parts. When the particle decays does it move, or vanish into thin air? It moves. Matter cannot be created or destroyed. The clock moves reporting the 'TIME' that occures up to the moment of decay. When the clock measures the 'non-decay' Period, it is measuring motion (or lack there of), same thing.

Strange
2010-Mar-22, 10:47 AM
Huh? Every unit of time we use is related to the MOTION of the earth. A minute is 1/60 of hour and a second is 1/60 of a minute.

The second is defined as 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.

There are no continuously moving parts. When the particle decays does it move, or vanish into thin air? It moves. Matter cannot be created or destroyed. The clock moves reporting the 'TIME' that occures up to the moment of decay. When the clock measures the 'non-decay' Period, it is measuring motion (or lack there of), same thing.

In the period before the particle decays there is no change, no motion. Yet that period changes when the particle is travelling at speed. So there is no "mechanics" involved.

Strange
2010-Mar-22, 10:48 AM
I guess I'm hung up on leangth contraction only occures in diection of travel, so in one dimention. So if "slowing" of clock is tied to leangth contraction, then the clock would need to be juxtaposed accordingly in order to be slowed - but TR does not demand this condition.

There is no direct connection between length contraction and time: one doesn't cause the other. They are both effects of relativistic motion.

dhd40
2010-Mar-22, 10:52 AM
I'd say that time dilation and length contraction are physical, but not
mechanical. Instead, they are geometric. It isn't possible to have time
dilation without length contraction, and it isn't possible to have length
contraction without time dilation.

Then, why do the twins see a "real and permanent" time difference (after return of the travelling twin) BUT no "real and permanent" length difference?

I look up and see the tip of the antenna on the Empire State Building.
It is at an angle of 50 degrees up from the horizontal. My friend, talking
with me on his cell phone, says that he, too, is looking up at the tip of the
Empire State Building's antenna, but that it is at an angle of 70 degrees up
from the horizontal. The difference between what I see and what he sees
is not a change in the Empire State Building, nor is it a difference between
he and I, but it is a difference between my geometric relationship with the
ESB and his geometric relationship with the ESB. Different measurements
of time due to time dilation works very similarly.

-- Jeff, in Minneapolis

(my bold)I don't think so. When your friend comes to your place, you will, both, agree on the same angle. Very different from the twin's time dilation situation

dhd40
2010-Mar-22, 11:03 AM
If particles of a given type take a known time to decay at rest, but at near light speed take significantly longer, then it is reasonable to deduce that time is passing slower for those particles.

Isn't any particle (with non-zero mass) travelling at v=const always at rest in it's own frame? And it's always slow by 300000 km/s as compared to c, no matter how fast it goes. Therefore, why should it live longer? I know, I know, this has been measured thousands of times.
But then it really boils down to uncommonsense's question. Something "inside" the particle must have happend during its acceleration phase.

uncommonsense
2010-Mar-22, 11:08 AM
There is no direct connection between length contraction and time: one doesn't cause the other. They are both effects of relativistic motion.

I am not interested in debating this. Just ask yourself if all motion in the universe stopped would time stop? Or is there an independent notion of time that does not depend upon motion of something? Thats all. Any way, we are off point. Thanx for your input Jeff.

uncommonsense
2010-Mar-22, 11:19 AM
There is no direct connection between length contraction and time: one doesn't cause the other. They are both effects of relativistic motion.

Now we are getting to it. Please explain how time dilation can occure w/out distance distortion. These are the ideas I am seeking.

Thank you.

Strange
2010-Mar-22, 11:24 AM
Something "inside" the particle must have happend during its acceleration phase.

In the case of something like a muon, there is nothing "inside" the particle.

I have a horrible sense of deja-vu and impending doom so we should probably drop this and stick to uncommonsense's questions...

Strange
2010-Mar-22, 11:26 AM
Isn't any particle (with non-zero mass) travelling at v=const always at rest in it's own frame? And it's always slow by 300000 km/s as compared to c, no matter how fast it goes. Therefore, why should it live longer? I know, I know, this has been measured thousands of times.

It is at rest in its own frame. In it's own frame it doesn't live any longer. Which, I suppose, is another argument against the "mechanical" explanation for time dilation.

loglo
2010-Mar-24, 01:42 PM

Assuming that there is one unique velocity for an object in motion is assuming a preferred reference frame.

speedfreek
2010-Mar-24, 08:38 PM
Then, why do the twins see a "real and permanent" time difference (after return of the travelling twin) BUT no "real and permanent" length difference?

If your twin is half their original length while they are away, but is restored to their original length when they get home, how can you tell?

dhd40
2010-Mar-25, 05:16 PM
If your twin is half their original length while they are away, but is restored to their original length when they get home, how can you tell?

Sorry, I'm afraid I don't understand what you mean.
What I wanted to say was that time dilation is something which shows up, can be measured, in our "reality". But I've never seen a measurement of length contraction.
Time dilation isn't restored when the clock gets home. Therefore, as commonsense said, something physical must have happend to the clock's hands (or atoms, or...). What is it?

Strange
2010-Mar-25, 05:47 PM
something physical must have happend to the clock's hands (or atoms, or...). What is it?

It was accelerated. I wonder if the difference between time and length in this case, is related to the fact you can move around in space dimensions but not time?

macaw
2010-Mar-25, 06:06 PM
Then, why do the twins see a "real and permanent" time difference (after return of the travelling twin) BUT no "real and permanent" length difference?

Very well put. Experiment confirms the above (see Haefele-Keating and its more recent reenactments).

macaw
2010-Mar-25, 06:22 PM
It was accelerated.

No, this is not a good explanation. Though many websites explain it through acceleration, the real reason is the difference in terms of respective paths through spacetime.
It all starts with the invariance of the Lorentz interval:

(cdt)^2-(dx^2+dy^2+dz^2)=(cdt')^2-(dx'^2+dy'^2+dz'^2)

Now, the clock that corresponds to the lowest dx'^2+dy'^2+dz'^2 (i.e. 0), will show the least elapsed time:

(cd\tau)^2=(cdt)^2-(dx^2+dy^2+dz^2)=(cdt)^2(1-v^2/c^2)

where v is the speed of primed clock as measured wrt the unprimed frame.

So:

d\tau=dt*sqrt(1-(v/c)^2)

So, if , from the POV of the unprimed frame, the clock in te primed frame takes a trip of time length T, then, the elapsed time on the primed clock is:

\tau=Integral_0_to_T (dt*sqrt(1-(v/c)^2))

If v=constant, then

\tau=T*sqrt(1-(v/c)^2) <T (the "travelling" clock shows less elapsed time).

If v=v(t), the result is the same, since the integrand sqrt(1-(v(t)/c)^2)<1.

The effect is real and happens independently of any acceleration. The fact that in order to compare the two clocks, one needs to return to the departing point is purely incidental, so the acceleration involved in "turning around" is purely incidental, has no effect on the behavior of the clock.
The fact that clock rate is insensitive to acceleration has been verified experimentally (http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html#Clock_Hypothesis) to a very high precision.

I wonder if the difference between time and length in this case, is related to the fact you can move around in space dimensions but not time?

Length contraction has not been verified yet only because of the enormous experimental difficulties. There is work in progress that will circumvent such difficulties in the next few years. Technological advancements in measurement are going to take care of this.

macaw
2010-Mar-25, 06:26 PM
[SIZE=2]As I further self study relativity, I repeatedly wonder: "by what mechanism do clocks described in relativity slow".

They don't. SR does not claim such a thing.
GR is a different type of animal, clocks deeper in a gravity well tick differetly than ones higher up. This is a direct prediction of Einstein's Field equations.A quick application of Schwarzschild solution produces the result:

dt_bottom/dt_top=sqrt((1-r_s/r_bottom)/(1-r_s/r_top))

t is the coordinate time

ShinAce
2010-Mar-25, 06:57 PM
Very well put. Experiment confirms the above (see Haefele-Keating and its more recent reenactments).

They don't see a distance difference? That's news to me.

Alive stays on earth and measures the distance Bob travels by sending pulses of light. Bob has a mirron on his ship. She says he travelled 10 light years.

Bob's odometer says 8 light years.

He's 8 years older, she's 10 years older.

Where's the beef?

macaw
2010-Mar-25, 07:04 PM
They don't see a distance difference? That's news to me.

Alive stays on earth and measures the distance Bob travels by sending pulses of light. Bob has a mirron on his ship. She says he travelled 10 light years.

Bob's odometer says 8 light years.

He's 8 years older, she's 10 years older.

Where's the beef?

The point was that when the two observers are reunited they see no difference in length but they see differences in elapsed times (http://sports.espn.go.com/oly/figureskating/news/story?id=5024469).

ShinAce
2010-Mar-25, 07:15 PM

When they reunite, are the clocks ticking at different rates? No!

edit: See response below, as it's explained more completely.

speedfreek
2010-Mar-25, 07:16 PM
Then, why do the twins see a "real and permanent" time difference (after return of the travelling twin) BUT no "real and permanent" length difference?

If your twin is half their original length while they are away, but is restored to their original length when they get home, how can you tell?
Sorry, I'm afraid I don't understand what you mean.
What I wanted to say was that time dilation is something which shows up, can be measured, in our "reality". But I've never seen a measurement of length contraction.
Time dilation isn't restored when the clock gets home. Therefore, as commonsense said, something physical must have happend to the clock's hands (or atoms, or...). What is it?

What I wanted to say is that, relative to your own frame of reference, your twin is time dilated and length contracted only whilst they are making their journey. Once they return home to you and thus share your frame of reference, there is obviously no time-dilation or length contraction - their clock is now "running at the same speed" as yours and they are now the same length as you!

If, whilst they were away, their clock was "running slower" than yours and so they experienced less elapsed time than you, you can see the evidence of this when they return.. they will now be younger than you, their hair and nails won't have grown so much and they have a clock that is now behind yours, even though it is now running at the same speed as your clock.

But what evidence would there be for their length contraction, upon their return? How could you tell they had less length whilst they were away, if their length is now the same as yours, once again?

Strange
2010-Mar-25, 07:29 PM
The effect is real and happens independently of any acceleration. The fact that in order to compare the two clocks, one needs to return to the departing point is purely incidental, so the acceleration involved in "turning around" is purely incidental, has no effect on the behavior of the clock.
The fact that clock rate is insensitive to acceleration has been verified experimentally (http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html#Clock_Hypothesis) to a very high precision.

OK. I accept that. But I am still slightly confused... If there is no acceleration, then won't the situation be completely symmetrical: both clocks would slow equally, as observed by the other. Isn't it the change(s) in inertial frame of reference to bring the clocks back together again that causes an asymmetry and means that one will definitely be slow wrt the other?

[You will see now, why I try and stay out of relativity discussions unless it is really basic :)]

DrRocket
2010-Mar-25, 07:30 PM
Length contraction has not been verified yet only because of the enormous experimental difficulties. There is work in progress that will circumvent such difficulties in the next few years. Technological advancements in measurement are going to take care of this.

On the other hand, time dilation and length contraction are really the same thing, and the textbook example of the decay of muons created high in the atomosphere by cosmic rays that shows time dilation in an earth reference frame also shows length contraction in the frame of the muon. The two perspectives agree, and produce the same physical effect -- the muon penetrates deeper into the atmosphere before decaying that would be explainable without relativity.

Strange
2010-Mar-25, 07:34 PM
If, whilst they were away, their clock was "running slower" than yours and so they experienced less elapsed time than you, you can see the evidence of this when they return.. they will now be younger than you, their hair and nails won't have grown so much and they have a clock that is now behind yours, even though it is now running at the same speed as your clock.

But what evidence would there be for their length contraction, upon their return? How could you tell they had less length whilst they were away, if their length is now the same as yours, once again?

Right. You can "accumulate" an elapsed time difference but not a length difference. I think that is what I was getting at when I said:

It was accelerated. I wonder if the difference between time and length in this case, is related to the fact you can move around in space dimensions but not time?

macaw
2010-Mar-25, 09:07 PM

When they reunite, are the clocks ticking at different rates? No!

It is not my problem that you don't understand what I wrote.

macaw
2010-Mar-25, 09:09 PM
On the other hand, time dilation and length contraction are really the same thing,

Correct. Nevertheless, while time dilation has benn measured directly (see all the experiments on transverse Doppler effect) , length contraction has not. This is about to get fixed in the next few years.

and the textbook example of the decay of muons created high in the atomosphere by cosmic rays that shows time dilation in an earth reference frame also shows length contraction in the frame of the muon. The two perspectives agree, and produce the same physical effect -- the muon penetrates deeper into the atmosphere before decaying that would be explainable without relativity.

Sure.

macaw
2010-Mar-25, 09:17 PM
OK. I accept that. But I am still slightly confused... If there is no acceleration, then won't the situation be completely symmetrical: both clocks would slow equally,

In SR, clocks do NOT "slow". Only in GR and that is due to differences in gravitational potential.

as observed by the other. Isn't it the change(s) in inertial frame of reference to bring the clocks back together again that causes an asymmetry and means that one will definitely be slow wrt the other?

Sure, absent the "turn-around" the effects are perfectly symmetric , each observer will see the same effect. Nevertheless, the differences in elapsed times are not due to acceleration, acceleration is only needed in order to bring the clocks back side by side such that we can compare them. The acceleration, being absolute, breaks the symmetry between the two so, we can say without doubt which one travelled the longest distance. To prove that, you can see that, even if the computation is made from the perspective of the accelerated "twin" (clock), the result is just the same: the one that travelled the longest path through space, shows the least elapsed time.See here (http://en.wikipedia.org/wiki/Twin_paradox#Difference_in_elapsed_times:_how_to_c alculate_it_from_the_ship).

[You will see now, why I try and stay out of relativity discussions unless it is really basic :)]

This is ok, you are a very sensible person, so I feel good about helping you.

DrRocket
2010-Mar-25, 09:20 PM
Correct. Nevertheless, while time dilation has benn measured directly (see all the experiments on transverse Doppler effect) , length contraction has not. This is about to get fixed in the next few years.

That sounds like a very interesting experiment.

Can you sketch out how it might be done ? In particular what is going to be actually measured ? This brings up images of the long fast train in the short tunnel, but that is clearly not the appropriate image.

ShinAce
2010-Mar-25, 09:24 PM
It is not my problem that you don't understand what I wrote.

No, but it is your problem that you don't understand what you are writing! This is inappropriate in most contexts, but you're asking for it.

Let's avoid attacking each other, shall we?

Show that the tests of SR are direct measurements of a time dilation and not length contraction. How can you prove the clock is ticking slower over the same distance versus the clock ticking at the same rate over a new distance? Those jets that flew atomic clocks did not measure distance down to any precision worth considering.

...carry on.

ShinAce
2010-Mar-25, 09:25 PM
That sounds like a very interesting experiment.

Can you sketch out how it might be done ? In particular what is going to be actually measured ? This brings up images of the long fast train in the short tunnel, but that is clearly not the appropriate image.

LOL! I wanted to say pole barn paradox, but that's just asking for 5 pages of trouble.

DrRocket
2010-Mar-25, 09:42 PM
No, but it is your problem that you don't understand what you are writing! This is inappropriate in most contexts, but you're asking for it.

Let's avoid attacking each other, shall we?

Show that the tests of SR are direct measurements of a time dilation and not length contraction. How can you prove the clock is ticking slower over the same distance versus the clock ticking at the same rate over a new distance? Those jets that flew atomic clocks did not measure distance down to any precision worth considering.

...carry on.

The muon decay phenomenon is a direct confirmation of time dilation, as are other experiments, including the Pond-Rebka experiment (gravitational time dilation) and the Hafele-Keating experiment which you apparently do not accept.

macaw is correct.

macaw
2010-Mar-25, 09:48 PM
That sounds like a very interesting experiment.

Yes, it is. I had to write the theoretical foundation as well as to devise the experimental setup.

Can you sketch out how it might be done ?

Unfortunately, I have to keep this under wraps but I can give a few glimpses. There is a very big competition in accomplishing this so I can't disclose details at this point in time. As soon as the measurements are complete, I will be able to give a detailed account.

In particular what is going to be actually measured ? This brings up images of the long fast train in the short tunnel, but that is clearly not the appropriate image.

You are awfully close, you need a "train" that stays rigid when accelerated to a very high percentage of c :-).
Measuring the length of a moving object requires marking its endpoints simultaneously in a frame that moves at very high speed wrt the object. This "simultaneous marking" combined with the "....moves at very hight speed" have been the stumbling block until I fixed both of them. Sorry, I can't say more about it.
Now, there are also indirect tests of length contraction that cannot be reduced to tests of time dilation per se, as described here.

macaw
2010-Mar-25, 09:53 PM
No, but it is your problem that you don't understand what you are writing!

Tough, eh?

Show that the tests of SR are direct measurements of a time dilation and not length contraction.

All tests of transverse Doppler effect are considered direct tests of time dilation by mainstream physicists. Are you really reading what I am writing?

How can you prove the clock is ticking slower over the same distance versus the clock ticking at the same rate over a new distance?

I already explained this as well. Twice. Please go back and read what I wrote on this subject.

Those jets that flew atomic clocks did not measure distance down to any precision worth considering.

They did not need to measure distance, they measured something entirely different. Do you know why they didn't need to measure distance? Do you know what they measured?

.

Really? :lol:

ShinAce
2010-Mar-25, 09:56 PM
The muon decay phenomenon is a direct confirmation of time dilation, as are other experiments, including the Pond-Rebka experiment (gravitational time dilation) and the Hafele-Keating experiment which you apparently do not accept.

macaw is correct.

I accept them for what they are, experiments.

I don't see how it's a direct confirmation in the sense that time dilates while space does not contract. For us, the muon is slowed. For the muon, we are shorter. I don't see how any experiment will separate time from space.

I personally think the HK experiment is cool, only because I'm a speaker builder.

A few posts back, I was arguing that saying 'time dilation leaves a stamp while length contraction undoes itself when the twins reunite', and now we are here.

...carry on.

Ken G
2010-Mar-25, 10:10 PM
In SR, clocks do NOT "slow". Only in GR and that is due to differences in gravitational potential.
I do not believe there is any fundamental difference in whether or not clocks "slow" in SR vs. GR. In either case, the statement is purely a choice of perspective. The general remark, which to me makes more sense, is that elapsed times depend on the path taken, in both SR and GR. The rest is geometry, or at least may be viewed that way.

Nevertheless, the differences in elapsed times are not due to acceleration, acceleration is only needed in order to bring the clocks back side by side such that we can compare them. The acceleration, being absolute, breaks the symmetry between the two so, we can say without doubt which one travelled the longest distance. It is also not clear that acceleration is absolute. It can be measured by an accelerometer, but the accelerometer also takes a path, just as a clock does. Absolute statements are of the form "accelerometer A read a," or "clock B read b." The rest is all coordinates. It is inconsistent to claim in the same breath that acceleration is absolute, but does not cause the difference in the elapsed times! That you are on shaky ground with these claims is no great sin, it's very hard to really be precise when talking relativity-- but it is also good reason to temper one's judgemental remarks.

To prove that, you can see that, even if the computation is made from the perspective of the accelerated "twin" (clock), the result is just the same: the one that travelled the longest path through space, shows the least elapsed time.See here (http://en.wikipedia.org/wiki/Twin_paradox#Difference_in_elapsed_times:_how_to_c alculate_it_from_the_ship).But of course, the calculation from the ship can also be attributed to the presence of a pervasive gravitational field, in which case, the ship does not accelerate, it merely holds its place against that field.

DrRocket
2010-Mar-25, 10:12 PM
OK. I accept that. But I am still slightly confused... If there is no acceleration, then won't the situation be completely symmetrical: both clocks would slow equally, as observed by the other. Isn't it the change(s) in inertial frame of reference to bring the clocks back together again that causes an asymmetry and means that one will definitely be slow wrt the other?

[You will see now, why I try and stay out of relativity discussions unless it is really basic :)]

Not quite, but you are on the right track.

If you stick to special relativity, then you must abide by the rules of SR. One of the rules is that the Lorentz transformations of SR apply only to inertial reference frames. In the twin paradox the phenomena of acceleration allows one to clearly distinguish between the intertial reference frame of the non-traveling twin and the accelerating/non-inertial reference frame of the traveling twin. Therefore it is only in the reference frame of the non-traveling twin that one can apply SR, and in that frame the traveling twin ages less.

In GR it can be shown that the proper time of any world line will be greater than the time line of the stationary twin. The mathematics in that case is a bit more complex than the simple algebra needed for SR. See proposition 2.9 here (http://arxiv.org/PS_cache/math/pdf/0603/0603190v3.pdf).

macaw
2010-Mar-25, 10:24 PM
I do not believe there is any fundamental difference in whether or not clocks "slow" in SR vs. GR.

Since the description of surrounding reality is GR, the point is moot.

which to me makes more sense, is that elapsed times depend on the path taken, in both SR and GR.

Time dilation ("clock slowdown") and difference in elapsed times are two different effects. They have different theories and different tests associated with the different theories. As in here (http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html#Tests_of_time_dilation) and here (http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html#Twin_paradox). So, both of them make equal sense, you can't say that one makes more sense than the other.

It is also not clear that acceleration is absolute. It can be measured by an accelerometer, but the accelerometer also takes a path, just as a clock does.

Huh? This is a breakthrough. If the twin in the non-accelerated frame looks at his accelerometer, will he detect an acceleration when the other twin takes off?

But of course, the calculation from the ship can also be attributed to the presence of a pervasive gravitational field, in which case, the ship does not accelerate, it merely holds its place against that field.

Sure, provided that the field is uniform, this is precisely what my friend, Preston Jones did in his paper (http://arxiv.org/abs/physics/0604025).

Ken G
2010-Mar-25, 10:30 PM
If you stick to special relativity, then you must abide by the rules of SR. Another way to put that is, there isn't a physical symmetry in the twin problem, so we shouldn't expect to be able to construct a way to look at the fundamental observables where there is a symmetry. For two inertial observers with no gravity, nothing physical breaks the symmetry, so it should be possible to do that, and finding out how is the basis of special relativity. But if either observer is noninertial, or gravity is present, it will not in general be possible to construct a way of looking at the observables in a symmetric way-- the symmetry is broken. What broke the symmetry is a matter of perspective (was it acceleration, was it gravity?), all we can say concretely is that the fundamental observables cannot be described in a way that is symmetric to both twins. Physically, there is no reason to expect that such a symmetry will be possible, either because of the presence of a real source of gravity (a big mass passed by one of the twins), or a blasting rocket engine attached to one twin but not the other.

DrRocket
2010-Mar-25, 10:33 PM
I accept them for what they are, experiments.

I don't see how it's a direct confirmation in the sense that time dilates while space does not contract. For us, the muon is slowed. For the muon, we are shorter. I don't see how any experiment will separate time from space.

An experiment will not separate time from space. The great lesson of Einstein's relativity is that time and space are the same thing, One observer's time is another observer's space. It is not space and time. It is spacetime.

Time dilation and length contraction are two aspects of one thing. They go hand in hand. What is invariant is neither time, nor space but t^2-x^2 (shorthand notation for invariance of the Minkowski metric and things determined by it).

But the coordinate measurements that are time or space, are affected by relative speeds, and that is what is called "time dilation" and "length contraction".

macaw
2010-Mar-25, 11:31 PM
Another way to put that is, there isn't a physical symmetry in the twin problem, so we shouldn't expect to be able to construct a way to look at the fundamental observables where there is a symmetry. For two inertial observers with no gravity, nothing physical breaks the symmetry, so it should be possible to do that, and finding out how is the basis of special relativity. But if either observer is noninertial, or gravity is present, it will not in general be possible to construct a way of looking at the observables in a symmetric way-- the symmetry is broken.

Correct, the symmetry is broken. It might be broken by acceleration, since acceleration is absolute (only one of the two twins experiences it) , it might be broken by its equivalent (moving against a gravitational field as in the Preston paper).
But symmetry may also be broken in the total absence of acceleration. Indeed, in this (http://www.phys.vt.edu/~jhs/faq/twins.html) example, it is shown that the twin that "remains" in the same reference frame, ages the most.

What broke the symmetry is a matter of perspective (was it acceleration, was it gravity?), all we can say concretely is that the fundamental observables cannot be described in a way that is symmetric to both twins.

Very true. Nevertheless, no matter whose perspective we use for predicting the result, the answer is the same, the twin that "remains" in the same reference frame, ages the most. By contrast, the twin that accelerates will experience a sequence of frames, never the same frame, so he will always be the one that ages the least.

DrRocket
2010-Mar-26, 12:10 AM
Unfortunately, I have to keep this under wraps but I can give a few glimpses. There is a very big competition in accomplishing this so I can't disclose details at this point in time. As soon as the measurements are complete, I will be able to give a detailed account.

When the experiment is complete and something committed to paper, I would love to see the draft in ArXiv. I have no doubt that it will make some science magazine (and be diced and scrambled beyond recognition there).

Cougar
2010-Mar-26, 12:33 AM
Measuring the length of a moving object requires marking its endpoints simultaneously in a frame that moves at very high speed wrt the object.

Wow, an experimentalist. :)

macaw
2010-Mar-26, 12:34 AM
When the experiment is complete and something committed to paper, I would love to see the draft in ArXiv. I have no doubt that it will make some science magazine (and be diced and scrambled beyond recognition there).

Sure thing :-)

macaw
2010-Mar-26, 12:35 AM
Wow, an experimentalist. :)

Yep. But I get to also write the theory of the experiments I run. You can't really design novel and meaningful experiments if you are weak on the theoretical aspects.

Ken G
2010-Mar-26, 03:25 AM
But symmetry may also be broken in the total absence of acceleration. Indeed, in this (http://www.phys.vt.edu/~jhs/faq/twins.html) example, it is shown that the twin that "remains" in the same reference frame, ages the most.Nah, I've seen that argument-- it's bogus. Its flaw is that it buys off on the complete fiction of special relativity that there is any physical significance to a "global reference frame". You can certainly use that format to get the right answers, but it is flawed as a way of making universal claims about what does and does not cause the twin effect-- it is a classic example of the error of using what is purely a choice of coordinates as if it contained some physical truth about what is the cause of the times that elapse. Coordinates don't cause things, nor can they be used to argue what does not cause things, such as acceleration.

A safe way to state the cause of the different times is quite straightforward: the cause is the different paths taken through spacetime. Since taking different paths between the same two points requires there be either gravity or acceleration, it is quite safe to say that acceleration or gravity does cause the twin effect-- what can be debated is whether there's any fundamental difference between those two potential ways it can happen. (The Machian says there's no fundamental difference there, a la the equivalence principle, but others argue that real gravity is distinguishable by its tidal effects, and I think that debate is quite alive and well at the moment, nor am I expert enough to comment on it any further.)

Nevertheless, no matter whose perspective we use for predicting the result, the answer is the same, the twin that "remains" in the same reference frame, ages the most.I agree, the answer is what really counts, as that is all that is testable.

By contrast, the twin that accelerates will experience a sequence of frames, never the same frame, so he will always be the one that ages the least.Yet there really is no such thing as "experiencing a sequence of frames", that's just an SR fiction. You are saying as much when you point out that clocks don't actually "tick slow"-- they are clocks, they tick like clocks. Similarly, observers don't "experience" frames, they are frames. The only "different frames" that has any demonstrable physical meaning is the frames of different observers, as each has its own frame.

Ken G
2010-Mar-26, 03:29 AM
An experiment will not separate time from space. The great lesson of Einstein's relativity is that time and space are the same thing, One observer's time is another observer's space.True, but note that your comments assume relativity is correct (typical rationalist!). The purpose of macaw's exciting experiment, it sounds like to me, is to check if relativity is correct, by finding a way to distinguish time dilation from length contraction if there is in fact any difference, i.e., if relativity is wrong.

DrRocket
2010-Mar-26, 04:02 AM
True, but note that your comments assume relativity is correct (typical rationalist!). The purpose of macaw's exciting experiment, it sounds like to me, is to check if relativity is correct, by finding a way to distinguish time dilation from length contraction if there is in fact any difference, i.e., if relativity is wrong.

Of course relativity is correct. Einstein knew that (http://www.nytimes.com/1992/03/24/science/letters-to-a-supporter-record-einstin-s-search-for-proof.html). :)

If the experiment does not show length contraction, I imagine that nearly everyone, probably including macaw, will be analyzing the experiment to find a flaw in the technique. I doubt that is going to happen.

This is less a check on relativity than a tour de force in experimental technique. I would also hazard a guess that the length contraction will be exceedingly small, if the object being measured is macroscopic, and that the methods used to measure the length will find application in other sophisticated experiments. I think it will be quite an accomplishment with ramifications far beyond the one experiment. Heck, macaw might even get to keep his job.:)

macaw
2010-Mar-26, 04:48 AM
Nah, I've seen that argument-- it's bogus. Its flaw is that it buys off on the complete fiction of special relativity that there is any physical significance to a "global reference frame".

Has nothing to do with any "global reference frame" . What gives you that idea?

You can certainly use that format to get the right answers, but it is flawed as a way of making universal claims about what does and does not cause the twin effect-- it is a classic example of the error of using what is purely a choice of coordinates as if it contained some physical truth

Did I ever tell you such a thing? What gives you this idea?

about what is the cause of the times that elapse. Coordinates don't cause things, nor can they be used to argue what does not cause things, such as acceleration.

True, so?

: the cause is the different paths taken through spacetime.

I think I already said that about three times in prior posts. Not only that, I provided the mathematical proof.

I agree, the answer is what really counts, as that is all that is testable.
Yet there really is no such thing as "experiencing a sequence of frames", that's just an SR fiction.

Are you developing yet another ATM? Are you aware that the sequence of inertial frames is SR's way of dealing with accelerated motion?

macaw
2010-Mar-26, 04:50 AM
Of course relativity is correct. Einstein knew that (http://www.nytimes.com/1992/03/24/science/letters-to-a-supporter-record-einstin-s-search-for-proof.html). :)

If the experiment does not show length contraction, I imagine that nearly everyone, probably including macaw, will be analyzing the experiment to find a flaw in the technique. I doubt that is going to happen.

This is less a check on relativity than a tour de force in experimental technique. I would also hazard a guess that the length contraction will be exceedingly small, if the object being measured is macroscopic, and that the methods used to measure the length will find application in other sophisticated experiments. I think it will be quite an accomplishment with ramifications far beyond the one experiment. Heck, macaw might even get to keep his job.:)

Correct on all acounts, DrR :-)
Except one , I definitely get to keep my job, no matter what. :-)

macaw
2010-Mar-26, 04:51 AM
True, but note that your comments assume relativity is correct (typical rationalist!). The purpose of macaw's exciting experiment, it sounds like to me, is to check if relativity is correct, by finding a way to distinguish time dilation from length contraction if there is in fact any difference, i.e., if relativity is wrong.

Umm, no. I don't think you got the gist. Not even close.

Ken G
2010-Mar-26, 05:09 AM
Of course relativity is correct. Einstein knew that (http://www.nytimes.com/1992/03/24/science/letters-to-a-supporter-record-einstin-s-search-for-proof.html). :)

If the experiment does not show length contraction, I imagine that nearly everyone, probably including macaw, will be analyzing the experiment to find a flaw in the technique. I doubt that is going to happen.
There would be absolutely no point in doing the experiment if that were true! Certainly a non-null result would first be carefully checked for an experimental flaw, that's always true whenever an experiment yields a surprise. But it is by no means a guarantee that there will be a flaw-- experiments are not done to increase our confidence in theories, they are done to test theories. That's science. (What on Earth is the point of "experimental tours-de-force" if we already know the theory is correct? And when has that ever been true in the history of science?)

Ken G
2010-Mar-26, 05:18 AM
Has nothing to do with any "global reference frame" . What gives you that idea?
Understanding relativity. A "global reference frame" is absolutely nothing but a coordinate choice-- did you think it was something else? What then, did you think it was?

Did I ever tell you such a thing? What gives you this idea?
Reading the link you gave gives me that idea-- the link makes exactly the error I cite.

True, so?
So the link is wrong, because that is exactly what it did.

I think I already said that about three times in prior posts. Not only that, I provided the mathematical proof.Your error was your statement that acceleration does not cause the different times in the gravity-free twin paradox. Your argument there is exactly the same thing as showing mathematically that the straight-line path is the shortest distance, but then claiming that the cause of other paths being longer is not the fact that they are curved or kinked! That is precisely the cause.

re you developing yet another ATM? Are you aware that the sequence of inertial frames is SR's way of dealing with accelerated motion?Obviously. The flaw was the fiction of "experiencing a sequence of reference frames." What, exactly, is a "sequence of reference frames?" An observer has a reference frame, period. Do you mean a sequence of inertial reference frames? Don't you know why Einstein didn't like inertial reference frames, and developed general relativity?

DrRocket
2010-Mar-26, 06:05 AM
A safe way to state the cause of the different times is quite straightforward: the cause is the different paths taken through spacetime. Since taking different paths between the same two points requires there be either gravity or acceleration, it is quite safe to say that acceleration or gravity does cause the twin effect-- what can be debated is whether there's any fundamental difference between those two potential ways it can happen. (The Machian says there's no fundamental difference there, a la the equivalence principle, but others argue that real gravity is distinguishable by its tidal effects, and I think that debate is quite alive and well at the moment, nor am I expert enough to comment on it any further.)
.

DrRocket
2010-Mar-26, 06:22 AM
Your error was your statement that acceleration does not cause the different times in the gravity-free twin paradox. Your argument there is exactly the same thing as showing mathematically that the straight-line path is the shortest distance, but then claiming that the cause of other paths being longer is not the fact that they are curved or kinked! That is precisely the cause.

You are letting your philosophical tendancies run wild.

The problem is that word "cause".

The shortest path joining two points is a straight line. Other paths joining two points are longer because they are not that straight line. The fact that they are curved or kinked is incidental.

Take a sphere. Take two points that are not antipodal. The shortest path joining them is a segment of a great circle, a geodesic/straight line. The remainder of the same great circle is also a geodesic/straight line joining those points. It is not the shortest path.

Not everything need have a "cause:.

"The Devil made me do it." -- Flip Wilson

Ken G
2010-Mar-26, 06:24 AM
"Remark 2.10. Proposition 2.9 can be interpreted as follows: if two observers (e.g. two twins) meet at some event, are separated, and meet again at a later event, then the free-falling twin will always measure more time to have passed between the meetings."
Note that what this means is that the free-fall trajectory has a family of nearby trajectories that all take less proper time to reach the endpoint (it does not mean any one free-fall trajectory must be the global maximum, but that doesn't really matter). What is the free-fall trajectory? The one with no proper acceleration. Ergo, whenever there is proper acceleration, there is reduced proper time, and whenever there isn't proper acceleration, there is maximal proper time. Since no one would suggest that reduced proper time causes acceleration, nor that some other factor causes both the acceleration and the reduced proper acceleration (what is that other factor? The rocket engine causes both the acceleration and the reduced proper time, but it does it via some mechanism other than its creation of acceleration?), we are left with proper acceleration being as close to a "cause" of reduced proper time as you ever get in physics-- you'd have to completely reject the entire concept of logical causation to reject that one. Which you can certainly do, but it's hardly the industry standard in physics-- we like to imagine that things happen for a reason.

Ken G
2010-Mar-26, 06:30 AM
The shortest path joining two points is a straight line. Other paths joining two points are longer because they are not that straight line. The fact that they are curved or kinked is incidental.That's not a coherent argument. How can you tell if a line in flat Euclidean space is straight or not? I see two options: you can assert that the straight line is the one that has the minimum distance, but then the claim that you can prove the straight line has the minimum distance is circular. Alternatively, you can say the straight line is the one with no curves or kinks, in which case it is quite clearly not incidental. None of this is philosophy, it is pure logic.

Take a sphere. Take two points that are not antipodal. The shortest path joining them is a segment of a great circle, a geodesic/straight line. The remainder of the same great circle is also a geodesic/straight line joining those points. It is not the shortest path.
That is a different geometry, so is relevant neither to flat Euclidean examples, nor to Minkowski examples. It is quite relevant to general relativity, but there one does not say that acceleration must be the cause of time differences, one has gravity as another possible cause-- as I mentioned.

Not everything need have a "cause:.That is arguing that the reason acceleration does not cause the times to be different is that there is no cause that the times are different. One can certainly take that tack, but one can also simply say that the path causes the proper time, and a path that involves acceleration therefore does indeed cause the larger proper time. It's all a question of whether or not one would like to be able to speak of causes of physical effects, which is quite a standard thing to want to do in physics.

DrRocket
2010-Mar-26, 06:46 AM
That's not a coherent argument. How can you tell if a line in flat Euclidean space is straight or not? I see two options: you can assert that the straight line is the one that has the minimum distance, but then the claim that you can prove the straight line has the minimum distance is circular. Alternatively, you can say the straight line is the one with no curves or kinks, in which case it is quite clearly not incidental. None of this is philosophy, it is pure logic.

Not at all. You can prove that the shortest line between two points in Euclidean space is a stright line using the calculus of variations. If you want to go beyond smooth curves I would prove that using some approximation techniques. Nothing circular.

That is a different geometry, so is relevant neither to flat Euclidean examples, nor to Minkowski examples. It is quite relevant to general relativity, but there one does not say that acceleration must be the cause of time differences, one has gravity as another possible cause-- as I mentioned.

Yep, it is differential geometry. So what ?

You prove that the shortest path between two points is a geodesic using calculus of variations. Just like in the Euclidean case.

Differential geometry includes Euclidean geometry.

It's all a question of whether or not one would like to be able to speak of causes of physical effects, which is quite a standard thing to want to do in physics.

Causes generally involve some sort of dynamics, and a markov-type process. Not all physical effects and characteristics have "causes".

You have two clocks that follow different world lines. They show different times. No surprise. Why should they not ? In fact both clocks show proper time for their world line. Proper time is the arc length of the world line. Two distinct world lines, two distinct arc lengths. What caused that ?

It is farther from New York to Los Angeles than it is from New York to Hoboken. What caused that ?

Blue is different from hot. What caused that ? When did it happen ?

Ken G
2010-Mar-26, 07:09 AM
Not at all. You can prove that the shortest line between two points in Euclidean space is a stright line using the calculus of variations. That's my point-- in that proof, you will find the place where you invoke an absence of kinks or curves in identifying the straight line. (By the way, I edited my post about proposition 2.9 to reflect the relevance to this causation issue, see the new version of that post.)
If you want to go beyond smooth curves I would prove that using some approximation techniques. Nothing circular. You are missing my point-- the circularity lies in how you identify what is the straight line, not how you prove it is the minimum distance. When you say the calculus of variations proves the straight line is the shortest distance (an exercise I'm well acquainted with, I just taught it a few weeks ago), what do you mean by "the straight line"?

You prove that the shortest path between two points is a geodesic using calculus of variations.Now there's the circularity-- the definition of a geodesic is the shortest distance, using some metric.

Causes generally involve some sort of dynamics, and a markov-type process. Not all physical effects and characteristics have "causes".
There are several meanings of "causes" in physics. One deals with formal "cause and effect", which is a kind of mechanistic connection between two physical events that can be clearly time ordered. That's not the type of "cause" we are talking about here, as we are talking about the cause of a reduced proper time, which is not an event. Instead, we are using the other way "causation" is used in physics: the logic of imperatives. Claustrophobia causes people to avoid confined spaces, avoiding confined spaces does not cause claustrophobia. The luminosity of a main-sequence star causes it to fuse hydrogen at a similar rate, the nuclear fusion rate does not cause the luminosity of the star to be what it is. That form of causation does bring insight, though it is not necessary to accept it as anything but an association.

That sort of meaning of "cause" is quite useful in physics, though one can certainly choose never to invoke it and just imagine that all the equations of physics are correlations and nothing more. But nobody does it that way, because we prefer to imagine things happen for a reason, even though we never test anything but associations.

Proper time is the arc length of the world line. Two distinct world lines, two distinct arc lengths. What caused that ?That's exactly like saying, I can take a fast highway to work, or a slow back road. I get to work faster on the highway. What causes that? Answer: the speed limit! It is perfectly standard for us all to view that as a cause, not just an association-- it's exactly the way we think when we make decisions about getting to work.

It is farther from New York to Los Angeles than it is from New York to Hoboken. What caused that ?

Blue is different from hot. What caused that ? When did it happen ?Merely drawing an analogy does not guarantee relevance. The first is two paths that don't share endpoints, the second has nothing at all to do with anything. That logical imperatives do not appear in every linguistic situation you can form, does not imply there is no such useful concept as a logical imperative in any situation. If you plan to reject the whole concept of logical imperatives, I certainly cannot say one has to use them-- but I'm sure that you don't really think that way, as no one does.

DrRocket
2010-Mar-26, 07:26 AM
That's my point-- in that proof, you will find the place where you invoke an absence of kinks or curves in identifying the straight line. (By the way, I edited my post about proposition 2.9 to reflect the relevance to this causation issue, see the new version of that post.)You are missing my point-- the circularity lies in how you identify what is the straight line, not how you prove it is the minimum distance. When you say the calculus of variations proves the straight line is the shortest distance (an exercise I'm well acquainted with, I just taught it a few weeks ago), what do you mean by "the straight line"?Now there's the circularity-- the definition of a geodesic is the shortest distance, using some metric.

You define a straight line in Euclidean space just like in high school with a simple equation. Then you can show it provides the shortest arc length between its end points (the exercise that you did for your class).

There are seveal ways to define a geodesic, and the shortest path is not the one used in many treatments of differential geometry. But this is a technical thing involving parallel transport and tangential to this discussion.

I don't think we are going to get anywhere with this line. Too philosophical.

Ken G
2010-Mar-26, 01:27 PM
You define a straight line in Euclidean space just like in high school with a simple equation.And you don't think it's possible to tell from that equation that the line doesn't curve or kink? Or in the actual case at hand, you don't think it's possible to tell from the equation of a straight line in spacetime that it does not accelerate?

macaw
2010-Mar-26, 02:14 PM
Obviously. The flaw was the fiction of "experiencing a sequence of reference frames." What, exactly, is a "sequence of reference frames?"

The inertial reference frames associated with an accelerated observer.Since the observer changes speed, you need a whole sequence of them frames. :-)
This is the standard way of dealing with acceleration in SR. You didn't know?

macaw
2010-Mar-26, 02:27 PM
Your error was your statement that acceleration does not cause the different times in the gravity-free twin paradox. Your argument there is exactly the same thing as showing mathematically that the straight-line path is the shortest distance, but then claiming that the cause of other paths being longer is not the fact that they are curved or kinked!

It is very easy to prove you wrong. I am going to show that again with an unaccelerated case. Two rockets with clocks on board travel in a straight line at a constant speed , with no turnarounds the same amount of time "dt" from the perspective of an observer attached to their launch site.

One travels a distance dX, the other a distance dx, with dX>dx.
The proper time elapsed on the two clocks are respectively:

d\tau=dt*sqrt(1-1/c^2*(dx/dt)^2)

and

d\Tau=dt*sqrt(1-1/c^2*(dX/dt)^2)

Since dX>dx it follows that d\Tau<d\tau.
No acceleration needed. It's all in the difference of travelled distance.

Ken G
2010-Mar-26, 04:47 PM
The inertial reference frames associated with an accelerated observer.Once again, I know SR dogma. What I'm telling you is that every observer has a "reference frame", it is local, it belongs to that observer, and this is all true whether the observer is inertial or not. This is the entire basis for general relativity, practically page 1 of any general relativity textbook. Inertial observers have inertial frames, others don't, but they have reference frames all the same-- they don't move through a "sequence of reference frames", as you claimed, and treating them as moving through a sequence of inertial reference frames is merely a mathematical artifice to allow us to use the convenient postulates of SR in the absence of gravity, instead of the much more physically realistic postulates of GR. Now, in SR Einstein didn't know anything better than to take arbitrary observers and ask what inertial observers they were instantaneously comoving with, giving rise to the SR dogma you take so seriously. But Einstein recognized the awkwardness of subjugating one observer to another, and indeed how that violates the very spirit of relativity itself, so he was quick to rectify that problem on the way to creating his theory of gravity. Now that the problem is fixed, we know not to take SR dogma as seriously as you do (and we avoid language like "an observer moves through a sequence of reference frames"-- every observer has a reference frame, period).

This is the standard way of dealing with acceleration in SR. You didn't know?Of course I knew, every first-year relativity student knows that-- but I also knew why it is so clunky and awkward a language for talking about what does and does not cause something else. I guess I've advanced beyond the limitations of SR thinking, as did Einstein himself.

Ken G
2010-Mar-26, 04:58 PM
It is very easy to prove you wrong.To repeat, the question at hand is precisely this: What causes two clocks that start and end at the same events to read different proper times? The situation in your "proof" is not that situation, so your arithmetic is quite irrelevant to the whole issue.

What DrRocket is saying is more potentially relevant, because he is calling into question the entire mindset of looking for a "cause" of those different elapsed times. I agreed that there is no necessary requirement to look for any such cause, one can always just say that's how it is. But that is rarely how we actually think, either in physics or in our own lives-- we generally do look for reasons, not just associations, and we recognize an arrow of logical implication. If you want to reduce the proper time registered by a clock present at any two events, you introduce acceleration, or gravity. That's just a fact, and it is quite natural to therefore conclude the presence of a logical implication that the acceleration is therefore the cause. Assuming there is no tidal gravity present, the following exhausts the options:
1) there is no point in looking for logical implication at all, it just is what it is (but then there's no point in saying "acceleration doesn't cause the time difference", because we have rejected the entire premise that there could be a cause, not because of the argument given in your link),
2) there is a point in looking for logical implication, and all the possibilities there are:
2a) acceleration is the cause of the time reduction
2b) the time reduction is the cause of the acceleration
2c) something else causes both the acceleration and the time reduction independently.

That's it, those are the possibilities here. Note that neither #1 nor #2a can be used to motivate the link you gave to support your contention. #2b and #2c are the only ones that do support it, but they have obvious problems of their own.

macaw
2010-Mar-26, 05:07 PM
Once again, I know SR dogma.

Dogma? It is stock SR. Why would you call it dogma?

What I'm telling you is that every observer has a "reference frame", it is local, it belongs to that observer, and this is all true whether the observer is inertial or not. This is the entire basis for general relativity, practically page 1 of any general relativity textbook. Inertial observers have inertial frames, others don't, but they have reference frames all the same-- they don't move through a "sequence of reference frames", as you claimed, and treating them as moving through a sequence of inertial reference frames is merely a mathematical artifice

Ahh, I see, it is your allergy to math again.

Of course I knew, every first-year relativity student knows that-- but I also knew why it is so clunky and awkward a language for talking about what does and does not cause something else. I guess I've advanced.

I guess not, since you didn't understand the counterexample I posted for you.You already explained that you "don't do math", it appears that that also includes the inability to follow someone else's math. So, I'll give you a different counterexample to your claims. See next post.

macaw
2010-Mar-26, 05:14 PM
To repeat, the question at hand is precisely this: What causes two clocks that start and end at the same events to read different proper times?

Contrary to the above, if the clocks followed a circular path of the same radius and in opposite directions with the same angular speed they would read exactly the same proper time when they met again, despite them being accelerated all along their closed paths. So, your statement is false.

Ken G
2010-Mar-26, 05:20 PM
Contrary to the above, if the clocks followed a circular path of the same radius and in opposite directions with the same angular speed they would read exactly the same proper time when they met again, despite them being accelerated all along their closed paths. So, your statement is false.Another utterly irrelevant point. My logic is quite simple, and quite solid. The path causes the elapsed proper time. The acceleration determines the path-- the path is logically reliant on whatever controls the acceleration. Ergo, the acceleration causes the proper time. That multiple paths can yield the same proper time is perfectly irrelevant to any of this.

macaw
2010-Mar-26, 05:25 PM
That multiple paths can yield the same proper time is perfectly irrelevant to any of this.

You asked the question: "What causes two clocks that start and end at the same events to read different proper times?"

I showed you that the clocks didn't "read different proper times". <shrug>

macaw
2010-Mar-26, 05:34 PM
Another utterly irrelevant point. My logic is quite simple, and quite solid.

:lol:

The path causes the elapsed proper time.

Not exactly, it is the integral over coordinate time that determines the elapsed proper time.

The acceleration determines the path-- the path is logically reliant on whatever controls the acceleration. Ergo, the acceleration causes the proper time.

Yet, you have cases (counterexample 1) when there is no acceleration and the proper times are still different, so, acceleration can't "cause the proper time" (actually this is a very bad way of putting things, especially for a purist like you)

Yet, you have cases (counterexample 2) where the acceleration is present and the elapsed proper times are identical.

So, acceleration can't "cause proper time" (ugh!). You may want to rethink your solid logic.

DrRocket
2010-Mar-26, 05:36 PM
And you don't think it's possible to tell from that equation that the line doesn't curve or kink? Or in the actual case at hand, you don't think it's possible to tell from the equation of a straight line in spacetime that it does not accelerate?

Of course I can tell that a straight line does not kink. That is completely irrelevant to the definition. The point is that I can show, and apparently so can you, that the locus of points defined by the equation for a straight line is the shortest path between two points in Euclidean space. The fact that the shortest path is a straight line is a result, not a "cause". It is simply a minimization problem, in this case the minimization of a function whose domain is a function space.

Lack of kinking is no more a cause that being 0 is the cause of the minimum of the function f(x)=x^2. If that is a "cause" to you then OK, but we have a different sense of the word.

I have no idea what it means for a a straight line in spacetime to not accelerate. World lines in spacetime do not accelerate or decelerate. In fact they don't move and have no speed at all -- they are paths. You can only talk about velocity (the tangent vector) along a parameterized path, and the velocity varies with parameterization (just like controlling the throttle on your car as you drive along a prescribed path).

In GR a path can be parameterized by proper time, which is the same as arc length. And that is why the 4-vector velocity is always 1 (in units where c is 1), because you have parameterized the curve with arc lenth/proper time.

Just as a side note, geodesics in GR are not paths of minimum length. They are in fact paths of maximum length, which in part explains the so-called twin paradox.

grav
2010-Mar-26, 06:31 PM
It would seem logical at first glance to say that the difference for elapsed times takes place when an observer changes frames, so that it is caused by the acceleration of the observer. However, since no such difference takes place when Alice and Bob coincide and Bob accelerates instantly from that point, but only when Bob changes frames in the same way at a distance, whereas a simultaneity shift takes place as Bob observes Alice at the point of turn-around, then it is really the relativity of simultaneity that causes the difference in elapsed times. This can also be seen if we have Bob always travelling at some relative speed to Alice, and Alice and Bob synchronize clocks when they pass, while Carl travels in the opposite direction toward Alice from some distance, and Bob and Carl synchronize when they pass also, so that Carl now carries Bob's time, whereas the same elapsed times will be seen between Alice's and Carl's clocks when they pass. There has been no acceleration involved, but relativity of simultaneity still exists between what Bob observes of Alice's clock and what Carl observes of Alice's clock, which directly affects the realities according to each frame.

Ken G
2010-Mar-26, 07:04 PM
integral[/b] over coordinate time that determines the elapsed proper time.
Hardly. Proper time is measured by a clock, and what the clock measures between any two specified events is found to be determined entirely by its path between the two events. Yes or no? Its path between two events is found to be determined entirely by its acceleration (let's ignore gravity for now). Yes or no? These are empirical facts, nothing you can say can turn them into not being empirical facts. The interpretation that is most naturally applied to these simple facts is that if the acceleration determines the path, and the path determines the elapsed time, then changing the acceleration explains why, i.e. is the "cause" or "reason", whenever the elapsed time is found to be different. That is very simple logic-- I discussed all the possibilities there in the cases above. Now you are confusing the actual progress of time that affects a clock with an arithmetic manipulation (specifically, an integral) that mathematicians and physicists can do.

Yet, you have cases (counterexample 1) when there is no acceleration and the proper times are still different, so, acceleration can't "cause the proper time" (actually this is a very bad way of putting things, especially for a purist like you)Nope, not in the case of interest, which is when the endpoints are shared (and there is no gravity). So much for that counterexample.

Yet, you have cases (counterexample 2) where the acceleration is present and the elapsed proper times are identical. Nowhere was it claimed that two situations that involved different acceleration could not produce the same proper time, that is an absurd requirement to place on the concept of a "cause" or "reason." The reason you get paid a salary is that you provide a service. Yes? So by your own logic, no two people can get paid the same salary unless they provide the same service. That is precisely the logic of your "counterexample 2".

Ergo, both your "counterexamples" are found to be irrelevant to the issue, as I already said. The logic that needs rethinking is your own, and I've shown precisely why.

Ken G
2010-Mar-26, 07:26 PM
Of course I can tell that a straight line does not kink. That is completely irrelevant to the definition. The issue here is not the definition of a straight line, which admits many options that all spawn the same meaning. The issue is, what are the logical imperatives associated with a straight line. Those logical imperatives include that they must obey a certain equation in a certain kind of coordinates, and they must not exhibit curving or kinking. Any straight line (in Euclidean space) obeys those requirements, it doesn't matter which we arbitrarily choose as our definition. The point is, anything that causes the path to deviate from the straight line will increase the distance. So if any curving or kinking is known to cause deviation from the straight line, as we know it is, then any curving or kinking will cause the distance to increase. That's it, that's the whole argument.

Now, as I said to macaw, the only other possibilities are that we punt any effort to identify cause or reasons, which is anathema to the thought patterns humans have cultivated over the millennia, or to say that the longer distance is what caused the path to deviate (as could certainly happen in a situation where we can manually manipulate the length of something, perhaps a stiff thread passing through a hole at one end and anchored at the other), or to conclude that something else caused both the length to increase and the path to deviate independently (I can't even think of an example of that). So the sole question that remains is, which of those makes the most sense for spacetime paths of clocks, and how we can actually manipulate said paths?

The fact that the shortest path is a straight line is a result, not a "cause".I never said that the shortest path being a straight line was a cause, that's a theorem! What I did say is that in light of that theorem, anything that "causes" deviation from the straight line "causes" the distance to increase. That's what I said, and it's a perfectly standard way for us to think about causes, we do it all the time in our daily lives to great usefulness.
Lack of kinking is no more a cause that being 0 is the cause of the minimum of the function f(x)=x^2. If that is a "cause" to you then OK, but we have a different sense of the word. Again I haven't the vaguest idea why you think that is a valid analogy with what I am talking about above.

I have no idea what it means for a a straight line in spacetime to not accelerate. World lines in spacetime do not accelerate or decelerate.Certainly, but it is acceleration of the clock following the world line that I am talking about, and that is what I have always been talking about. I apologize if more precise language would have made that clearer.

In GR a path can be parameterized by proper time, which is the same as arc length.Yes, and in GR, clocks can follow world lines parametrized by proper time, and indeed the parametrization is intentionally set up to be the same as the clock reading-- that's its raison d'etre, empirically.

And that is why the 4-vector velocity is always 1 (in units where c is 1), because you have parameterized the curve with arc lenth/proper time.
Because that's its raison d'etre, empirically.

DrRocket
2010-Mar-26, 07:37 PM
. Assuming there is no tidal gravity present, the following exhausts the options:
1) there is no point in looking for logical implication at all, it just is what it is (but then there's no point in saying "acceleration doesn't cause the time difference", because we have rejected the entire premise that there could be a cause, not because of the argument given in your link),
2) there is a point in looking for logical implication, and all the possibilities there are:
2a) acceleration is the cause of the time reduction
2b) the time reduction is the cause of the acceleration
2c) something else causes both the acceleration and the time reduction independently.

Let me very clear. I am not arguing against thinking of things in terms of cause and effect in appropriate situations. I am simply saying that in this case, the notion of "cause" is not a particularly useful one.

In other situations, cause is an extremely useful notion. It is not a one-size-fits-all concept.

There is no "cause" for one path being longer than another path. There are characteristics that make one path longer than another, but "cause" to me is quite a different thing.

On the other hand, if you want to chase this philosophical ghost, then that is OK with me.

DrRocket
2010-Mar-26, 07:40 PM
I never said that the shortest path being a straight line was a cause, that's a theorem! What I did say is that in light of that theorem, anything that "causes" deviation from the straight line "causes" the distance to increase. That's what I said, and it's a perfectly standard way for us to think about causes, we do it all the time in our daily lives to great usefulness.Again I haven't the vaguest idea why you think that is a valid analogy with what I am talking about above.

Yep a straight line is the shortest path, and anything that makes a path not a straight line will guarantee it is not the shortest path.

A lion is a cat and whatever makes a giraffe not a cat makes it not a lion. So, apparently hooves are the cause of a giraffe not being a lion.

macaw
2010-Mar-26, 08:04 PM
Nowhere was it claimed that two situations that involved different acceleration could not produce the same proper time,

:lol: You argued (repeatedly) that "acceleration causes proper time (sic!).

Ken G
2010-Mar-26, 08:16 PM
A lion is a cat and whatever makes a giraffe not a cat makes it not a lion. So, apparently hooves are the cause of a giraffe not being a lion.Again, a poor analogy. An analogy far closer to the issue at hand would be to say that if we constrast two animals, one that is a lion and the other that is a lion which has had its head removed and replaced by the head of a giraffe, then the "reason" or "cause" of one of the animals not being a lion is the operation that was done on it. That's the analogy to how acceleration "causes" a clock to not follow the path of least proper time between two events. Is there such a thing as "argument by intentionally bad analogy"?

But let's agree that you don't like thinking in terms of causes, and I do. Let's go back to the original purpose of this aside, and look at macaw's original bold assertion that acceleration is not the cause of the decreased proper time. To support that claim, he cited a link that said you can look at a kinked path comprising of two straight lines, i.e. two inertial paths connected by a kink, and claim that the existence of such a path is an argument that acceleration cannot cause the difference in proper time, because such a path is made of two inertial pieces. I said that argument was bogus, expressly because connecting two inertial paths with a kink (i.e., with a change of velocity), was hardly a way to claim that acceleration (i.e., a change in velocity) is not the cause here. You can certainly hold to the position that causes of the decreased time are not a productive thing to ask about, but that's not the same as concluding that macaw's argument is valid. What we really need here is a precise understanding of why we are looking for causes and reasons, and when we should just not bother with that effort.

Ken G
2010-Mar-26, 08:30 PM
:lol: You argued (repeatedly) that "acceleration causes proper time (sic!).To slaughter what I said, perhaps. And I would also argue that selling an item that others want to buy causes them to pay you the amount that it is worth to them. Using your exact logic, that could not be true, because people can pay the same price for different objects, so how could their desire be the cause of what they will pay? The logic is identical, and wrong for the same reason. But you just chose to ignore that. I'm not surprised, you would have to.

Jeff Root
2010-Mar-26, 08:42 PM
I have a couple of replies to uncommonsense ready to post, and a
couple more to dhd40 being drafted. These are replies to posts back
on page two of the thread. I'll post them all when I'm done.

Right now I want to give my take on the question of "causes".

It is clear to me that acceleration is an enabling factor which makes it
possible for one twin to age more than the other. The time spent in
relative motion is the direct cause, but that relative motion cannot
happen unless one of the twins accelerates more than the other.

We can imagine a universe in which two clocks have always been in
motion relative to each other, and will always have that same relative
motion. Time dilation still affects these two clocks in exactly the same
way as it affects the twins, even though neither clock ever accelerates,
but the time dilation can never be observed because the clocks cannot
be synchronized or compared at more than a single instant.

Relative motion causes the time dilation; accelerations cause the relative
motions and enable observation of the time dilation.

-- Jeff, in Minneapolis

Ken G
2010-Mar-26, 08:55 PM
It is clear to me that acceleration is an enabling factor which makes it
possible for one twin to age more than the other.
Yes, I think "enabling factor" has much the same meaning as "cause". Lest people think this is becoming a semantic discussion of little import, let me try to make it more concrete by pointing out that the issue in science of "what is a reason" is closely allied with "what counts as an explanation", and these are quite important, though very subtle, issues. Let me address how the search for reasons might apply to the fact that the proper time registered on a clock depends on the path it takes.

Imagine the following discussion in a gravity-free environment:
A:" I have here a clock that was at two events, but did not register the maximum proper time between them. Why not?"
B: "Apparently it did not follow an inertial path between them."
A: "But why didn't it follow an inertial path?"
Now we have two choices for B. B can now choose, without error, to adopt a DrRocket-esque stance:
Ba: "It just didn't. Why ask why?"
Or, B can try to dig into it a little deeper, and see the asking of why as a means toward asking other useful questions:
Bb: "Hmm, well, does the clock have a big rocket engine attached to it, or is it on a different rocket than it started out on?"
This is how seeking causes and reasons gets us deeper into understanding what is going on, and why the search for reasons is not sheer semantics. It guides us toward asking useful questions, like is there a rocket engine around here somewhere. Or, to directly address macaw's link, if there was any passing of the clock between rockets going on (which also accelerates the clock, of course).

DrRocket
2010-Mar-26, 10:24 PM
The issue here is not the definition of a straight line, which admits many options that all spawn the same meaning. The issue is, what are the logical imperatives associated with a straight line.

In that case the "cause" (of damn near everything mathematical) is the Zermelo-Fraenkel axioms, plus choice. But that is not very satisfying.

macaw
2010-Mar-27, 02:44 AM
But let's agree that you don't like thinking in terms of causes, and I do. Let's go back to the original purpose of this aside, and look at macaw's original bold assertion that acceleration is not the cause of the decreased proper time.

....because it isn't the only reason. I have been telling you this since post 78, hence the counterexamples. I am trying to show you that there are other reasons that are responsible for difference in the elapsed proper times. This is why I gave you examples where:

-acceleration does NOT cause differences in elapsed proper time
-differences in elapsed proper time are observed in the ABSENCE of acceleration

Do you understand proof through counterexample?

To support that claim, he cited a link that said you can look at a kinked path comprising of two straight lines, i.e. two inertial paths connected by a kink,

Umm, first off, I gave you a counterexample that contained no "kinks" (just an open path).
Second off , I gave you a counterexample that contains two independent straight line paths, with two clocks. This example is actually a classical counterexample for the people that claim that "acceleration causes proper time (http://www.bautforum.com/space-astronomy-questions-answers/102117-mechanical-reasons-tr-clock-slowing-4.html#post1706734)" (sic!)
Finally, I gave you another counterexample that uses two counter-revolving clocks that are continously accelerated , yet showing the same elapsed proper time.

and claim that the existence of such a path is an argument that acceleration cannot cause the difference in proper time, because such a path is made of two inertial pieces. I said that argument was bogus, expressly because connecting two inertial paths with a kink

The paths aren't "connected", they are two independent paths, so there is no acceleration present. I made it quite clear that there is frame jumping though (I made this point about three times) and that the twin that "lives" in the same frame throughout the duration of the experiment experiences the longest elapsed proper time. I think that I mentioned this about three times as well. How could you have missed this important "detail"?

DrRocket
2010-Mar-27, 03:08 AM
AgIs there such a thing as "argument by intentionally bad analogy"?

No, but there is certainly "argument by misrepresenting the other guy", which is what you are doing. It is also known as the straw man technique, which has been perfected by politicians. Answer the question that you wish they had asked and counter the argument that you wish they had made.

Jeff Root
2010-Mar-27, 03:41 AM
That's much more what macaw is doing, rather than Ken, or even you.

-- Jeff, in Minneapolis

Jeff Root
2010-Mar-27, 03:43 AM
I'd say that time dilation and length contraction are physical, but not
mechanical. Instead, they are geometric. It isn't possible to have time
dilation without length contraction, and it isn't possible to have length
contraction without time dilation. They are two different aspects of the
same phenomenon: Geometric distortion of spacetime.

One clock undergoes time dilation and length contraction relative to
another clock when it is accelerated so that it has a different speed for
a while. In order to compare the two clocks it is necessary to accelerate
the first clock a second time, to bring it back to the unaccelerated clock.

I look up and see the tip of the antenna on the Empire State Building.
It is at an angle of 50 degrees up from the horizontal. My friend, talking
with me on his cell phone, says that he, too, is looking up at the tip of the
Empire State Building's antenna, but that it is at an angle of 70 degrees up
from the horizontal. The difference between what I see and what he sees
is not a change in the Empire State Building, nor is it a difference between
he and I, but it is a difference between my geometric relationship with the
ESB and his geometric relationship with the ESB. Different measurements
of time due to time dilation works very similarly.
Jeff,

I feel I must humbly suggest that this answer is a non-answer to my query.
I understand time is simply a ratio, and length is a parameter thereof.
I agree that it is a non-answer. On the other hand, you aren't asking
relativity. You're actually asking "What is time?".

"What is time? If someone asks me, I know. If I wish to explain it
to him who asks, I know not." -- Augustine, Confessions, 398 AD.

I know what time is, through experience. The fact that you think
time is a ratio tells me that you don't know what it is. I expect
that understanding relativity would be quite a problem for someone
who doesn't know what time is. Unfortunately, I doubt that I can
do any better than Augustine in explaining time. It is so basic a
thing that it really can only be learned through experience.

Further, my feeble mind cannot find any meaning in comparing the two
returned twins in the classic example to the antenna in your example.
What have I missed? It wouldn't be the first time I have been confused.
The comparison is simple, not deep. My friend and I see different
angles to the top of the Empire State Building because our locations
are different. The twins measure different times for their separation
because each twin's history of acceleration is different. The main
reason for this comparison was to show how a difference between two
measurements can be real without any physical difference between the
observers or any change in the thing being measured. It was intended
for other discussions and may be of only marginal use here.

The comparison that I hope you'd get is that the difference between
observations of the ESB is due to geometry (3-D Euclidean), and the
difference in ages of the twins is due to geometry (4-D Reimannian,
with time being one of the four dimensions). In both scenarios, the
difference in measurements is due purely to differences in the
geometric relationships.

-- Jeff, in Minneapolis

Jeff Root
2010-Mar-27, 03:44 AM
Well, start by considering just what is an hour - an hour is
NOTHING more than the standardized syncronization of the earth's
rotation and a machine / device, (clock), 24 of which represent
one full rotation of the earth. So when a clock MOVES 1 hour,
the earth MOVES 1/24 rotation.
An hour is approximately 1/24th of a day, but the length of a day
varies considerably, due to several different causes. Some of the
variations make it desireable to occasionally add a leap second
at the end of December or June, in order to keep the standard
clocks synchronized with the Earth. So motion of the Earth does
not define time, because Earth's motion varies, and standard clocks
do not define time, because they are adjusted to conform to the
motions of the Earth.

Time is simply a comparison of motion of different objects. Thats it.
What motions of what objects?

So, to say time slowed, is really saying motion of one thing
changed in relation to another thing. That's it.
Give a real example. GPS satellites show relativistic time dilation.
Use them for your example. At the altitude of the Navstar satellites,
clocks aboard those satellites are slowed by their relative motion by
about 7 microseconds per day compared to clocks on the ground, and
effectively speeded up by their separation from Earth's gravity by
about 45.9 microseconds per day compared to clocks on the ground.
The combination of these two relativistic effects gives a net speeding
up of Navstar clocks of about 38 microseconds per day compared to
clocks on the ground.

What motions of what objects are compared when the relativistic
effects on Navstar clocks is observed?

To say time slows is actually saying motion or distance decreased.
It's that simple.
What motion or distance decreases (or increases) in the case of the
Navstar clocks?

-- Jeff, in Minneapolis

Jeff Root
2010-Mar-27, 03:50 AM
I'd say that time dilation and length contraction are physical, but not
mechanical. Instead, they are geometric. It isn't possible to have time
dilation without length contraction, and it isn't possible to have length
contraction without time dilation.
Then, why do the twins see a "real and permanent" time difference
(after return of the travelling twin) BUT no "real and permanent"
length difference?
There's no reason to think it shouldn't be that way. Time and length
are not the same.

displacement in space returns to zero, but your displacement in time
continues to increase.

I look up and see the tip of the antenna on the Empire State Building.
It is at an angle of 50 degrees up from the horizontal. My friend, talking
with me on his cell phone, says that he, too, is looking up at the tip of the
Empire State Building's antenna, but that it is at an angle of 70 degrees up
from the horizontal. The difference between what I see and what he sees
is not a change in the Empire State Building, nor is it a difference between
he and I, but it is a difference between my geometric relationship with the
ESB and his geometric relationship with the ESB. Different measurements
of time due to time dilation works very similarly.
(my bold)I don't think so. When your friend comes to your place, you
will, both, agree on the same angle. Very different from the twin's time
dilation situation
While we were staring at the top of the ESB, we both got stiff necks,
which remained stiff after we got back together. His neck is in worse
shape than mine because he was looking up at a higher angle. Some
things go back to their former values; some things only increase; some
only decrease; some go all the way back down to zero. Some things
depend on location; some depend on direction; some depend on time;
some depend on speed; some depend on acceleration.

-- Jeff, in Minneapolis

Jeff Root
2010-Mar-27, 03:52 AM
Something "inside" the particle must have happend during its
acceleration phase.
Nothing needs to happen during the acceleration. The acceleration
is just a means to get the particle or whatever into a different
state of motion relative to some observer than it had previously
been in. What happens "inside" is completely irrelevant. What is
relevant is the geometric relationship in spacetime between the
observer and the observed.

The amount of time dilation is directly proportional to the speed
difference, and to the length of time spent with that difference.
It is independant of the acceleration or the length of time spent
accelerating.

-- Jeff, in Minneapolis

Jeff Root
2010-Mar-27, 03:54 AM
Just ask yourself if all motion in the universe stopped would
time stop? Or is there an independent notion of time that does
not depend upon motion of something?
Motion depends on time. Time makes motion possible. In general,
time makes change possible. Without time, nothing could change,
and nothing could move. The passage of time does not guarantee
change, but the existence of change shows that time has passed.

Time is what the motion of a clock measures, but the motion of a
clock is not time.

-- Jeff, in Minneapolis

macaw
2010-Mar-27, 04:28 AM
That's much more what macaw is doing, rather than Ken, or even you.

-- Jeff, in Minneapolis

You will need to back up your assertion. What did you understand from my posts?

macaw
2010-Mar-27, 04:34 AM
There's no reason to think it shouldn't be that way. Time and length
are not the same.

displacement in space returns to zero, but your displacement in time
continues to increase.

This is not the reason. You obviously don't understand the relativistic effects that govern length contraction and differential aging of the twins.
The physical explanations have nothing to do with your simplistic and naive attempt at explaining the two effects.

macaw
2010-Mar-27, 05:36 AM
Hardly. Proper time is measured by a clock, and what the clock measures between any two specified events is found to be determined entirely by its path between the two events.

Wrong, it isn't determined by the path, it is determined by the length of the path. See the proof in post 100.

Jeff Root
2010-Mar-27, 05:56 AM
You will need to back up your assertion.
Okay, here's an example:

Hardly. Proper time is measured by a clock, and what the clock measures
between any two specified events is found to be determined entirely by
its path between the two events.
Wrong, it isn't determined by the path, it is determined by the length of
the path.

What did you understand from my posts?
That you like to tell people who know what they are talking about that
they don't know what they are talking about. That's the main thing
I get from your posts. There is some physics in them, too. It isn't
all bluster. But the bluster is what stands out.

-- Jeff, in Minneapolis

Ken G
2010-Mar-27, 12:25 PM
....because it isn't the only reason. I have been telling you this since post 78, hence the counterexamples.I realize you have been repeating that point, but it is incorrect. The only thing you need to know about a spacetime path, to determine whether or not it is going to give the maximum proper time between two events, is whether or not an object following that path is accelerated or not. That's it, the answer to the second question is the answer to the first. If you want to know how much the proper time deviates, you need to know the details about when and how much acceleration occured. That's it, that's all you need to know to do it. You are claiming that just because these details about the acceleration matter, somehow that is a proof that acceleration is not the cause or reason for the deviation. That's incorrect, which is what I keep repeating to you.

Do you understand proof through counterexample?
I understand irrelevance being misrepresented as counterexample.

Umm, first off, I gave you a counterexample that contained no "kinks" (just an open path).And I told you why that was irrelevant. I guess I have to again: we are comparing proper times over spacetime paths that share the same endpoints. Hence DrRocket's comment about the calculus of variations. I will assume you know the assumptions that go into the calculus of variations-- DrRocket does, and so do I.

Second off , I gave you a counterexample that contains two independent straight line paths, with two clocks.Again look up the calculus of variations-- we are discussing paths that share the same endpoints, so examples that do not are irrelevant and cannot logically be construed as counterexamples. To spell it out for you, what I have said is that acceleration causes, or is the reason for, the differences in proper time, among paths that share the same endpoints. That is what the entire discussion is about, as I have repeated many times now.

inally, I gave you another counterexample that uses two counter-revolving clocks that are continously accelerated , yet showing the same elapsed proper time.And I already told you why the fact that two different accelerations can yield the same proper time does not prove acceleration isn't the cause of deviations in proper time. I will assume you know what a many-to-one function is, and how it is still a type of function. The presence of a function that connects an output to an input is one very classic way that we physicists look for the reason that things are the way they are, even many-to-one functions.

The paths aren't "connected", they are two independent paths, so there is no acceleration present.You need to read your link again. It involves the calculation of a proper time over a spacetime path that has a kink in it. That is simply a fact, denying it doesn't change it.

Ken G
2010-Mar-27, 12:28 PM
Wrong, it isn't determined by the path, it is determined by the length of the path.I'd say the logical content of that statement pretty much sums up the quality of the argument you are presenting. As there isn't much progress going on, I'll simply take this moment to sum up the points I am making:

1) When talking about proper times elapsing (on clocks, empirically) between two specified events, what determines whether or not the maximal proper time occurs is whether or not a clock following that path undergoes acceleration (if we ignore gravity for simplicity). Further, how much it deviates from the maximal proper time is determined by the details of when and how much acceleration (proper acceleration, of course) occured, and nothing else. Ergo, it is natural to associate the details of the acceleration as the determining cause, or reason, that the elapsed proper time between any two events is what it is. This leads us to look for the physical elements of the problem that are capable of causing acceleration of a clock when we want to understand the elapsed proper time between any two events that clock is present at (called "proper time"). Of course, all that is also tantamount to saying that the spacetime path determines the proper time between events, but this purely mathematical statement is not as helpful in motivating our search for the processes capable of inducing acceleration, when we want to understand why the path was what it was. (This is also why the low-velocity version of this theory, Newton's laws, focus entirely on acceleration.)

2) Observers have reference frames, they do not "move through a sequence" of them, nor borrow them from a mathematical theory. However, the postulates of special relativity apply only to inertial observers, so to use special relativity to understand what noninertial observers experience, we must apply the mathematical artifice of borrowing the reference frames of a sequence of instantaneously comoving inertial observers. This works, but only when there is no gravity, and is a very awkward way of thinking about observers and reference frames. It's fine for getting calculations correct in SR, but it is inferior as a language for talking about what is going on there, and that point should be made when such language is passed off as a description of what is really going on there.

Despite all the smoke and heat above, neither of those claims has been refuted, nor demonstrated as ATM (though it has been claimed), nor are any of the claims of counterexamples relevant to either above statement.

dhd40
2010-Mar-27, 03:52 PM
Time and length
are not the same.

Is this contradicting DrRockets statement in post # 61?

DrRocket: On the other hand, time dilation and length contraction are really the same thing

Jeff Root: Some things go back to their former values; some things only increase; some
only decrease; some go all the way back down to zero. Some things
depend on location; some depend on direction; some depend on time;
some depend on speed; some depend on acceleration.

-- Jeff, in Minneapolis

OMG, please bear with a papermaker :(

grav
2010-Mar-27, 04:37 PM
It is interesting how many different views are contained within this one thread. Ken is looking at the cause in terms of the physical attributes with the acceleration required of a single observer when switching frames, I am looking at the cause in terms of the mathematical deviations with the relativity of simultaneity between the frames themselves, DrRocket claims there is no real cause because it is all just a manifestation of the wordlines using spacetime rather than space and time, macaw is comparing the lengths of paths of observers, Jeff Root is comparing the perspectives of the observer's realities, dhd40 is comparing the permanent differences in time and length that result, and uncommonsense is looking for the mechanical cause in terms of the motion involved, while Strange claims that something is not mechanical if no moving parts have ever yet been observed. With all of these different outlooks on things, is this perhaps why philosophy is still so important to science? Is this why it is difficult to gain and maintain a consensus in science as well?

Ken G
2010-Mar-27, 05:15 PM
It is probably one of the main reasons that the language of physics is mathematics, not philosophy-- of all the perspectives, only the mathematics is the same. So the overriding moral of this cautionary tale is: beware when ye leave the language of the mathematics. Nevertheless, physicists always do, because "shut up and calculate" just never really foots the bill, even among those who purport that view.

grav
2010-Mar-27, 05:35 PM
Time and length
are not the same.Is this contradicting DrRockets statement in post # 61?In that post, DrRocket was not referring to the resulting permanent lengths and times observers measure of each other when they become stationary again, but to the measure of spacetime intervals along the paths of travel. In this case, one observer's measure of time becomes another observer's measure of length, but it is all the same thing in terms of the overall path of the worldlines involved. In the example given in the post, while in motion to each other, an Earth observer measures a time dilation for the muon with the further distance it passes through the Earth's atmosphere in relation to its relative speed so the muon takes longer to decay, while from the muon's frame, the Earth's atmosphere is length contracted, so the muon travels a further distance through it in a normal time of decay while considering the muon at rest.

Jeff Root
2010-Mar-27, 06:31 PM
Time and length are not the same.
Is this contradicting DrRockets statement in post # 61?

DrRocket: On the other hand, time dilation and length contraction
are really the same thing
1) Yes
2) No
3) It depends on whether DrRocket said what he meant.

I was very aware that I was contradicting his statement, and wondered
if you would bring it up. Very first thing. Hmph.

I agree with what I think DrRocket meant, but I disagree with a literal
interpretation of what he said. He also said (as have I) that time and
length are aspects of the same thing. I am emphasizing that they are
different aspects of the same thing, although that statement logically
follows from simply saying that they are aspects of the same thing.
In any case, time and space are not the same thing, and I think
DrRocket will readily agree with that.

Just as important as the fact that time and space are different is the
fact that they are aspects of a single thing, which we call spacetime.
So whenever there is a change in spacetime, there is a change in both
space and in time. It is physically, geometrically, and logically impossible
to have a change in one without a corresponding change in the other.
When you have some amount of time dilation, you have a corresponding
amount of length contraction, and vice-versa.

Some things go back to their former values; some things only increase;
some only decrease; some go all the way back down to zero. Some things
depend on location; some depend on direction; some depend on time;
some depend on speed; some depend on acceleration.
OMG, please bear with a papermaker :(
I wasn't at all sure that that would be helpful. Can you explain to me
what is wrong with it so that I can improve it or try something else?
Should I write up a more detailed description of either the analogy to
angles or some other analogy? Or are analogies not helpful? I like
analogies, myself, so I use them whenever possible.

-- Jeff, in Minneapolis

macaw
2010-Mar-28, 04:24 AM
we are comparing proper times over spacetime paths that share the same endpoints.

macaw
2010-Mar-28, 04:27 AM
It is probably one of the main reasons that the language of physics is mathematics, not philosophy-- of all the perspectives, only the mathematics is the same. So the overriding moral of this cautionary tale is: beware when ye leave the language of the mathematics.

But you are unable to use the language of mathematics, you reduce any discussion to your philosophy level. Even worse, you can't follow the simplest mathematical presentations (see your inability to understand post 100)

Ken G
2010-Mar-28, 04:30 AM
But you are unable to use the language of mathematics, you try reducing any discussion to your philosophy level. Your inability to tell mathematical language when it is not framed in terms of basic arithmetic is an issue I have pointed out to you many times, as has the mathematician DrRocket, apparently to no avail. Again, no one is interested in your personal assessment of my mathematical capabilities, you only recognize arithmetic arguments, which is a relatively low form of mathematical thinking. The arithmetic behind post #133 is elementary, and in no way bolsters what is said there, because what is said there is at the deeper level of how physics works independently of the coordinates that can be plugged into metric expressions and arithmetic computations. I'm sorry you don't understand that, but I don't know how else to say it.

macaw
2010-Mar-28, 04:31 AM
You need to read your link again. It involves the calculation of a proper time over a spacetime path that has a kink in it. That is simply a fact, denying it doesn't change it.

There is no "kink" since there is no turnaround. There would have been one if there was a turnaround. But there isn't any.

macaw
2010-Mar-28, 04:34 AM
All the same, it is the subject we are talking about. You are missing a good conversation.

The conversation has nothing to do with physics.

macaw
2010-Mar-28, 04:37 AM
Despite all the smoke and heat above, neither of those claims has been refuted, nor demonstrated as ATM (though it has been claimed), nor are any of the claims of counterexamples relevant to either above statement.

Most ATM proponents claim the same exact thing notwithsanding that their claims are shown to be ATM.

Ken G
2010-Mar-28, 04:50 AM
Most ATM proponents claim the same exact thing notwithsanding that their claims are shown to be ATM.This argument is pure logical fallacy. Do you need the name of the fallacy? On this forum, if your logic is faulty, you should expect to have that pointed out to you.
There is no "kink" since there is no turnaround. The link talks about a proper time that is associated with a spacetime path. Yes or no? That spacetime path is which of the following:
a) straight
b) curved
c) kinked
d) none of the above.

DrRocket
2010-Mar-28, 04:54 AM
In any case, time and space are not the same thing, and I think
DrRocket will readily agree with that.

Time and space are effects of a choice of coordinates in spacetime.

Unless and until you select a specific local reference frame (i.e. choose a set of coordinates) there is no meaning to either time or space, only to spacetime. One observer's time is another observer's space, even locally. Globally, there is no meaning at all to either time or space.

So, yes I agree that time and space are not the same thing, in any given local reference frame. They are not even invariant well-defined entities. That is the lesson of relativity. It is not time and space it is spacetime. Space and time are inextricably intertwined.

Ken G
2010-Mar-28, 05:55 AM
So, yes I agree that time and space are not the same thing, in any given local reference frame. They are not even invariant well-defined entities. That is the lesson of relativity. It is not time and space it is spacetime. Space and time are inextricably intertwined.This is certainly an effective and standard way of looking at the situation, and I'm largely in agreement. However, to make contact with empiricism, which I do feel is an important goal of physics, we can say a bit more. We can take your first sentence and expand its meaning, as saying that time and space actually do exist in a local reference frame, i.e., they exist, as different things, for an observer, but in very different ways I'll expand on. What's more, a different version of (integrated) time and (infinitesmal) space will exist for each different observer-- time and space are owned by the observers (hence "proper", or really "propre" in the French meaning of "owned by"). They are part of the observer reality.

However, as you say, they are not invariants when they are extended to mean anything other than what a particular observer can measure with a clock or a ruler, which makes us suspicious that these extensions have parted company from objective reality. It is interesting to note that we suffer no such problem if we restrict to the empirical reality, i.e., to the measurements on clocks and rulers, along with the information of who or what did the measurement (including hypothetical measurements, like the lifetime of an elementary particle in its rest frame).

So time and space are indeed real, and different from each other, but they are a reality that is owned by the observer, and are not extendable to "global inertial reference frames" and other such special relativistic fictions. Having thus rended each observer into a kind of separate reality, we must not leave it so in an objective science like physics-- we need to connect the observers, so that each observer's physics includes being able to calculate what other observers will observe-- what other observers observe is also part of the reality we wish to understand. Enter spacetime.

Sticking to this empirically supportable description, the only integrated observation possible by a single observer is proper time. All other integrated (quasi-global) quantities are intellectual constructs involving arbitrary coordinate choices, such as the proper distance between us and a simultaneous event in the Andromeda galaxy. To the extent that a ruler is short enough that it can be construed as rigid, a single observer can measure proper distance, but only locally, it's not the same thing as a time measurement, which is integrated nonlocally.

Here's the point: in this more empirical view, spacetime is the exact same thing as proper time, accounting for all real and hypothetical observers who could measure a proper time along any and all possible spacetime paths. The global "space" part is pure intellectual construct, a kind of web or milieu for weaving together all these various different observers and their proper times, the milieu in which all the separate empirical realities unite into a single coherent whole. As this whole is coherent, any observer can use it to discern what other observers will experience, but all we are really talking about here is their proper times, and the only comparisons we need to make are between proper times that begin and end in the same two events.

So it might be more correct to say, instead of space and time have no independent meaning, rather that the only non-infinitesmal entity that has independent meaning is the time between two specified events, elapsed for a clock that is at both events. A separate reality is then given to the infinitesmally small rigid rulers that generate the concept of local space that "tags along for the ride" with these clocks, and we use that local spatial concept to bring in the concept of the locally constant speed of light. It all spawns a local physics that can single out the action of rigid matter, which is probably a necessary thing to do if we want to elevate time to a real quantity and have a concept of empiricism in the first place. In short, the necessary role of space is quite subtle, but I think we need it to have measurements at all.

After that, space plays no independent role-- it is pure mental convenience, pure coordinatization, with no integrable global empirical reality but exhibiting more and less convenient ways to use it. So it is indeed quite different from time. The spacetime is like spaghetti-- lots of thin worms of empirical experience (real or hypothetical), weaved together into a coherent whole by measurable concepts of length (proper time) and thickness (infinitesmal rigid distances) of the spaghetti strands. And if we find physical objects traipsing around between specified events, we can understand their dance by knowing the sources of acceleration of the objects, and the milieu of proper times that connect those events.

dhd40
2010-Mar-28, 10:11 AM
Can you explain to me
what is wrong with it so that I can improve it or try something else?

-- Jeff, in Minneapolis

I don't think that there's something "wrong". I simply didn't understand the context

macaw
2010-Mar-28, 01:41 PM
The link talks about a proper time that is associated with a spacetime path. Yes or no? That spacetime path is which of the following:
a) straight
b) curved
c) kinked
d) none of the above.

a). Straight. You need to read (and try to understand the gedank). There are two straight paths for two different clocks. There is no acceleration. Yet, there is differential in elapsed proper time. It is a very simple explanation, really. I don't know why you have so much trouble with it.

DrRocket
2010-Mar-28, 02:33 PM
Here's the point: in this more empirical view, spacetime is the exact same thing as proper time, accounting for all real and hypothetical observers who could measure a proper time along any and all possible spacetime paths.

I am OK with your perspective up to here, at least if forced to look at things through the eyes of an empiricist (in which case large corrections for myopia are required).

Proper time is a scalar -- one dimensional. Spacetime is 4-dimensional. They cannot be the same thing, even locally.

Looking at spacetime as strands of "proper time spaghetti" interwoven does not seem to help. If anything, I find it obscures things -- a tangled ball of soggy pasta. I think you are way beyond merely speculative here.

Ken G
2010-Mar-28, 03:32 PM
a). Straight. You need to read (and try to understand the gedank). There are two straight paths for two different clocks. I'm sorry, the correct answer was (c). The gedank involves a proper time comparison. Yes? The proper time comparison is between the inertial path between the events, and another path. So far so good? That other path is (c), kinked.
It is a very simple explanation, really. I don't know why you have so much trouble with it.I guess I know a kink when I see one.

Ken G
2010-Mar-28, 03:50 PM
I am OK with your perspective up to here, at least if forced to look at things through the eyes of an empiricist (in which case large corrections for myopia are required). I realize you are just being snarky, but I point out, without fear of contradiction, that no use of mathematics in physics would be the least bit useful if empiricism did not work first. Further, most people are quite comfortable framing physics as an empirical science. And didn't Feynman say that science is the belief in the ignorance of experts? Empiricism embodies that mindset, because in empiricism, nature itself is the only expert.

Proper time is a scalar -- one dimensional. Spacetime is 4-dimensional. They cannot be the same thing, even locally.The way I described proper time is not one-dimensional. I realize that the standard way to think of proper time, mathematically, is as a mapping from spacetime paths to the complex plane. But I have offered a different way to interpret proper time, which is empirical-- it is the time elapsed on a clock that follows any possible spacetime path, including the clock (and the path) that registered it. Remember, empirically, what is real is statements of the form "clock A measured a", including all the necessary information about clock A. That the clock reads the proper time is a mapping onto the reals, but the proper time itself includes what is doing the reading.

That is what I am saying spacetime is, along with the concept of the infinitesmal space occupied by rigid objects (most notable, rulers), which I feel is necessary to give measurements meaning (we need to build the clocks out of something, and we need that something to support a concept of rigidity and speed of light). So the result of all this is that proper time is not one-dimensional, it is the spaghetti that links the events of spacetime-- the length of the spaghetti and the spaghetti itself (a proper time does not have its meaning if its just a number on a clock-- you need to know something about the clock or the number is not helpful).

Looking at spacetime as strands of "proper time spaghetti" interwoven does not seem to help. If anything, I find it obscures things -- a tangled ball of soggy pasta. I think you are way beyond merely speculative here.Actually, my way of framing things is not that unusual. A more common methaphor is tree limbs (a "foliation"), but I think spaghetti is actually better, as it conveys the density of these paths a bit better. The people who use "foliations" understand the precise meaning of the term far better than I, what I am using is my physics-sense to frame it in an empirically supported way. I am confident the connections are fairly direct, though I am not suggesting my way of looking at it is anything but a useful picture-- I'm not about to use it do calculations I have not the expertise to carry out.

grav
2010-Mar-28, 04:56 PM
Sorry Ken, but I think DrRocket's assessment of that particular post is a fair one, as I was thinking the same thing about those couple of things he pointed out. Maybe it was a late night? ;) On a lighter note, if spacetime were a ball of yarn, would it then be string theory? Just kidding. :shifty: Maybe it's too early for me now. :)

...no use of mathematics in physics would be the least bit useful if empiricism did not work first. Further, most people are quite comfortable framing physics as an empirical science. And didn't Feynman say that science is the belief in the ignorance of experts? Empiricism embodies that mindset, because in empiricism, nature itself is the only expert.I like the way you put that, though. It makes sense.

I have a question. Spacetime is said to be a four dimensional entanglement of three dimensions of space and one dimension of time. But if that were the case, wouldn't it really just be the same as Euclidean space and regular time? I mean, that is the way I have always thought of Euclidean space anyway, a portion of three dimensional space represented by a cube and time represented by the motion of a particle through the cube. That is four dimensional simply by combining the space with the motion of the particle in a normal way. But spacetime does more than that. The same dimensions of space and time are still represented in precisely the same way, but only from the perspective of a particular observer. So if we were to change to the perspective of another observer with some relative speed to the first, then the dimensions of the space of the cube and the motion of the particle will change. So isn't that representative of a fifth dimension, one that takes the individual perspectives of each particular observer into consideration?

Ken G
2010-Mar-28, 05:32 PM
Sorry Ken, but I think DrRocket's assessment of that particular post is a fair one, as I was thinking the same thing about those couple of things he pointed out.No, you are both missing my point, which is not terribly surprising given that what I'm saying is quite foreign to the standard language we usually deal with. Yet, there's nothing speculative about it, it is perfectly true to the tenets of both empirical physics and relativity. Let me try to say it another way.

Back when we thought time was absolute, it was natural to think time was just a number, like "5 seconds", and it didn't matter which clocks measured it. But with relativity, we found that time cannot be divorced from the clock registering it. Specifically, two clocks can be present at the same two events and register different elapsed times. Ergo, we need a new concept of time ("proper" time), which is not divorced from the clock measuring it-- it is not just a number any more. Instead, it is a more sophisticated notion-- the number ("5 seconds") is still there, but now it only has meaning when considered along with the clock, including the motion of the clock between the two events in question. When time is framed in this more complete way, we find that it is the stuff of spacetime-- there is nothing more that one needs to know (with one exception I'll get to), to understand and use spacetime, other than the proper time registered by clocks (real or hypothetical) that link any two events along every possible path.

So what is the exception I mentioned, and what happened to space? Space is the exception-- we also need an infinitesmal concept of local space, mediated by the concept of rigid rulers, to allow ourselves to talk about time measurements. That's also where the speed of light, as a physical parameter, comes into play-- it is embedded in our understanding of rigid materials, without which empiricism itself would be impossible.

I have a question. Spacetime is said to be a four dimensional entanglement of three dimensions of space and one dimension of time. But if that were the case, wouldn't it really just be the same as Euclidean space?No. When one envisions spacetime as a global manifold, it does not need to support Euclidean geometry. Indeed, there are two ways it can deviate-- it can have a non-Euclidean metric, and it can be curved. The curvature can be locally handled by looking at flat tangent spaces, but the Minkowski metric is still different from a 4D Euclidean metric.

Nevertheless, other spaces can be substituted for spacetime to restore the 4D Euclidean metric of the tangent spaces. One example is what I call "myspaceyourtime", where I take the proper time of any object I (the observer) am interested in, and conceptualize that object as moving through my own concept of space (locally, using my rigid ruler, or if there's no gravity I can borrow Einstein's global spatial coordinatization). By taking the proper time as the time coordinate (often called "dtau"), and marrying it to my own local distance measurements (often called "dx"), I create a new manifold that supports Euclidean tangent spaces-- and the Euclidean metric on that tangent space gives me the result of my Einsteinian (local) time coordinate (often called "dt"). This coordinatization also has the advantage of being comprised of the two elements that I have mentioned above as being the "real stuff" of spacetime-- the (integrable empirically) proper time dtau, and the (nonintegrable empirically) local proper distance dx, where the former is measured by a single clock, and the latter by a single rigid ruler.

I mean, that is the way I have always thought of Euclidean space anyway, a portion of three dimensional space represented by a cube and time represented by the motion of a particle through the cube.You may have pictured that as 4D Euclidean space, and for a long time physicists thought it was, but it isn't.

So isn't that representative of a fifth dimension, one that takes the individual perspectives of each particular observer into consideration?It's a lot more than a fifth dimension-- taking account of who is doing the observer spawns a very different kind of "space" altogether-- a spaghetti space if you will. What is often overlooked about spacetime is that it is only the local instructions for how to generate the whole story-- the whole story involves all the different paths in spacetime, not just the points in spacetime. Standard SR is a differential theory, in that it gives you the local instructions for how to find out what you need to know about these paths, but you still have to integrate that information over the path. The way I'm framing spacetime is already integrated-- the instructions are already associated with the paths themselves. That also connects with our experience, any time we are dealing with time intervals longer than the light travel time across objects we can trust to remain rigid over that time, in that over such times, we are dealing with integrated quantities (basically, with proper times), not local ones.

Basically, everything I'm saying emerges more or less immediately as soon as we require that what we mean by a "time" always involves the elapsed time on a single clock, and never involves an interval that starts at a reading of one clock and ends at a reading of a different clock. As soon as we banish that non-empirical concept of time, we no longer need any simultaneity convention, and many of the convenient fictions of special relativity (such as "relativity of simultaneity"), vanish. I'm not saying there is anything wrong with convenient fictions, they are handy at times-- I'm saying we can dig deeper to find a more empirically supportable version of what space and time "really are."

dhd40
2010-Mar-28, 08:22 PM
Time and space are effects of a choice of coordinates in spacetime.

Unless and until you select a specific local reference frame (i.e. choose a set of coordinates) there is no meaning to either time or space, only to spacetime. One observer's time is another observer's space, even locally. Globally, there is no meaning at all to either time or space.

So, yes I agree that time and space are not the same thing, in any given local reference frame. They are not even invariant well-defined entities. That is the lesson of relativity. It is not time and space it is spacetime. Space and time are inextricably intertwined.

Maybe, it's a perfectly silly remark. But from my SR/GR-layman's point of view, if I look at this

dsē=dxē+dyē+dzē-cēdtē

and focussing on the left side of the equation, I see only SPACE (ds), no time, no spacetime, ...

Which makes me wonder whether space is "real" and time is an "illusion"

grav
2010-Mar-28, 09:10 PM
Maybe, it's a perfectly silly remark. But from my SR/GR-layman's point of view, if I look at this

dsē=dxē+dyē+dzē-cēdtē

and focussing on the left side of the equation, I see only SPACE (ds), no time, no spacetime, ...

Which makes me wonder whether space is "real" and time is an "illusion"The square of the distance measured is dx^2 + dy^2 + dz^2 where dx, dy, and dz are measured along the three spatial dimensions, whereas ds in this case is the Minkowski metric, an interval of spacetime. ds is an invariant, meaning that all observers will measure the same spacetime interval between two events, regardless of the specific frame of the observer or what they measure for the coordinate distance sqrt[dx^2 + dy^2 + dz^2] between the two events with a ruler and the coordinate time they measure dt between the two events with their own clock that remains stationary to them.

Ken G
2010-Mar-28, 10:30 PM
Maybe, it's a perfectly silly remark. But from my SR/GR-layman's point of view, if I look at this

dsē=dxē+dyē+dzē-cēdtē

and focussing on the left side of the equation, I see only SPACE (ds), no time, no spacetime, ...

Which makes me wonder whether space is "real" and time is an "illusion"The way I like to frame it is
dtau2 = dt2 - (dx2+dy2+dz2)/c2
This makes more sense because it is positive when the events are causally connected (i.e., connected period). Then the question you ask is whether only time is "real" and space is the illusion-- that's what I argued above, only I think we need to let local space be real or we do not have a concept of rigid matter and cannot make measurements.

DrRocket
2010-Mar-28, 10:45 PM
Actually, my way of framing things is not that unusual. A more common methaphor is tree limbs (a "foliation"), but I think spaghetti is actually better, as it conveys the density of these paths a bit better. The people who use "foliations" understand the precise meaning of the term far better than I, what I am using is my physics-sense to frame it in an empirically supported way. I am confident the connections are fairly direct, though I am not suggesting my way of looking at it is anything but a useful picture-- I'm not about to use it do calculations I have not the expertise to carry out.

I don't think this is gonna work.

Your spaghetti is way too tangled. You don't have a foliation, you have a tangle.

Maybe some informal discussion and and example of a foliation will help.

A foliation is basically a generalizatioon of a cartesian produce, an indexed set of submanifolds which are disjoint, the union of which is the whole space (here spacetime) and for which the indexing set is also a manifold (and the correspondence is "smooth").

So consider the ordinary plane. A usual set of coordinates is the set of pairs (x,y). But you can also consider the set of all parabolas of the form y=ax^2 +a. That set of parabolas, indexed by the real number a is a foliation of the plane. So you have a map from the plane to itself
(x,a)----->(x, a(1+x^2)) that is invertible which "coordinatizes" the plane.

This is not so interesting for the flat plane, but the concept becomes more useful when you foliate curved manifolds and that is what is done in cosmology, where the indexing manifold is a time-like curve and the leaves of the foliation are space-like hypersurfaces.

You can think of a foliation as a sort of "lamination" of the original manifold, and the laminates do not necessarily have to be flat, of the same curvature or even of constant curvature.

The usual cartesion set of coordinates for the plane foliates the plane as a family of parallel lines indexed by another parallel line, and can be viewed as foliating 3-space as a family of planes indexed by a line, and 4-space as a set of 3-dimensional hyperplance indexed by a line (or a set of planes indexed by another plane).

The formal definition is a bit more mysterious, but that is what it boils down to. http://mathworld.wolfram.com/Foliation.html

Ken G
2010-Mar-28, 11:23 PM
Maybe some informal discussion and and example of a foliation will help.I agree that what I am talking about goes beyond just foliation, as your lucid description demonstrates. A foliation is still trying to create a kind of global coordinatization of the manifold, so it still supports a kind of global concept of space. There's no problem with that, it is fine to think of spacetime as a manifold and it's nice to have the flexibility to coordinatize it even when it is curvy or topologically obscure. What I'm talking about goes even farther-- it throws out the whole concept of a global spacelike submanifold, which is really nothing but a type of conceptual coordinatization, involving arbitrary elements that "nature" hasn't a clue about. Instead, my approach sticks entirely to what are empirical observables, and notes that to do the mathematics of relativity, all you ever would need is the empirically supportable proper times between any two events along every possible path connecting them. Then I added that such empirical times can only be defined if we have a concept of rigid matter, i.e. rulers, so a local concept of space is needed and we cannot banish space entirely (that's also where the physical meaning of the speed of light appears). However, we can banish a global (integrated) concept of space, expressly because no such object can ever be measured by a single instrument (real or hypothetical)-- it would always require some arbitrary choice, because no object, even in principle, could be relied on to be rigid over such scales.

In short, what I'm saying is not just a single global foliation, but more like a set of local foliations, tracking every possible path in spacetime, and only "foliating" over the empirically measurable infinitesmal local distance dx, over which we can rely on rulers to be rigid, and clocks to work like clocks. The foliation set is the "spaghetti".

Now, I'm not suggesting that the spaghetti would be easier to use to do calculations-- no doubt the global foliations work fine in most situations. But they propagate vestiges of the SR fiction of a "global reference frame", albeit noninertial now, so still do not escape the fundamental ontological flaw of the old mechanics. So I'm talking about a consistent picture of what spacetime "really is", meaning, as would be empirically supportable, and for what I'm saying to be valid requires only that it be true that all relativistic calculations could be done if the proper times along all necessary paths were known. These are the "stuff" of the spacetime I'm talking about, and could be computed in the standard ways, but they would pre-exist the calculations-- the calculations would be viewed not as what determines these proper times, but rather as what successfully predicts them.

macaw
2010-Mar-29, 01:35 AM
I'm sorry, the correct answer was (c).

It is not my problem that you don't understand basic relativity. The link is very clear.

I guess I know a kink when I see one.

Obviously not.

DrRocket
2010-Mar-29, 02:18 AM
Maybe, it's a perfectly silly remark. But from my SR/GR-layman's point of view, if I look at this

dsē=dxē+dyē+dzē-cēdtē

and focussing on the left side of the equation, I see only SPACE (ds), no time, no spacetime, ...

Which makes me wonder whether space is "real" and time is an "illusion"

Suppose you called it d(duck). Would that make it a bird ?

ds is NOT SPACE. It is not time either. It really is not anything, but a poor shorthand for the Minkowski metric. ds^2 defines the Minkowski metric. ds does not really exist. It is an extreme abuse of notation.

Ken G
2010-Mar-29, 03:05 AM
It is not my problem that you don't understand basic relativity. The link is very clear.Care to answer the question I put to you? The link does, or does not, contrast the proper time along the inertial path between two events, with the proper time along a kinked path between those two same events. Yes or no?

DrRocket
2010-Mar-29, 03:28 AM
Care to answer the question I put to you? The link does, or does not, contrast the proper time along the inertial path between two events, with the proper time along a kinked path between those two same events. Yes or no?

Restrict attention to time-like curves.

Inertial path = geodesic

Any curve between the end points of the geodesic will have an arc length (aka proper time along the path) less than or equal to the arc length (aka proper time) along the geodesic.

A geodesic is not "kinked" (i.e. not differentiable) and therefore a "kinked" curve is not the geodesic. Ergo the proper time along the non-geodesic/kinked world line will less than than the proper time along the geodesic.

macaw
2010-Mar-29, 03:42 AM
Care to answer the question I put to you? The link does, or does not, contrast the proper time along the inertial path between two events, with the proper time along a kinked path between those two same events. Yes or no?

NO.
The path ain't "kinked". As such there is NO acceleration involved in the experiment just TWO INERTIAL rockets passing each other.
There are TWO DIFFERENT STRAIGHT paths corresponding to TWO DIFFERENT clock carrying rockets moving INERTIALLY . When the first rocket reaches a particular location, the clock on the second rocket "inherits" the proper time read off the first clock (I am quite sure that you can figure by yourself how this is accomplished, it is fairly simple). The procedure is trivial. Lots of freshman students understood it , why can't you?

Jeff Root
2010-Mar-29, 04:55 AM
The path you are talking about appears to be the path of the information
required to determine whether and how much time dilation is measured.
That path is obviously kinked at the point where the information is
transferred from the second clock to the third clock.

-- Jeff, in Minneapolis

DrRocket
2010-Mar-29, 05:13 AM
The path you are talking about appears to be the path of the information
required to determine whether and how much time dilation is measured.
That path is obviously kinked at the point where the information is
transferred from the second clock to the third clock.

-- Jeff, in Minneapolis

???

prove it

dhd40
2010-Mar-29, 09:57 AM
The square of the distance measured is dx^2 + dy^2 + dz^2 where dx, dy, and dz are measured along the three spatial dimensions, whereas ds in this case is the Minkowski metric, an interval of spacetime. ds is an invariant, meaning that all observers will measure the same spacetime interval between two events, regardless of the specific frame of the observer or what they measure for the coordinate distance sqrt[dx^2 + dy^2 + dz^2] between the two events with a ruler and the coordinate time they measure dt between the two events with their own clock that remains stationary to them.

Yes, I think what you say is correct. My question arose from the thought that cēdtē is also a "space-like" dimension because the "time-like" units (e.g. seconds) of c and dt cancel out.
Most probably a very naive thinking.

dhd40
2010-Mar-29, 10:23 AM
Suppose you called it d(duck). Would that make it a bird ?
Why not? If there were only birds on the right side of the equation I wouldn't hesitate to call it duck :):doh:

ds is NOT SPACE. It is not time either. It really is not anything, but a poor shorthand for the Minkowski metric. ds^2 defines the Minkowski metric. ds does not really exist. It is an extreme abuse of notation.

Yes, seems to be in agreement with grav's and Ken G's arguments

macaw
2010-Mar-29, 01:30 PM
The path you are talking about appears to be the path of the information
required to determine whether and how much time dilation is measured.
That path is obviously kinked at the point where the information is
transferred from the second clock to the third clock.

-- Jeff, in Minneapolis

Nope. Wrong on all accounts.

grav
2010-Mar-29, 01:42 PM
The path you are talking about appears to be the path of the information
required to determine whether and how much time dilation is measured.
That path is obviously kinked at the point where the information is
transferred from the second clock to the third clock.

-- Jeff, in MinneapolisIs that all that part of the discussion has been about? I haven't been keeping up. Yes, that sounds perfectly reasonable, and would be the point where the the paths of the two inertial observers that exchange the reading intersect, as it does not matter what the second observer's clock reads after that point or what the third observer's clock read before meeting and synchronizing with the second observer. From the point of view of any observer that sees the first observer travelling away while the second observer moves off at some angle and the third observer travels back, whether in Euclidean space or a Minkowski diagram, the three paths will form a triangle. The time dilation observed is the same with the same relative speed both ways and there is no acceleration involved, but the point of intersection on that triangle where the reading is exchanged is where the simultaneity shift between the frames takes place. At least, that's what it would be mathematically, so that is the way I am looking at it.

grav
2010-Mar-29, 02:23 PM
Yes, I think what you say is correct. My question arose from the thought that cēdtē is also a "space-like" dimension because the "time-like" units (e.g. seconds) of c and dt cancel out.
Most probably a very naive thinking.Oh yes, okay. It would be expressed in units of distance in that case, whereas s = sqrt[Δx^2 + Δy^2 + Δz^2 - (c Δt)^2] would be the spacetime interval measured from any frame using the coordinates between two events according to that frame, and is also the proper distance that would be measured by the ruler of an observer that sees both events occur simultaneously in some particular observer's frame, such that Δt = 0 (using delta here because we are discussing finite quantities). But that is only if the events are separated such that nothing can travel between them faster than the speed of light, so that the events are space-like. If they are time-like, then we would use tau = sqrt[(c Δt)^2 - (Δx^2 + Δy^2 + Δz^2)] / c as Ken mentioned. An object can travel between the events at a speed less than c from the point of view of any observer when the events are time-like, so no observer in any frame can see the events occur simultaneously in that case and proper distance cannot be measured, but an observer with a clock can travel with the events so that the events are observed to occur in the same place, whereas Δx = Δy = Δz = 0, so sqrt[Δx^2 + Δy^2 + Δz^2] = 0, and tau is the proper time measured by a clock that travels with the events. Two events cannot be space-like or time-like at the same time, otherwise related by tau = i s / c where i is the complex number sqrt(-1), although they can be light-like if only light can travel between the events such that Δt = 0 and sqrt[Δx^2 + Δy^2 + Δz^2] = 0, whereas s = 0 and tau = 0, so light always follows a null path inertially, when the influence of gravity is not present.

macaw
2010-Mar-29, 02:47 PM
so that the events are space-like. If they are time-like,

Events can't be "space-like" and/or "time-like".
The terms "space-like" and "time-like" define something entirely different.

grav
2010-Mar-29, 02:56 PM
Events can't be "space-like" and/or "time-like".
The terms "space-like" and "time-like" define something entirely different.
Please do not confuse people with your pop interpretation of relativity.The spacetime interval (http://en.wikipedia.org/wiki/Spacetime#Spacetime_intervals) between two events is defined as space-like, time-like, or light-like.

macaw
2010-Mar-29, 03:11 PM
The spacetime interval (http://en.wikipedia.org/wiki/Spacetime#Spacetime_intervals) between two events is defined as space-like, time-like, or light-like.

Yes, the correct notion is "interval" .
Events themselves can't be "space-like" or "time-like".
Events and intervals are different notions.

grav
2010-Mar-29, 03:18 PM
Yes, the correct notion is "interval" .
Events themselves can't be "space-like" or "time-like".
Events and intervals are different notions.Fair enough. I should have said "... so that the spacetime interval between the events is space-like. If it is time-like, ..." .

macaw
2010-Mar-29, 03:20 PM
Fair enough. I should have said "... so that the spacetime interval between the events is space-like. If it is time-like, ..." .

Or you could have started studying the Rindler book. It is all there, why would you waste money buying it and not reading it?

Ken G
2010-Mar-29, 04:35 PM
A geodesic is not "kinked" (i.e. not differentiable) and therefore a "kinked" curve is not the geodesic. Ergo the proper time along the non-geodesic/kinked world line will less than than the proper time along the geodesic.All true. The issue about the kink is in reference to the link macaw gave, claiming it was some kind of proof. Read that link and you will find it calculates the proper time along a kinked path, and compares it to the geodesic proper time, and erroneously argues that somehow this means acceleration is not required to get a proper time that deviates from the geodesic result. It is tantamount to claiming that acceleration is not required to get a path that deviates from a geodesic, which is a false claim as long as one is adopting the empirical meaning of a proper time as the measurement a clock makes when it follows a spacetime path. (It is also unresponsive to the physical question of how you get objects to follow paths that are not geodesics in the first place.) The link makes explicit reference to clocks, so is either using the empirical meaning, or is badly confusing the empirical and rationalistic meanings of proper time. Either way, its argument is incoherent, which was my point.

Ken G
2010-Mar-29, 04:42 PM
The path ain't "kinked". As such there is NO acceleration involved in the experiment just TWO INERTIAL rockets passing each other.
There are TWO DIFFERENT STRAIGHT paths corresponding to TWO DIFFERENT clock carrying rockets moving INERTIALLY .I'm well aware of all that, but you are still not answering my question. There is a proper time comparison there, is there not? And the two proper times being compared, they do associate with two different spacetime paths between the same two events, do they not? What are those two paths, do you think? Is one of them kinked, yes or no?

Ken G
2010-Mar-29, 04:45 PM
The spacetime interval (http://en.wikipedia.org/wiki/Spacetime#Spacetime_intervals) between two events is defined as space-like, time-like, or light-like.

Don't worry about macaw's objection there, what you were saying before was perfectly obvious to the rest of us despite the slightly imprecise language. You could have simply appended the word "separated", saying that "the two events were timelike separated." To most of us, appending that word mentally was a trivial exercise. Most of us also think it is rude to badger people over imprecise language when the meaning is perfectly clear, though a polite correction is certainly acceptable.

macaw
2010-Mar-29, 05:03 PM
I'm well aware of all that, but you are still not answering my question.

I not only answered the question, I also gave you the precise description as to how the gedank is set-up. Even grav understood it (see his post), why do you have such a hard time?

And the two proper times being compared, they do associate with two different spacetime paths between the same two events, do they not?

There are THREE separate paths:
-the "stay at home" twin
-the "leaving" twin
-the "returning" twin

As such, there is no "kink" (and no acceleration).

macaw
2010-Mar-29, 05:04 PM
Read that link and you will find it calculates the proper time along a kinked path,.

Nope, see previous post.

Ken G
2010-Mar-29, 05:43 PM
There are THREE separate paths:
-the "stay at home" twin
-the "leaving" twin
-the "returning" twin
Obviously, but there are not three paths over which proper times are being compared. That comparison is between two paths, one if which is kinked, and comprises of the last two sub-paths you mention above. That's just a fact.

macaw
2010-Mar-29, 05:50 PM
Obviously, but there are not three paths over which proper times are being compared.

You are splitting hairs. There are THREE paths that proper time is being calculated. (due to symmetry, the calculations for the "leaving" and for the "returning" twins are identical).
Even more importantly, there is NO acceleration. You repeatedly failed to accept this fact which easily refutes your misconception about acceleration being the origin of the proper time difference.

Jeff Root
2010-Mar-29, 05:56 PM
macaw,

I agree with you and disagree with Ken that there is no acceleration in
the scenario with three passing clocks. However, I agree with Ken and
disagree with you that the path of the information which is used to show
and quantify the time dilation is "kinked". The information is in the second
clock up until the instant that information is transferred to the third clock.
At that instant the path changes direction, from moving away from the
first clock, to moving toward the first clock. The event at which the
path of the information suddenly changes direction is obviously a kink in
the path.

I find nothing wrong with the analysis, though. There is no acceleration
involved, only a change in velocity relative to the first clock. The second
clock has one velocity away from the first clock, and the third clock has
a different velocity toward the first clock.

I accept the unstated assumption that the clocks are identical, and so
would tick synchronously if they were not in motion relative to each other,
and that this is adequate for them to stand in for an accelerated twin.

-- Jeff, in Minneapolis

macaw
2010-Mar-29, 05:59 PM
macaw,

I agree with you and disagree with Ken that there is no acceleration in
the scenario with three passing clocks. However, I agree with Ken and
disagree with you that the path of the information which is used to show
and quantify the time dilation is "kinked".

The debate is about the origin of the proper time differential. KenG has long claimed that it is acceleration, I showed him that it isn't.

BTW, the discussion is not about "time dilation", it is about a different phaenomenon.

Jeff Root
2010-Mar-29, 06:19 PM
When I have used the term "time dilation" here I have meant it to include
all the time and/or spacetime differences you are talking about, whether it
is the term you prefer or not.

-- Jeff, in Minneapolis

speedfreek
2010-Mar-29, 06:27 PM
Isn't the proper time differential due to one of the clock readings swapping between inertial frames at "turnaround"? The "clock" has changed frames, by moving at c between two frames in motion in opposite directions. Why therefore is the path of the clock showing less proper time not "kinked"?

Jeff Root
2010-Mar-29, 07:03 PM
speedfreek,

I sympathize with both sides of that argument, but I haven't analyzed it
sufficiently to determine how to correctly use the term. Like other sloppy
use of terminology used here, what you meant is completely clear.

-- Jeff, in Minneapolis

speedfreek
2010-Apr-21, 10:28 PM
It seems as if my question has been forgotten... was the path that showed less proper time kinked, or not?

Is transmitting a clock reading at the speed of light between two observers travelling in opposite directions in any way equivalent to physically passing a clock between the frames where the clock undergoes "instantaneous" accelerations? Obviously, one cannot physically move a clock at the speed of light, but is the end result not similar in both cases?

uncommonsense
2010-Apr-22, 02:31 AM
Wow, sorry, I didn't know this thread was still going. I tried to read as much of the posts as possible just now, and obviously different members have several different fundemental understandings of relativistic basics.

I am a total beginner with zero academic background, but I am in the process of self learning Relativity and Quantum. I have nothing to say about Quantum yet, but from my readings of Einsteins papers, translated into english, there are, imho, several understandings held by Einstein that if you actually trust them, trust them together, as a working set of ideas, then a deeper sense of what the man was telling us unfolds, imho.

Please read in his own words how Einstein defines "time", he uses the word often throughout his work, but only after he defines it. Please read how he explains "the relativity of length and time", and consider why he said "relativity of length", then "time".

Understand how in SR he described length contraction in the direction of motion along a single axis experienced by a body in velocity along that axis, in terms of length (distance) properties along that axis becoming something "different than those of the other two axes, and that when compared to a body at rest wrt to that coordinate system, neither body was the preferred frame of reference. As an understanding of what happened, most people wade in the waters of a time centric (therefore the clock) understanding, whereby "time" slowed down for the body moving wrt the coordinate system's "non-moving" clock. When asked "how exactly did time slow" - they rely on an antiquated understanding of "time" that is an independent element of the universe with self attributes. Imho, nonsense, or, commonsense that needs to be unlearned. Don't take it from me, the layman, read Einstein WORD FOR WORD for this analysis.

All this, from what underlying principle? THE CONSTANCY OF c. Not many here apparently realy get what Einstein meant by this, or, how it "plays out". I don't say this to insult anyone, but due to the number of disagreements on the subject just in this thread, some of us must be misunderstanding.

I may be one of them, but my unschooled mind chewed on this monster for months. Finally I came up with something that makes sense to me and is not contrary to Relativity:

I decided to use a light clock cause everyone seems to like that one. Imagine you are looking at a long straight road, your prsective is perpendicular to the road and you are far enough away that you can view a very long section of the road.

Far off to your left is the start of the road (point A). Far off to your right is the finish line (point B). There are two cars lined up at A. They are at rest. The have identicle clocks in each. The clocks work like this, everytime a wave of light passes thru the clock, the clock counts one. A beam of light is shone from B, all the way down the road in a straight line tot point A. Therefore, while both cars are stationary at point A, each clock measures the speed of the light from B as being c.

A starter says go. Car 1 does not move. Car 2 accelerates to 1/2 c instantly and maintains this speed to point B, at which time the light isshut off.

Relativity tells us the clock in car 2 will have ran slower, and will have a final time slower than clock in car 1, ie, time slowed in car 2. But EXACTLY HOW.

My take on it is that the entire time car 2 was raceing down the track, car one was being hit by light waves, traveling at c, each wave adding to the count of car 1's clock. Meanwhile, car 2 was moving toward the beam of light at 1/2 c, BUT, since its velocity was not c + 1/2 c (a violation of relativi) it's clock encountered the light waves at only c.(I believe there is an equasion here, but it results in velocity no greater than c) HOVEVER, nothing in relativity demands that the light from point B actually slows down car 2, only that it experiece c as a contant, and so car 2's clock was "ticking" at c, HOWEVER, the car was racing toward B at 1/2 c, therefore, now get this -in th end, cars 2's clock encountered LESS waves of light because when car 2 reached B, the light was shut off. So car 2 clock hit light waves at c AND exercized velocity in the direction of the light source. NO VIOLATION. In fact, this is the crux of distance / time relativity.

Now I may be out to lunch, please real me in.

Ken G
2010-Apr-22, 03:02 AM
It seems as if my question has been forgotten... was the path that showed less proper time kinked, or not?Yes, it was kinked, and that's "why" it showed less proper time. The proper time of a path can be calculated from the history of proper acceleration as a function of location along the path, i.e., from its length and kinkiness.

Is transmitting a clock reading at the speed of light between two observers travelling in opposite directions in any way equivalent to physically passing a clock between the frames where the clock undergoes "instantaneous" accelerations? Obviously, one cannot physically move a clock at the speed of light, but is the end result not similar in both cases?Proper times are calculated along paths, and measured by clocks that follow those paths. The rest is not saying much at all, including sending clock readings around. It's all smoke and mirrors, in physics we have calculations, and we have measurements, and the rest is hooey-- as were all those claims that acceleration is not the cause of the reduced proper time between two events in spacetime. I'd accept that the causality depends on the context-- we can find situations where both the acceleration and the reduced time are caused by something else (a field that alters the path of least action, let's say), but you are still looking for what caused the acceleration when you want to know why the proper time was reduced.

Celestial Mechanic
2010-Apr-22, 04:41 AM
Please read the dialog here (http://www.bautforum.com/showthread.php?p=718941#post718941). It is post #5 in that thread. There is nothing wrong with anybody's clock. There is no need to search for "mechanical reasons" for clocks "slowing".

DrRocket
2010-Apr-22, 05:30 AM
Please read the dialog here (http://www.bautforum.com/showthread.php?p=718941#post718941). It is post #5 in that thread. There is nothing wrong with anybody's clock. There is no need to search for "mechanical reasons" for clocks "slowing".

Absolutely correct, as is the dialogue in the link that you provided.

Proper time is arc length.

Ken G
2010-Apr-22, 06:24 AM
I certainly agree that it is downright wrong to imagine that something is happening to the clock but not to time itself, as though there was some mechanical problem with the clock where it was not keeping proper time (in every sense of the word). But there is another way to frame the concept of something making a clock run slow, which is something happening that makes time itself run slow. I have never liked that way of framing things, because it implies a preferred comparison between two times that are better treated on an equal footing. However, I would stop short of saying that one is correct and one is incorrect-- we must not mistake the language we use to talk about reality for the reality itself. In my view, it is just as wrong to say that someone's clock is being slowed in some absolute or categorical way, as it is to say no clock is being slowed. It's all pedagogy, it's all different ways of picturing what is happening.

The theory is the equations, that's what reality tests, but their meaning is added by us-- and there are better and worse ways to do that. I agree that telling people that the twin paradox happens because time goes more slowly for the traveling twin is a weak and limited way of understanding that paradox, it is far better to start with the demonstrable statement that the proper time depends on the path and not give any explanation for that. But when we wish to take the next step, and erect a picture for why the proper time so depends, then we open up the question of language. At this point we must recognize we have left the realm of what we can demonstrate as true, we are merely comparing the advantages and disadvantages of various word usages-- we cannot correctly state that one usage is correct and another erroneous, but we can discuss preferences and why.

I will give an example to clarify my point-- the action of gravity on time. The equations of general relativity that predict the motion of a baseball are normally framed as a geometric curvature of a spacetime manifold, yet Feynman himself liked to point out that one can also view it as something that represents a slowing of time in a gravitational potential. In either case the path is a geodesic, a path of least action, but in the geometric approach that is "due to" curvature of an otherwise locally normal spacetime, and in the time-slowing approach it is "due to" the favoring of certain paths for the action they generate. If we instead consider a charged clock moving in an electric field that accelerates it, and a neutral clock that starts and ends at the same two events as the charged clock, we can say that the charged clock will register less proper time-- but we can also say that this is "because" the interaction with the electric field creates a different action environment, which in effect slows time relative to the neutral clock. That's basically a mechanical slowing of the clock, because the same action environment that tells the clock what path it can take also tells its hands how they can tick! It's just language, it isn't reality, so it cannot be the truth or a lie-- if it motivates the right equations, it's a pedagogy.

In other words, the "shut up and calculate" approach gets it right that the equations are what counts, but it gets it wrong in that it dismisses all pedagogies, when we should do the opposite-- master them all.

Jeff Root
2010-Apr-22, 12:41 PM
uncommonsense,

Could you reply to my post #124 ?

Also take another look at my very short post #127.

-- Jeff, in Minneapolis

uncommonsense
2010-Apr-22, 04:31 PM
An hour is approximately 1/24th of a day, but the length of a day
varies considerably, due to several different causes. Some of the
variations make it desireable to occasionally add a leap second
at the end of December or June, in order to keep the standard
clocks synchronized with the Earth. So motion of the Earth does
not define time, because Earth's motion varies, and standard clocks
do not define time, because they are adjusted to conform to the
motions of the Earth.

What motions of what objects?

Give a real example. GPS satellites show relativistic time dilation.
Use them for your example. At the altitude of the Navstar satellites,
clocks aboard those satellites are slowed by their relative motion by
about 7 microseconds per day compared to clocks on the ground, and
effectively speeded up by their separation from Earth's gravity by
about 45.9 microseconds per day compared to clocks on the ground.
The combination of these two relativistic effects gives a net speeding
up of Navstar clocks of about 38 microseconds per day compared to
clocks on the ground.

What motions of what objects are compared when the relativistic
effects on Navstar clocks is observed?

What motion or distance decreases (or increases) in the case of the
Navstar clocks?

-- Jeff, in Minneapolis

Jeff,

I think this may answer all of the above, it's from another post I entered in another thread:

"If we wish to describe the motion of a material point, we give the values of its co-ordinates as functions of the time. Now we must bear carefully in mind that a mathematical description of this kind has no physical meaning unless we are quite clear as to what we understand by time.'' We have to take into account that all our judgments in which time plays a part are always judgments of simultaneous events. If, for instance, I say, That train arrives here at 7 o'clock,'' I mean something like this: The pointing of the small hand of my watch to 7 and the arrival of the train are simultaneous events.''3

It might appear possible to overcome all the difficulties attending the definition of time'' by substituting the position of the small hand of my watch'' for `time.'' And in fact such a definition is satisfactory when we are concerned with defining a time exclusively for the place where the watch is located; but it is no longer satisfactory when we have to connect in time series of events occurring at different places, or--what comes to the same thing--to evaluate the times of events occurring at places remote from the watch."

On the Electrodynamics of Moving Bodies, 1905

Further reading of Einstein reveals length contraction occures along the single axis of motion according to velocity. So velocity and length (distance) are interchangeable, therefore velocity/distance measurement ("time") is said to be relative. It is perhaps more accurate to understand that the moving object realizes 3 dimentional space with one dimention (axis of motion) "contracted". All time/clock explanations follow from there - in my humble opinion.

uncommonsense
2010-Apr-22, 04:38 PM

I disagree. Imho, you got it backwards, time is dependent on motion. Time cannot sustain itself without its components (ex. distance and velocity). I challenge you to give me 1 single independent attribute of the abstract you refer to as "time". Independent here means "a characteristic of time that is not dependent on something other than time".

Thank you.

Strange
2010-Apr-22, 04:41 PM

I disagree. Imho, you got it backwards, time is dependent on motion. Time cannot sustain itself without its components (ex. distance and velocity). I challenge you to give me 1 single independent attribute of the abstract you refer to as "time". Independent here means "a characteristic of time that is not dependent on something other than time".

Thank you.

The canonical example that seems to come up whenever this is discussed is the decay of a muon: it happens after a time interval indpendent of any movement - apart from relativistic effects of course.

uncommonsense
2010-Apr-22, 05:29 PM
The canonical example that seems to come up whenever this is discussed is the decay of a muon: it happens after a time interval indpendent of any movement - apart from relativistic effects of course.

What is the source, nature, and value of the time interval that passes as referenced above?

Strange
2010-Apr-22, 05:43 PM
What is the source, nature, and value of the time interval that passes as referenced above?

The "source"? Dunno. It just is! Or at least, the standard model doesn't tell us where it comes from, as far as I know.

Nature? What does that mean?

Value? About 2 microseconds (I think).

Jeff Root
2010-Apr-22, 05:47 PM
uncommonsense,

The quote from Einstein doesn't answer my questions.

Einstein did not try to define time. What he did was define how to specify
a measurement of time.

If you believe that motion defines time, do you believe that time passes
more rapidly inside a hot oven, where all the atoms are moving faster than
outside the oven? Do you believe that time passes more rapidly yet in the
Sun's interior, where the temperature is millions of degrees, and the ions
move much faster?

Time is simply a comparison of motion of different objects. Thats it.
What motions of what objects? Give a real example. What motions of
what objects are compared when the relativistic effects on Navstar clocks
is observed? What motion or distance decreases (or increases) in the
case of the Navstar clocks?

-- Jeff, in Minneapolis

uncommonsense
2010-Apr-22, 05:49 PM
The "source"? Dunno. It just is! Or at least, the standard model doesn't tell us where it comes from, as far as I know.

Nature? What does that mean?

Value? About 2 microseconds (I think).

Thanks.

Without looking this muon decay thing up, I conclude that if the "decay interval" is "about 2 microseconds", then the "motion" of the decay was compared to the motion of a timing device. So this answer does not satisfy the query.

Ken G
2010-Apr-22, 06:25 PM
Einstein did not try to define time. What he did was define how to specify
a measurement of time.I believe that Einstein was adhering to the strictest standards of empirical science, whereby time is defined by how it is measured. The most ironclad way to talk about science is to assert that all its fundamental quantities, those we use to assess the success of the science, are defined entirely by how they are measured. What really matters in making science useful is the wideness of the set of "similar observations", such that we can assert that the action of a clock will mimic the action of a wide variety of physical systems, that all function as "similar" to the action of a clock (even those that are not being used as measurements or even have no scientists present, yet function as part of that similar class, call them "hypothetical measurements"). Therefore, I would say that time, insofar as it is a concept of physics, is the combination of how it is measured, and this wide domain of similar systems to which that measurement is relevant.

uncommonsense
2010-Apr-22, 06:25 PM
uncommonsense,

The quote from Einstein doesn't answer my questions.

Einstein did not try to define time. What he did was define how to specify
a measurement of time.

I disagree, he says "what we understand by time". You misquoted Einstein.

If you believe that motion defines time, do you believe that time passes
more rapidly inside a hot oven, where all the atoms are moving faster than
outside the oven? Do you believe that time passes more rapidly yet in the
Sun's interior, where the temperature is millions of degrees, and the ions
move much faster?

I never made that claim, now you misquoted me. I said time is dependent upon motion. I sincerely mean no disrespect and seek no enemies, but is English your 1st language? If not I will act accommodate accordingly.

What motions of what objects? Give a real example. What motions of
what objects are compared when the relativistic effects on Navstar clocks
is observed? What motion or distance decreases (or increases) in the
case of the Navstar clocks?

Clocks on the earth are within GR space (gravity) which is likened to being accelerated, according to EFE. So the motions of clock in gravity/acceleration are being compared to clocks that are in motion further away from the gravity. As far as what portion of the distance decreases, you need to read and understand general relativity and mass/warped space.

Hope I didn't sound flippant, I just thought from reading your prior posts you had some...............different understandings. :)

-- Jeff, in Minneapolis[/QUOTE]

Jeff Root
2010-Apr-22, 06:36 PM

Just ask yourself if all motion in the universe stopped would
time stop? Or is there an independent notion of time that does
not depend upon motion of something?
Motion depends on time. Time makes motion possible. In general,
time makes change possible. Without time, nothing could change,
and nothing could move. The passage of time does not guarantee
change, but the existence of change shows that time has passed.

Time is what the motion of a clock measures, but the motion of a
clock is not time.
I disagree. Imho, you got it backwards, time is dependent on motion.
Time cannot sustain itself without its components (ex. distance and
velocity).
You are confusing time with a measurement of time. It is no more or
less complicated than the difference between length and a measurement
of length, or mass and a measurement of mass.

A measurement of length is a comparison between the length you
want to measure and a standard. The standard might be a ruler or
the width of your hand. It might be an interferometer reading, or
the time it took a light pulse to go from your laser measuring device
to the wall and back.

A measurement of mass is a comparison between the mass you
want to measure and a standard. The standard might be weights
on a balance, or the extension of a calibrated spring.

A measurement of time is a comparison between the time you
want to measure and a standard. The standard might be the
positions of the hands on a clock, or the orientation of the Earth's
surface to the stars, or a count of the number of oscillations of
an electrical circuit.

Motion expresses time. Motion is used to measure time. But
time does not derive from moton. Without time, there could be
no motion. Time allows motion to be possible. Nothing has to
move. But whether anything moves or not, time passes.

I challenge you to give me 1 single independent attribute of the abstract
you refer to as "time". Independent here means "a characteristic of time
that is not dependent on something other than time".
This reminds me of the notion I came up with 25 or 30 years ago:
----
Time is a factor in everything that happens, but it is never the only factor.
----
I understand what time is, through experience. But I can't define it.
I think the reason I can't define it is that it is too fundamental. All
definitions and explanations depend on existing understanding of more
fundamental concepts. Time is one of those concepts that are at the
very base of experience.

-- Jeff, in Minneapolis

Strange
2010-Apr-22, 06:47 PM
Without looking this muon decay thing up, I conclude that if the "decay interval" is "about 2 microseconds", then the "motion" of the decay was compared to the motion of a timing device. So this answer does not satisfy the query.

I'm not sure what you mean by the "motion" of the decay. But it sounds like ou are making a circular, self-confirming argument. If there was no timing device, the muon would take the same time to decay. If the timing device does not involve motion, then the muon would still decay. There is no necessity for "motion".

But, I suspect, you think there must still be motion and hence you confirm your idea that their cannot be something that happens that is dependent solely on time. In which case, any other example you are given will be rejected by you saying there is still motion in some sense (however abstract that needs to be).

To put it in the form of a haiku (which obviously makes it a stronger argument:))

A muon decays
All by itself. Nothing moves.
Time still passes.

uncommonsense
2010-Apr-22, 06:58 PM
Time allows motion to be possible. Nothing has to
move. But whether anything moves or not, time passes.

Jeff,

You are a truly wise individual, but I urge you to use your deepest imagination and imagine if EVERYTHING in the universe stopped, this includes all human brain function (which is based upon motion), and all light, and everything, everything else. explain how time would still "exist" without using motion as part of the explanation?

uncommonsense
2010-Apr-22, 07:04 PM
If there was no timing device, the muon would take the same time to decay

No, there would still be decay of the muon, though, just no other "standardized" motion to compare with the decay.

If by decay you mean it "disappeared", then thats magic and belongs in ATM:)

Jeff Root
2010-Apr-22, 07:31 PM
Einstein did not try to define time. What he did was define how to specify
a measurement of time.
I disagree, he says "what we understand by time". You misquoted Einstein.
I rarely agree to disagree, but that might be appropriate here. I believe
that my interpretation is correct, but I can't argue against yours.

If you believe that motion defines time, do you believe that time passes
more rapidly inside a hot oven, where all the atoms are moving faster than
outside the oven? Do you believe that time passes more rapidly yet in the
Sun's interior, where the temperature is millions of degrees, and the ions
move much faster?
I never made that claim, now you misquoted me. I said time is dependent
upon motion. I sincerely mean no disrespect and seek no enemies, but is
English your 1st language? If not I will act accommodate accordingly.
Blame my memory of what I thought I remembered you saying.

So, if you believe that time is dependent upon motion, do you believe that
time passes more rapidly inside a hot oven, where all the atoms are moving
faster than outside the oven? Do you believe that time passes more rapidly
yet in the Sun's interior, where the temperature is millions of degrees, and
the ions move much faster?

What motions of what objects? Give a real example. What motions of
what objects are compared when the relativistic effects on Navstar clocks
is observed? What motion or distance decreases (or increases) in the
case of the Navstar clocks?
Clocks on the earth are within GR space (gravity) which is likened to
being accelerated, according to EFE. So the motions of clock in
gravity/acceleration are being compared to clocks that are in motion
further away from the gravity. As far as what portion of the distance
decreases, you need to read and understand general relativity and
mass/warped space.
Another thing I rarely do is complain about "handwaving" explanations.
In fact, I'm not sure I have ever done so before. I will now. Your reply
does not answer my questions. I provided some numbers you can use
in a specific example of what you claimed about the nature of time.
Here is what you claimed:

Time is simply a comparison of motion of different objects. Thats it.

So, to say time slowed, is really saying motion of one thing changed in
relation to another thing. That's it.

To say time slows is actually saying motion or distance decreased.
Here is the information I provided:

GPS satellites show relativistic time dilation.
Use them for your example. At the altitude of the Navstar satellites,
clocks aboard those satellites are slowed by their relative motion by
about 7 microseconds per day compared to clocks on the ground, and
effectively speeded up by their separation from Earth's gravity by
about 45.9 microseconds per day compared to clocks on the ground.
The combination of these two relativistic effects gives a net speeding
up of Navstar clocks of about 38 microseconds per day compared to
clocks on the ground.

What motions of what objects are compared when the relativistic
effects on Navstar clocks is observed? What motion or distance
decreases (or increases) in the case of the Navstar clocks?

In general, when you claim:

"Time is simply a comparison of motion of different objects."

What motion? What objects?

If everything moved at the same speed, would there be no time?

-- Jeff, in Minneapolis

Jeff Root
2010-Apr-22, 07:47 PM
Oh, since this came up again... You might notice that the numbers
I gave don't exactly add up. 45.9 - 7 = 38.9, which is approximately
39, not approximately 38. I asked three physicists and a person
knowledgeable about Navstar why the numbers (from the Wikipedia
article on GPS) don't add up, but I didn't get any useful answers from
them, either. I think that the Wikipedia numbers are correct, but
they don't bother to explain the small anomaly.

-- Jeff, in Minneapolis

Jeff Root
2010-Apr-22, 08:22 PM
imagine if EVERYTHING in the universe stopped, this includes all human
brain function (which is based upon motion), and all light, and everything,
everything else. explain how time would still "exist" without using motion
as part of the explanation?
Why would time *not* still exist? You are stopping all changes that occur
over time. Stopping everything which could be used to detect or measure
the passage of time. Doing that doesn't stop time.

We know about time because of the changes that take place over time.
Those changes probably do all depend on motion. Our measurements
of time thus depend on motions, but the motions depend on time.

-- Jeff, in Minneapolis

speedfreek
2010-Apr-22, 10:23 PM
imagine if EVERYTHING in the universe stopped, this includes all human brain function (which is based upon motion), and all light, and everything, everything else. explain how time would still "exist" without using motion as part of the explanation?

The only way I can imagine everything has stopped is to step outside and watch it for a while to make sure it's not moving. ;)

Hornblower
2010-Apr-22, 10:30 PM
If all change stopped, my idea is that the concept of time would be a moot point.

Strange
2010-Apr-22, 10:35 PM
No, there would still be decay of the muon, though, just no other "standardized" motion to compare with the decay.

I don't know why you put "no" at the beginning of that. You seem to agree with me: the muon would still decay after an interval. Whether something else is there to measure it or not. And whether that "thing" measuring the time is moving or not. Some some "other standardized motion" has nothing to do with it. (I guess that any moment now, we are going to get in to the argument about whether an atomic clock has any moving parts or not...)

If by decay you mean it "disappeared", then thats magic and belongs in ATM:)

Don't worry, it decays into other particles: electrons and neutrinos, I think.

uncommonsense
2010-Apr-22, 10:43 PM
What motions of what objects are compared when the relativistic
effects on Navstar clocks is observed? What motion or distance
decreases (or increases) in the case of the Navstar clocks?

In general, when you claim:

"Time is simply a comparison of motion of different objects."

What motion? What objects?

If everything moved at the same speed, would there be no time?

-- Jeff, in Minneapolis

First off, most of our clocks are designed to move at a rate that is standardized according to the movement of the earth.

I never read up on the Navstar issue, but from how you explain it above, you say

"slowed by their relative motion by

so the clock in space has a greater velocity than the clock on earth (I assume the satellite is in geostationary orbit) --and so, just as I spin my body, my arms fly out, my hands are moveing faster than my elbows. SR explains length is contracted on the path down which my hands (the satellite) move.

Therefore while my hands still encounter light moving toward them at c, they are still moving at a higher velocity than my elbows, who also experiences light at c. But since my hands move faster than elbows, shouldnt light hit them faster (we all know this violates SR). No, but my hands are still moving faster than my elbows, that is reality.

It is also reality that since light hits my hands and elbows both at c, then my hands are "encountering" less light than are my elbows.
motion v. motion v. motion v. motion

If everything moved at the same speed, would there be no time?

I take everything to mean everything, including light. I am finding it difficult to imagine a universe that would work..

But, I guess, Yes, because some things may be moving toward eachother on the same path from exact opposite directions and would therefor collide sooner as compared to two objects moving towads eachother along paths whereby the collision will occure later. Time would help describe these diferences in motion.

Strange
2010-Apr-22, 10:52 PM
First off, most of our clocks are designed to move at a rate that is standardized according to the movement of the earth.

Not any more. Since 1967, the second has been defined as "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" (http://www.bipm.org/en/si/si_brochure/chapter2/2-1/second.html)

uncommonsense
2010-Apr-22, 10:55 PM
Not any more. Since 1967, the second has been defined as "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" (http://www.bipm.org/en/si/si_brochure/chapter2/2-1/second.html)

I did not know that. Thanks, but it is still based upon a standardized "motion", right?

Jeff Root
2010-Apr-22, 11:50 PM
Strange,

I strongly suspect that uncommonsense has a valid point that everything
which measures time (every type of clock) does so via motion, including
atomic clocks. That makes it hard to show that the passage of time allows
motion to occur, as opposed to motion causing time to pass.

Clocks cause time, scales cause mass, surfboards cause waves, ...

-- Jeff, in Minneapolis

Hornblower
2010-Apr-23, 01:31 AM
Maybe time does not "pass". Maybe it is just there, and we and other changing stuff pass through it.

As usual, don't take this as gospel. I yield to active physicists who are up to date in the fine points.

Ken G
2010-Apr-23, 01:54 AM
We can probably agree that time has something to do with change, and it's hard to imagine change without motion. What isn't clear is if time exists because of motion, or if motion exists because of time (there are "zero point" motions even at absolute zero temperature), or if neither really exist at all (as the Greek philosopher Parmenides questioned).

Personally, I suspect the most accurate way to talk about time is to say that it is a mental construct that our intelligence finds useful in making sense of our perceptions. Mathematically, it serves as an excellent way to parametrize the changing conditions around us. The coupling between perception and mathematical theory is very difficult to understand, but clearly is quite tight. If nothing ever changed, we would have no use for the concept of time, but then we also could not have intelligence, because intelligence is processing, and processing involves change. In the end we are always looking in the mirror, but we can certainly imagine that "time" is something outside of us if we like. Whether or not that is actually true is far from obvious.

DrRocket
2010-Apr-23, 02:25 AM
The theory is the equations, that's what reality tests, but their meaning is added by us-- and there are better and worse ways to do that. I agree that telling people that the twin paradox happens because time goes more slowly for the traveling twin is a weak and limited way of understanding that paradox, it is far better to start with the demonstrable statement that the proper time depends on the path and not give any explanation for that. But when we wish to take the next step, and erect a picture for why the proper time so depends, then we open up the question of language. At this point we must recognize we have left the realm of what we can demonstrate as true, we are merely comparing the advantages and disadvantages of various word usages-- we cannot correctly state that one usage is correct and another erroneous, but we can discuss preferences and why.

I have a hard time with statements like "time goes more slowly for the traveling twin" also. It begs the questioin as to what one could possible mean by the "rate of time". We have only one way to to quantify rates, and that is with respect to time . One cannot compare time with itself, so time has no "rate" other than 1 second per second, which is not particularly enlightening.

Clearly what you can do is compare the proper time of two world lines with coincident initial and terminal points. Because general relativity tells us that time is local, you cannot do any better than that.

We can probably agree that time has something to do with change, and it's hard to imagine change without motion. What isn't clear is if time exists because of motion, or if motion exists because of time (there are "zero point" motions even at absolute zero temperature), or if neither really exist at all (as the Greek philosopher Parmenides questioned).

Personally, I suspect the most accurate way to talk about time is to say that it is a mental construct that our intelligence finds useful in making sense of our perceptions. Mathematically, it serves as an excellent way to parametrize the changing conditions around us. The coupling between perception and mathematical theory is very difficult to understand, but clearly is quite tight. If nothing ever changed, we would have no use for the concept of time, but then we also could not have intelligence, because intelligence is processing, and processing involves change. In the end we are always looking in the mirror, but we can certainly imagine that "time" is something outside of us if we like. Whether or not that is actually true is far from obvious.

Yes time has sometihng to do with change, but almost as a tautology. Change requires comparison of two states, states at different times, and the realization that those two states are different. But without some notion of time there is no meaning to this comparison.

The problem that you and everybody else are grappling with is the search for some more fundamental definition of time. Nobody has one. We have the operational definition that "time is what clocks measure" but nothing more fundamental. I am not at all convinced that any more fundamental definition is possible, although I would certainly like to have one as much as does the next guy. At this stage musings on some more funcamental definition are pretty futile, and arguments based on this concept that we don't have are not going anywhere. We are for the moment pretty much stuck with time being what clocks measure and dynamics being based on derivatives with respectd to time.

Einstein may have showed that Newton's "flowing river of time" is not absolute but he did not replace it with anything more fundamental, but only showed that the current of the river depends on who is driving the boat, and where he happens to be. We don't even know why the river always flows in one direction and never backs up, or maybe it does at some quantum level (only the Shadow knows for sure).

uncommonsense
2010-Apr-23, 05:27 AM
We can probably agree that time has something to do with change, and it's hard to imagine change without motion. What isn't clear is if time exists because of motion, or if motion exists because of time (there are "zero point" motions even at absolute zero temperature), or if neither really exist at all (as the Greek philosopher Parmenides questioned).

Personally, I suspect the most accurate way to talk about time is to say that it is a mental construct that our intelligence finds useful in making sense of our perceptions. Mathematically, it serves as an excellent way to parametrize the changing conditions around us. The coupling between perception and mathematical theory is very difficult to understand, but clearly is quite tight. If nothing ever changed, we would have no use for the concept of time, but then we also could not have intelligence, because intelligence is processing, and processing involves change. In the end we are always looking in the mirror, but we can certainly imagine that "time" is something outside of us if we like. Whether or not that is actually true is far from obvious.

Now thats hitting onto somthing deep. I believe this is the reason most people conceptualize time as an independent "thing", and have such a hard time even considering that time is possibly a construct, or an abstract, that gives humans, and some animals, superior survival and analytical skills. And," time" is the perceptual framework that naturally manifests in beings of higher intelligence, in that.....

our brains are wired to experience reality from 3 persectives, past, present, future, and we can controll our present thoughts and actions with consideration of one, or all 3 perspectives, in a variety of combinations, which combinations are our minds' framework of reality.

Many combinations of past present future thoughs are instinctual, or learned very early in life. ex., you see a ball thrown thru the air - present perception starts when you see the ball in someones hands, next present perception is the ball is in a different location from where you rember it was in the past - as if you can "see" the ball in your memory at a past location. Repeat this a few times (present, past memeory, present, past memory and you percieve motion.

Once your brain developes further, you are wired to have a sense of future. Then your reality expands into a "knowing" of where the ball will be in the future. When all 3 perceptions analyze motions that occure over small distances, you remember the many percetions as a single event, that took place over a certain amount of "time".

Then eventually, rather than thinking "I need to execute many motions in order make desired changes in my surroundings, simultaniously with the motion of the sun from one horizon to the other", we started saying "I only have so much time today to get everything done. We started "racing" the clock, or racing time. Time moved, whether we beat it, or dropped out of the race and played sick and laid in the couch all day. Time moved.

The reason we have such a hard time abandoning these instinctual notions of time is because they make perfect sense - they feel so natural - we are wired to think like this. As science progresses, however, these historical notions of time are a barier to a more accurate understanding of the universe.

Imho, Einstein was telling us something much more than simply - time can have different values from different perspectives-. Because Einstein gave so many examples using clocks, many conversations about Relativity are centered around clocks/time. How many times recently have you been given an answer to a Relativity question that simply states "because of time dilation"

Here's how webster defines it : a slowing of time in accordance with the theory of relativity that occurs in a system in motion relative to an outside observer and that becomes apparent especially as the speed of the system approaches that of light  called also time dilatation

Last thought - time is an abstact comprised of distance and velocity of varying values. If time dilates, I want to know which of it's componants caused it, and exactly why and how.