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Sheki
2004-Aug-03, 05:15 PM
I have been hung up on a concept for some time now, and was hoping that the board might help me out a little. The concept, for lack of a better term, I call "apparent velocity". It is the velocity percieved to be achieved by those experiencing it.

Of course for normal, everyday velocities (well below c), the velocity percieved by those experiencing it (say the occupants of an automobile), and those observinging it (some nearby pedestrians) will be equal. Eg. both the pedestrians and the driver would percieve the vehicle and its occupants to be travelling at, say, 100 kph (approx. 60 mph). However, this relationship would not appear to hold for velocities approaching c because of time-dilation.

Using some online reference material and javascript calculators I have been able to determine that time dilation at 0.867c would be approximately 0.5. In other words, time passes at half the normal rate. This leads directly into the following thought experiment:

You are in a vehicle travelling at 0.867c (suppose we put you in a capsule and launced you using the propulsive force of a megaton nuke - note my calculations using an online javascript realivistic energy calculator indicate you would only really need 21 kilotons for a 10 ton capsule). Now the fun part - the observers at the launch site are tracking your progress. After one year they note that you have travelled 0.867 light years. They know this because you pass the 0.867 light year marker that they set up special in advance of the launch. As for you, experiencing time dialtion of 0.5, it will only seem like half of a year has passed before you reach the 0.867 light year marker. So..... from your perspective, you travelled 0.867 light years in half of a year. Twice as fast as those at the launch site percieve you to be travelling.

The logical conclusion here is that you, in the capsule, percieve yourself to be travelling at 1.734c! An "apparent velocity" of 1.734c.

Note, that taking this to an extreme, at 0.9999c, the occupants would feel like they were travelling at 24c. However, this scenario is somewhat less than realistic, as the launch energy would be in the order of several hundred gigatons.

Does this make sense to you people? Or should I perhaps be getting more sleep?

daver
2004-Aug-03, 06:15 PM
I have been hung up on a concept for some time now, and was hoping that the board might help me out a little. The concept, for lack of a better term, I call "apparent velocity". It is the velocity percieved to be achieved by those experiencing it.

Of course for normal, everyday velocities (well below c), the velocity percieved by those experiencing it (say the occupants of an automobile), and those observinging it (some nearby pedestrians) will be equal. Eg. both the pedestrians and the driver would percieve the vehicle and its occupants to be travelling at, say, 100 kph (approx. 60 mph). However, this relationship would not appear to hold for velocities approaching c because of time-dilation.

Using some online reference material and javascript calculators I have been able to determine that time dilation at 0.867c would be approximately 0.5. In other words, time passes at half the normal rate. This leads directly into the following thought experiment:

You are in a vehicle travelling at 0.867c (suppose we put you in a capsule and launced you using the propulsive force of a megaton nuke - note my calculations using an online javascript realivistic energy calculator indicate you would only really need 21 kilotons for a 10 ton capsule). Now the fun part - the observers at the launch site are tracking your progress. After one year they note that you have travelled 0.867 light years. They know this because you pass the 0.867 light year marker that they set up special in advance of the launch. As for you, experiencing time dialtion of 0.5, it will only seem like half of a year has passed before you reach the 0.867 light year marker. So..... from your perspective, you travelled 0.867 light years in half of a year. Twice as fast as those at the launch site percieve you to be travelling.

The logical conclusion here is that you, in the capsule, percieve yourself to be travelling at 1.734c! An "apparent velocity" of 1.734c.

Note, that taking this to an extreme, at 0.9999c, the occupants would feel like they were travelling at 24c. However, this scenario is somewhat less than realistic, as the launch energy would be in the order of several hundred gigatons.

Does this make sense to you people? Or should I perhaps be getting more sleep?

Welcome to the wonderful world of relativity.

You are launched at a velocity of .867 c. Earth sees you recede at .867 c, you see Earth recede at .867c. From Earth's point of view, the Earth is stationary, you are moving. From your point of view, you are stationary, the Earth is moving.

Earth, watching you through a big telescope, notes that after one year you pass the .867 light year post, and that your clock indicates that 0.5 years have passed since launch.

You, after 0.5 years, see the 0.867 light year post sail by. You're a bit puzzled, because this post to you seems to be only 0.433 light years from earth, but you get your special relativity primer out and read about length contraction and you're happy.

For giggles, you decide to see what time it is on earth; you flash them a message as you pass the mile post. You think earth is receeding from you at .867 c, so you think it takes .433 / .133 = 3.25 years for them to get your message. Add in the .5 years since you left, and you get 3.75 years. Divide by two (you notice that clocks on earth are running at half speed) and you think that their clocks will indicate 1.88 years have passed.

Earth sees your message at the same time it sees you pass the mile marker (both events travel at the speed of light); it sees this after 1 year (the time it took you to get to the marker) + 0.88 years (the time it takes the signal to travel back from the marker). And Presto! Observers in both reference frames agree as to how much time had elapsed on earth, even though they got the same answer in remarkably different fashions.

Sheki
2004-Aug-03, 06:34 PM
Daver Wrote:

"You, after 0.5 years, see the 0.867 light year post sail by. You're a bit puzzled, because this post to you seems to be only 0.433 light years from earth, but you get your special relativity primer out and read about length contraction and you're happy."

So then, it seems that "length contraction" is just a convenient construct to get around the fact that the observer percieves himself to be exceeding c.

Clearly the moving observer would know full well how far away the marker was when he was launched. Thus, the contraction of length, would simply be percieved as increased speed. no?

Additionally, I could argue that lenght contratction is irrelevant in the example, as the traveller is not doing any length measurement. he only knows that the waypoint is a certain distance away, and that it takes him a certain amount of time to achieve it.

I would also note that your calculation of "what time it is on earth" is rather odd. Afterall the traveller would know full well that his velocity is 0.867c (regardless of the great time he appears to be making). Thus, it should be pretty obvious that one year has passed since launch (for those back home) when he passes the 0.867 lightyear marker...

Sheki

gritmonger
2004-Aug-03, 06:40 PM
I read a science-fiction short story on this from sometime in the 1950's- one researcher was sure he could exceed c, and proceeded to prove this to his associates by getting in his rocket and blasting off - when they returned, after what seemed to them an hour travelling far faster than light, their civilization (on the moon- this was the 1950's remember?) had collapsed, and they were the only ones left.

daver
2004-Aug-03, 07:13 PM
So then, it seems that "length contraction" is just a convenient construct to get around the fact that the observer percieves himself to be exceeding c.

No, it's as real as time dilation. As a spaceship passes, you'll notice both that its clocks are running slowly, and that it has been contracted in the direction of motion.


Clearly the moving observer would know full well how far away the marker was when he was launched. Thus, the contraction of length, would simply be percieved as increased speed. no?

No, it's an artifact of relativity. If you took a photograph of a ruler as it passed by at relativistic speeds, you'd notice that it was shorter than it was supposed to be.


Additionally, I could argue that lenght contratction is irrelevant in the example, as the traveller is not doing any length measurement. he only knows that the waypoint is a certain distance away, and that it takes him a certain amount of time to achieve it.

There could be a tape measure along the route; he'd notice that all of the markings in the direction of his travel were too close together.


I would also note that your calculation of "what time it is on earth" is rather odd. Afterall the traveller would know full well that his velocity is 0.867c (regardless of the great time he appears to be making). Thus, it should be pretty obvious that one year has passed since launch (for those back home) when he passes the 0.867 lightyear marker...

Why? He thinks only half a year has passed for him; if he looked at the Earth as he passed it he would think the clocks on earth were running slowly.

It's time for you to go to your library and pick up a book on special relativity. It's not that hard--you don't need any math more involved than algebra and a bit of geometry.

Lorentz
2004-Aug-04, 12:05 AM
It's time for you to go to your library and pick up a book on special relativity. It's not that hard--you don't need any math more involved than algebra and a bit of geometry.[/quote]

I think Einstein used a little bit of calculus in one of his approximations. At some point, he uses the approximation that if F=mv^2/r (the formula for centripetal acceleration) then dF=2mvdv/r. Both the "F=mv^2/r" and the "dF=2mvdv/r" can be derived using elementary calculus, or derived
in some more convoluted way using the concept of continuity. These were known since the time of Newton, but still constitute a part of elementary calculus.

Einstein rushes by this point, and there are ways to estimate this using geometry. No big deal, just don't tell people that there is "absolutely no"calculus in special relativity.

I note that that term is important in analyzing the Hafele and Keating experiment. Folks who have trouble with the fundamental operation of calculus, which in my view is "taking the limit," may have difficulty understanding the H and K experiment. [/img]

Normandy6644
2004-Aug-04, 01:16 AM
It's time for you to go to your library and pick up a book on special relativity. It's not that hard--you don't need any math more involved than algebra and a bit of geometry.

I think Einstein used a little bit of calculus in one of his approximations. At some point, he uses the approximation that if F=mv^2/r (the formula for centripetal acceleration) then dF=2mvdv/r. Both the "F=mv^2/r" and the "dF=2mvdv/r" can be derived using elementary calculus, or derived
in some more convoluted way using the concept of continuity. These were known since the time of Newton, but still constitute a part of elementary calculus.

Einstein rushes by this point, and there are ways to estimate this using geometry. No big deal, just don't tell people that there is "absolutely no"calculus in special relativity.

I note that that term is important in analyzing the Hafele and Keating experiment. Folks who have trouble with the fundamental operation of calculus, which in my view is "taking the limit," may have difficulty understanding the H and K experiment. [/img]

Yeah but you can get the basic concepts of SR with little more than algebra.

Sheki
2004-Aug-04, 11:52 AM
Daver wrote:


No, it's as real as time dilation. As a spaceship passes, you'll notice both that its clocks are running slowly, and that it has been contracted in the direction of motion.

OK, fair enough. My earlier statement "convenient construct" was ill chosen. I fully acknowledge the reality of such contraction. I did not actually mean to suggest that it did not exist - contrary to what I stated. Sorry.


No, it's an artifact of relativity. If you took a photograph of a ruler as it passed by at relativistic speeds, you'd notice that it was shorter than it was supposed to be.

Keep in mind that, as per the original post, we are talking about perception of velocity, rather than the reality of the situation. In such circumstances, whether or not the effect is an "artifact" is irrelevant. The traveller, not being disposed to abstract inquiries and meditations on sr, will no less percieve himself to be exceeding c. More on this in a later.


There could be a tape measure along the route; he'd notice that all of the markings in the direction of his travel were too close together.

Understood. But irrelevant. To better illustrate what I am getting at here, consider the following example:

I got in my car this morning to start my daily commute to work. It is 40km to my workplace from home. I normally travel at about 100kph average, and on average it takes about 24 minutes to get to work. Now suppose something truly bizarre happened this morning, and c was reduced to about 130 kph in my little corner of the universe. I pull out on the highway, and as I am getting up to cruising speed (approaching c) a curious thing happens. All of the scenery starts to compress, and things start to look much thinner than they used to. My speedometer still reads 110 kph, but the landmarks are just flying by because the distance between them has shrunk dramatically, I also get the impression that time is passing slowly for me (eg. I can see birds in the sky that are flying at very unusual rates). I finally get to work, I check my watch and wow, only 12 minutes have passed since I left home. I do the math (v=d/t), and figure I effectively travelled at an average velocity of about 200 kph. The fact that I blew past several speed traps, and my speedometer never registered anything above 120 kph for the whole trip, are pretty irrelevant. There is no arguing with 40 km in 12 minutes.


Why? He thinks only half a year has passed for him;

Yes, but he should know his true velocity, and he knows the distance to the marker. he would have to be pretty daft not to deduce that a year has passed on earth.


if he looked at the Earth as he passed it he would think the clocks on earth were running slowly.

Hmmm. I think you are mistaken here. If time is travelling more slowly for him, and he looks at a clock outside of his capsule, the outside clock should appear to be running faster, not slower. (if I am experiecing time dilation of 0.5, then for every second that goes by for me, two will go by for you - my clock will tick once, where yours will tick twice over the same period).


It's time for you to go to your library and pick up a book on special relativity. It's not that hard--you don't need any math more involved than algebra and a bit of geometry.

Perhaps. I will admit I am not expert in this particular field, which is why I came here to start the discussion in the first place. Thanks for the advice. However, if I might offer some of my own: It 's time for you to go to your library and pick up a book on how not to be condescending. "Its not that hard -- you don't need any math" at all.

One final point - to be absolutely clear on why length dilation is irrelevant: suppose we modify the original thought experiment. The capsule has no windows, and its only contact with the outside world is a single light that will switch on when an outside sensor detects that the capsule has passed the marker. The only piece of scientific equipment the traveller has is a chronometer. In effect, the traveller knows very little: He knows he is going to be launched with a tremendous amount of energy, and can expect to be going very quickly. He is also going to know that a little light will turn on when he passes a marker that is 1 lightyear from his origin. He is going to know the amount of time (as measured on his own chronometer) that it took him to get to the marker. Also, suppose he is woefully ignorant of sr.

So, when he achieves the marker in less than one year, how could he not percieve that he has travelled faster than c?

Sheki

Wally
2004-Aug-04, 12:17 PM
Quote:
if he looked at the Earth as he passed it he would think the clocks on earth were running slowly.


Hmmm. I think you are mistaken here. If time is travelling more slowly for him, and he looks at a clock outside of his capsule, the outside clock should appear to be running faster, not slower. (if I am experiecing time dilation of 0.5, then for every second that goes by for me, two will go by for you - my clock will tick once, where yours will tick twice over the same period).


Nope. He's correct. Remember relativity is "relative"! You perceive your own time as going by at a "normal" rate, and for you, it actually IS going by at a "normal" rate. It's only to observers on Earth that your time appears to be going by at half the rate as their own (and it actually IS going by at half of their rate. . . it's RELATIVE!!!).

Conversely, you look back at Earth, and see their time going by at half the rate as your own "normal" time. And from your own frame of reference, time really IS going by at half of your rate back on Earth. Again, time and length contraction is completely RELATIVE to your frame of reference. It's amazing stuff man! Boggles the mind, doesn't it!

Sheki
2004-Aug-04, 12:26 PM
Wally,

If so, then query me this:

I experience time dilation of 0.5, I measure off 5 minutes, and then revert to normal time (1.0). My chronometer will read 5 minutes having passed. an external chronometer will indicate 10 minutes having passed. How could the external chronometer indicate twice as much time having passed, yet have run slow?

Sheki

Sheki
2004-Aug-04, 12:29 PM
Wally,

Upon further consideration, I concede your point. It makes sense. But I am still perplexed by the apparent paradox illustrated in my last post.

Sheki

worzel
2004-Aug-04, 12:41 PM
There is no arguing with 40 km in 12 minutes.
Your milometer will tell you that it was less when you get there. As soon as you start moving that distance for you is reduced. I think your caculation of your speed using your contracted distance and your watch comes out the same as your stay-at-work boss's calculation using 40km and his watch.

Wally
2004-Aug-04, 12:43 PM
You do not "experience" time dilation from your own reference frame. That's where your getting mixed up. For you, time is going by at a perfectly acceptable, "normal" rate. You do not, nor should you, attempt to compensate your time for the dilation you know people on Earth are seeing for you. (well, you can, but just keep in mind, it's all RELATIVE!!!). You KNOW from your reference frame, 1 year has passed. This is absolutely true, from your reference frame. You KNOW that on earth, only 1/2 a year has passed. Again, this is completely true, from your reference frame. On Earth, the exact opposite is observed (they have aged a year, while your time has only gone by at half the rate). There is no paradox, because time itself is all RELATIVE to your frame of reference. (I don't mean to shout, but relativity is the key to understanding SR :) ).

If you were to suddenly turn around and head back to Earth, then you've just introduced a 3rd frame of reference, which causes all kinds of things to happen that we won't get into here (yet anyways. . .).

worzel
2004-Aug-04, 12:47 PM
Wally,

If so, then query me this:

I experience time dilation of 0.5, I measure off 5 minutes, and then revert to normal time (1.0). My chronometer will read 5 minutes having passed. an external chronometer will indicate 10 minutes having passed. How could the external chronometer indicate twice as much time having passed, yet have run slow?

Sheki

To do this you would have to have them next to each other, then move one relative to the other, then move it back again. During the periods of motion they will observe each other's clocks running slow. But when they're brought back together the one that actually moved will have lost time. This is known as the twin paradox and does my head in, but it does work.

Sheki
2004-Aug-04, 01:26 PM
Re: calculation of velocity:

The distance that my odometer (milometer) indicates that I have travelled has nothing to do with the fact that I live 40 km from my place of work. V=d/t is still valid, and d = 40, t=12 minutes. I percieve myself to have travelled 200kph.

To simplify what I am trying to say even further - suppose my wife drove me to work, and slept the whole way. All I know is that we left the house at 7:00 and we got to work (40 km every other time I have driven it over the past 6 years) at 7:12. I did not check the odometer before leaving the house. How could I not conclude that she had driven like a maniac (200 kph) to work?

Re: Twin paradox:

Just giving something a name "twin paradox" does not resolve the paradox. But I concede that in order for it to truly be a paradox I would have to invoke a time dilation "field" somehow, without moving. So, with respect to the original discussion, it is rather academic.

Wally,

I understand what you are saying, but nevertheless, when the traveller gets back home (suppose it was an eliptical trip) it is the travelling twin that will be young and the "stationary" twin that will be old. No amount of screaming about the relativity of it all will change that fact. I realize that this invokes the third reference frame, but as the time dilation effect involves velocity, not displacement, it does not seem to matter.

Sheki

Wally
2004-Aug-04, 01:47 PM
Re: calculation of velocity:

The distance that my odometer (milometer) indicates that I have travelled has nothing to do with the fact that I live 40 km from my place of work. V=d/t is still valid, and d = 40, t=12 minutes. I percieve myself to have travelled 200kph.

lves velocity, not displacement, it does not seem to matter.

Sheki

Sheki. If you want to treat 100kph as a relatistic speed (as in your example), then once you are travelling 100kph, your distance to work is no longer 40km! Length contraction is also relative to your frame of reference. It's still 40km from your "old" reference frame (before you took off at the relativistic speed of 100kph), but once you switch reference frames, the distance shortens to "x" (I don't have the formula in front of me. . .someone else can do it for ya, I'm sure!). Once you get to work, you don't say "wow, I must have travelled at 200kph". Instead, you would say "wow, it's only "x" km to work when I'm when my relative speed is .8 of c".

Wally
2004-Aug-04, 01:54 PM
Wally,

I understand what you are saying, but nevertheless, when the traveller gets back home (suppose it was an eliptical trip) it is the travelling twin that will be young and the "stationary" twin that will be old. No amount of screaming about the relativity of it all will change that fact. I realize that this invokes the third reference frame, but as the time dilation effect involves velocity, not displacement, it does not seem to matter.

Sheki

It's whomever enters the 3rd frame of reference that'll be the younger of the twins. Say, for instance, that the earthbound twin waits a year, then takes his own rocket and heads after his twin at .9 c. When he finally catches up to the first twin, he's the one that would be younger, not the first twin (provided the first maintained his initial frame of reference, i.e. he didn't accellerate at all). Again, there's formulas that you can use to see all this in reality.

time dilation involves relative velocities, not just velocities. . .

Sheki
2004-Aug-04, 02:33 PM
Wally:


Once you get to work, you don't say "wow, I must have travelled at 200kph". Instead, you would say "wow, it's only "x" km to work when I'm when my relative speed is .8 of c".

Not when you do not automatically view the world through an sr filter. I think you are at just the cusp of understanding the point that I am trying to make.

Please answer this simple question:

You are Isaac Newton. You discover a nearby celestial object, conveniently placed 1 lightyear from earth. you are absolutely sure it is one light year away. You are visited by aliens who agree to take you to said object. You grab your best timepiece and jump in their ship. 150 days later you arrive at the object. How fast do you think that you have travelled?


Sheki

worzel
2004-Aug-04, 02:52 PM
Wally:


Once you get to work, you don't say "wow, I must have travelled at 200kph". Instead, you would say "wow, it's only "x" km to work when I'm when my relative speed is .8 of c".

Not when you do not automatically view the world through an sr filter. I think you are at just the cusp of understanding the point that I am trying to make.
You wouldn't need to know anything about SR to observe that the distance you had travelled was less than what you thought it should be.


Please answer this simple question:

You are Isaac Newton. You discover a nearby celestial object, conveniently placed 1 lightyear from earth. you are absolutely sure it is one light year away. You are visited by aliens who agree to take you to said object. You grab your best timepiece and jump in their ship. 150 days later you arrive at the object. How fast do you think that you have travelled?
You would figure you went faster than light. But if you measured the distance as you covered it you would find out you hadn't travelled one light year after all.

You just have to accept that our intuitive sense of absolute distance is just wrong.

Wally
2004-Aug-04, 03:02 PM
Worzel is right. There is no absolute distance and time! It is all relative to your frame of reference (I Know, I'm repeating myself. But this point is the key to understanding!) You must free your mind (to quote from the matrix. . .). As soon as you obtain relativistic speeds, you'd measure your distance to the object and see it's in fact much closer than 1 ly away, and that due to your relative speed and the "new" distance to the object, you're gonna reach it in 150 days. You never exceed the speed of light. The distance really, truly, all-kidding-aside, becomes much less than 1 ly once you change your frame of reference to one that is moving at relativistic speeds as compared to the object's frame of reference. There no SR filter being used here. It all works out in the math (which, again, I'll leave to those who like the math part. . . )

editted to add: Keep in mind. The object, since it's in the same frame of reference as the earth (i.e. it's not moving relative to earth), remains at exactly 1 ly from earth during your whole trip. That does not change. The distance only changes for you and the aliens once you begin moving at relativistic speeds relative to the object.

Sheki
2004-Aug-04, 04:19 PM
:( Oh man, I just wasted 1/2 hour of my lunch break working on a response, and lost it by accidentally closing my browser. Ouch, that will teach me...

Anyhow, here is the essence of the lost post:

Worzel:

:) Yes you would figure that you went faster than light. Especially if all the information you were given was the distance and the time that you experienced (but not the distance that you experienced). Please note that this is the only point that I ever tried to make. I am not arguing against sr, simply that based on what sr predicts, I can assume that a person ignorant of sr could perceive that they have travelled faster than c. (much like a man ignorant of obital mechanics could quite validly perceive the sun to "go down" - his observation is correct, but his interpretation is wrong, leading to the incorrect perception)

Wally:

Re: "open your mind"
You continue to argue as though I either do not understand or refuse to accept sr. This is not the case (hence I did not start the thread in "Against the Mainstream"). See above. Moreover, i could argue that it is you who is suffering from a closed mind. You refuse to consider what an ignorant observer experiencing relativistic effects would perceive. Instead you are hung up repeatedly interpreting the ignorant observer's observations in accordance with sr. Please recognize that I am not actually arguing with you, but rather just repeatedly failing to make myself understood.

Sheki

worzel
2004-Aug-04, 04:40 PM
Worzel:

:) Yes you would figure that you went faster than light. Especially if all the information you were given was the distance and the time that you experienced (but not the distance that you experienced). Please note that this is the only point that I ever tried to make. I am not arguing against sr, simply that based on what sr predicts, I can assume that a person ignorant of sr could perceive that they have travelled faster than c. (much like a man ignorant of obital mechanics could quite validly perceive the sun to "go down" - his observation is correct, but his interpretation is wrong, leading to the incorrect perception)
Yes, he would draw an incorrect conclusion if they relied on the distance he already "knew" from a different frame of reference. But if by "perceive" you mean what he actually experiences rather than what he assumes from previous perceptions then his perception will still be that he is travelling less than c - with no knowledge of SR.


Wally:

Re: "open your mind"
You continue to argue as though I either do not understand or refuse to accept sr. This is not the case (hence I did not start the thread in "Against the Mainstream"). See above. Moreover, i could argue that it is you who is suffering from a closed mind. You refuse to consider what an ignorant observer experiencing relativistic effects would perceive. Instead you are hung up repeatedly interpreting the ignorant observer's observations in accordance with sr. Please recognize that I am not actually arguing with you, but rather just repeatedly failing to make myself understood.

Sheki
I think this is a bit unfair. I think he can clearly see your point of view (we've all been there, scratching our heads at the absurdity of relativity) and is just trying to help. SR makes predictions about what you will perceive irrespective of your knowledge of SR. You seem hung up on using a notion of distance from one frame of reference as if it were valid in another frame of reference. This is an assumption (which is wrong but seems completely intuitive), not a perception.

Sheki
2004-Aug-04, 05:05 PM
Fair enough, my apologies to Wally.

On the whole I think our differences are based largely on semantics, specifically with respect to the word "perceived".

To clarify: 1st One observes (gathers data), 2nd one judges/interprets that data against his previous experience, 3rd one perceives/ derives meaning from the data or observation.

1. I observe relative motion between the sun and the horizon
2. I judge the observed motion against what I know (or think I know) about the sun and the horizon.
3. I perceive that the earth has rotated - blocking the sun from view.

Note how point two is the critical point here. Applied to our situation:

1. I observe that two points are a light year apart and that I travelled between them and measured that it occured in less than a year.
2. I (as an ignorant observer) judge these observations against what I know about velocity.
3. I perceive that I have travelled faster than c.

From Wally's perspective:
1. He observes that two points are a light year apart and that he travelled between them, and measured that it occured in less than a year.
2. He judges these observations in light of a thorough understanding of sr.
3. He perceives that he achieved a relativistic velocity, but not faster than c.

The interesting thing that falls out of this, is that if Wally chooses to ignore SR, he can get the giddy feeling that he has exceeded c. Afterall, there he is, scant days older, lightyears away from where he started...

Perhaps it would have been easier for all involved if I had used "incorrect perception of of velocity" instead of "perceived velocity" at the outset?

01101001
2004-Aug-04, 05:14 PM
The logical conclusion here is that you, in the capsule, percieve yourself to be travelling at 1.734c! An "apparent velocity" of 1.734c.
You can experience this at nonrelativistic speeds, slow enough that the fluid nature of time doesn't complicate things. As a passenger (never the driver!) of an automobile, view ahead through a pair of binoculars, both normally, which seems to bring things closer, and reversed, which makes things appear farther away. Normal viewing will give you the feeling that you are moving much more slowly than you really are, while reversed viewing makes your speed seem much faster -- if I recall correctly.

Don't worry. Your driver won't be ticketed for the speed that you perceive you are traveling.

Wally
2004-Aug-04, 06:53 PM
:( Oh man, I just wasted 1/2 hour of my lunch break working on a response, and lost it by accidentally closing my browser. Ouch, that will teach me...


Wally:

Re: "open your mind"
You continue to argue as though I either do not understand or refuse to accept sr. This is not the case (hence I did not start the thread in "Against the Mainstream"). See above. Moreover, i could argue that it is you who is suffering from a closed mind. You refuse to consider what an ignorant observer experiencing relativistic effects would perceive. Instead you are hung up repeatedly interpreting the ignorant observer's observations in accordance with sr. Please recognize that I am not actually arguing with you, but rather just repeatedly failing to make myself understood.

Sheki

First off. My condolences for losing your response! #-o

Secondly. I will concede to you that to an ignorant rider on a ship, yes, he would (incorrectly) assume he travelled faster than light to get to an object that is 'x' light years away from his previous, stationary reference frame. I didn't realize that was your point.

In my own defense, we're more used to discussing accepted conclusions here rather than mistaken ones! :lol: Have a nice day. I've gotta run now (at totally non-relativistic speeds, of course. . .).

daver
2004-Aug-04, 07:25 PM
Keep in mind that, as per the original post, we are talking about perception of velocity, rather than the reality of the situation.

If you like. I'd look out at the window and say that your tape measure is moving past at 0.867 light seconds/second, but i'd see that the light second markings on the tape measure are only 0.5 light seconds apart. So i'd say that the tape measure is moving bast at 1.734 little light seconds/second.

I'd also notice that the distance between the stars is different from what's in the astronomy books--stars along my direction of travel are only half as far away as the astronomy books say, whereas stars perpendicular to my direction of travel are just as far away as the books say.

Anyway, if there was a star 3.4 light years away from where I started, and I was headed towards that star, I'd think it only took 2 years to reach it. Now, once I was going at speed, I'd think that that star was really only 1.7 light years away, and I wouldn't be surprised that it only took me two years to reach it.

Anyway, this is precisely the time contraction that makes it possible to reach the Andromeda galaxy in one human lifetime if only that human were accelerated to within a smidgeon of light speed. That human wouldn't think he was travelling faster than light, just that the distances to things suddenly got a lot shorter.


Yes, but he should know his true velocity, and he knows the distance to the marker. he would have to be pretty daft not to deduce that a year has passed on earth.

He might be a bit confused, though. If he looked out his window when he passed the earth, he would note that the times on earth were passing only half as fast as his. He would think that, at the time he passed the mile marker, only half as much time would have passed on earth as passed for him.

This is the "simultaneity" problem of relativity--people in different reference frames have different concepts of "simultaneous".




if he looked at the Earth as he passed it he would think the clocks on earth were running slowly.

Hmmm. I think you are mistaken here. If time is travelling more slowly for him, and he looks at a clock outside of his capsule, the outside clock should appear to be running faster, not slower.

No, you're off here. If i'm in my spaceship and pass earth at .867 c, i see the earth clocks as ticking slowly. An observer on earth sees my clock as ticking slowly. This might seem like a paradox (see the innumerable discussions on the twin paradox on the net), but isn't. It's a natural consequence of the speed of light being the same in all reference frames.


However, if I might offer some of my own: It 's time for you to go to your library and pick up a book on how not to be condescending. "Its not that hard -- you don't need any math" at all.

I tried fairly hard not to be condescending; obviously I didn't succeed. SR is not that hard, but it is non-intuitive. It took me a few years and quite a few examples to "get it". You have the choice of either watching a bunch of amateurs argue back and forth over it or going to a library and picking up a book on it and working through the examples. There's a chance that you can pick it up by watching the arguments, but the book would have nice pictures and have the advantage of being told from a consistent point of view.


One final point - to be absolutely clear on why length dilation is irrelevant: suppose we modify the original thought experiment. The capsule has no windows, and its only contact with the outside world is a single light that will switch on when an outside sensor detects that the capsule has passed the marker. The only piece of scientific equipment the traveller has is a chronometer. In effect, the traveller knows very little: He knows he is going to be launched with a tremendous amount of energy, and can expect to be going very quickly. He is also going to know that a little light will turn on when he passes a marker that is 1 lightyear from his origin. He is going to know the amount of time (as measured on his own chronometer) that it took him to get to the marker. Also, suppose he is woefully ignorant of sr.

So, when he achieves the marker in less than one year, how could he not percieve that he has travelled faster than c?

Sheki

He could open his eyes. If he were travelling faster than c, he'd have a hard time seeing either the front of the capsule or the back.

However, from the point of view of the person inside the capsule, he'd have to either decide that he'd travelled faster than light or that the marker wasn't as far away as he thought it was.

Sheki
2004-Aug-04, 07:28 PM
Wally

Excellent! Thank you for that response. You see, I consider mistaken perceptions extremely interesting. Especially where one has no way of knowing what is the correct explanation for a given phenomenon.

It is like sitting there on the beach watching "the sun go down", and every once in a while, asking myself "how do I REALLY KNOW that it is the earth that is moving..."

Sheki

Edited to clarify that I was responding to Wally

Sheki
2004-Aug-05, 12:33 AM
daver:

Unlike Wally, you are still trying to answering a question that was never asked.

I apologize for wasting your time.

Sheki

Wally
2004-Aug-05, 02:44 AM
I tried fairly hard not to be condescending; obviously I didn't succeed. SR is not that hard, but it is non-intuitive. It took me a few years and quite a few examples to "get it". You have the choice of either watching a bunch of amateurs argue back and forth over it or going to a library and picking up a book on it and working through the examples. There's a chance that you can pick it up by watching the arguments, but the book would have nice pictures and have the advantage of being told from a consistent point of view.


Uhm. . . Ok daver. I know I'm an amateur here, but ya don't have to throw it in my face! You need to work a little harder on the "not being condescending" thing. . . :lol: (notice the smiley thing. . . I'm only half serious. Sometimes, us novices can reach common ground a little easier than you experts!)

Sheki. I do have to add. If the ignorant rider of the ship has a speedometer on board the ship he was riding on, he will clearly see that he never exceeded the speed of light. Based on that, he can only conclude (regardless of his knowledge of SR) that the distance to the object must have gotten shorter.

Minus the speedometer, yes, he could easily conclude that he must have exceeded the speed of light, impossible as that is!

Tacitus
2004-Aug-05, 06:17 AM
So Sheki's original point was that a "Newtonian" person (ignorant of relativity), travelling at relativistic speeds would be suprised to find himself arriving at his destination before they expected to - i.e. they would assume that they travelled faster than light since they do not understand the importance of their frame of reference in an "Einsteinian" Universe.

His point is not really that surprising since we evolved in a setting (here on Earth) where relativity is of no consequence - its effects are not normally observeable. Our brains did not have to worry about such things in our daily battle for survival.

If, on the other hand, the speed of light was say, 50kmph, it would not have been surprising if we had developed the mental capacity to innately understand the effects of relativistic speeds. But that did not happen so, without the right education or evidence we find the whole idea of relativity paradoxical at first glance.

Just imagine if instead of living in an Einsteinian world we lived in a world where the effects of quantum mechanics were not restricted to "nanoscopic" sizes. You would find that on occasion you could walk through walls, liquids would not stay put in their containers, and forget about 10-pin bowling! All sorts of wierd and mind bending things would happen.

Mike

Sheki
2004-Aug-05, 11:25 AM
Tacitus:

Exactly, and well put. It is that idea of "perceived velocity" (based on our non-relativistic) preconditioned minds that I find interesting. Unfortunately, it seems that I am the only one. However, I thought of a new analogy last night that might shed some light on the subject, and this one does not invlolve relativity at all:

Suppose someone develops a really good flight simulator, one that is not distiguishable from reality. A "pilot" is blindfolded, placed inside, and told to "fly the plane". He flies the plane for a while. We then knock him out/blindfold him (whatever) and remove him from the simulator, wake him up later for a debriefing. At the debriefing we ask some simple questions" "what was your top speed during the flight?" "what was your altitude?" "how far did you go?".

Of course, the "correct" answers are 0 mph, 0 ft, and 0 miles. Nevertheless, if we have succeeded in building a truly realitistic simulator, the pilot would probably give answers in accordance with what he perceived, eg. "500 mph, 20,000 ft, and 1,000 miles".

Now, was our pilot incorrect in his answers? Of course! But, did he nevertheless perceive that he flew? You betcha! Later, when we tell him that he was in a simulator the whole time, he will most assuredly realize that he did not fly anywhere at all. But before then, in his version of reality, he sure flew.

It is this concept, applied to our theoretical near-c traveller, that I find so interesting. Its not that he is violating sr or anything, just that he could quite reasonably think that he is exceeding c - until he is made to understand the reality of the situation.

Sheki

worzel
2004-Aug-05, 12:38 PM
Tacitus:

Exactly, and well put. It is that idea of "perceived velocity" (based on our non-relativistic) preconditioned minds that I find interesting. Unfortunately, it seems that I am the only one.
I think everyone would agree that it on the surface it is bizarre that our notion of absolute distance is actually wrong. But you seemed to be saying that our notion of absolute distance was not wrong and that length contraction was just a convenient way of looking at things in SR.

So then, it seems that "length contraction" is just a convenient construct to get around the fact that the observer percieves himself to be exceeding c.

There is no arguing with 40 km in 12 minutes.


It is this concept, applied to our theoretical near-c traveller, that I find so interesting. Its not that he is violating sr or anything, just that he could quite reasonably think that he is exceeding c - until he is made to understand the reality of the situation.
That is, learn SR, or makes the observation that all those distances he assumed were absolute had in fact shrunk in the direction of his movememt. He then might deduce SR from these observations.

In your simulator example, either the pilots feels no acceleration and therefore directly experiences being at rest the whole time (so it is not indistinguishable from the real thing) or we've figured out how to simulate acceleration without movement which probably isn't allowed in SR or GR (we could hurl planets around him to simulate the acceleration but would this count as a simulator?)

Sheki
2004-Aug-05, 01:55 PM
Worzel,


But you seemed to be saying that our notion of absolute distance was not wrong and that length contraction was just a convenient way of looking at things in SR.

Yes, I greatly regret of that comment - about length contraction. Did you notice my post above where I recanted the statement?
Nevertheless, I feel that the reality of length contraction need not invalidate what I am saying. Picture yourself in that spaceship, with a nice big picture window up front. You are accelerating up to speed, what will you observe? I suspect the length contraction, if anything, will only contribute to your sense of increased velocity - supposing that you only look forward.

Re: the simulator

All I am saying is that until you learn otherwise, your perception is your reality. Please don't get hung up on the seeming impossibility of fooling someone into thinking they were flying an airplane. If you simply must get hung up on this point, then simply assume that the "simulator" is just a bunch of electrodes that we wire into the pilot's brain to directly stimulate those areas that interpet acceleration and movement (Matrix style).

Sheki

Edited for spelling

daver
2004-Aug-05, 09:27 PM
Uhm. . . Ok daver. I know I'm an amateur here, but ya don't have to throw it in my face!

I was including myself in the amateur assessment.

Could you point out where I was being condescending?

worzel
2004-Aug-06, 12:51 PM
Worzel,


But you seemed to be saying that our notion of absolute distance was not wrong and that length contraction was just a convenient way of looking at things in SR.

Yes, I greatly regret of that comment - about length contraction. Did you notice my post above where I recanted the statement?
Ok, sorry.

Nevertheless, I feel that the reality of length contraction need not invalidate what I am saying. Picture yourself in that spaceship, with a nice big picture window up front. You are accelerating up to speed, what will you observe? I suspect the length contraction, if anything, will only contribute to your sense of increased velocity - supposing that you only look forward.
Yes, you certainly can be fooled, but see below.


Re: the simulator

All I am saying is that until you learn otherwise, your perception is your reality. Please don't get hung up on the seeming impossibility of fooling someone into thinking they were flying an airplane. If you simply must get hung up on this point, then simply assume that the "simulator" is just a bunch of electrodes that we wire into the pilot's brain to directly stimulate those areas that interpet acceleration and movement (Matrix style).

Ok, you're talking about the falibility of human perception. When the words like "observe", "perceive", "measure" are used in physics I don't think they have the usual human connotations. People talk about a particle "observing length contraction" or "experiencing time dialation". What is meant is that that is the reality in that frame, whether you are a falible sentient being or and infalible quark just following the laws of physics.

I'm not accusing you of being argumentative, but it just seems from your opening and subsequent posts that you were trying to understand what's really going on according to SR.

Sheki
2004-Aug-06, 02:32 PM
Worzel:


I'm not accusing you of being argumentative,

You would if you knew me! :wink:



but it just seems from your opening and subsequent posts that you were trying to understand what's really going on according to SR.

I gather that it must have seemed that way to those who responded - much to my frustration. Actually, in a way they were right, but there is a very fine point of distinction. I will have to choose my words carefully here to avoid falling into the same trap. You see, I was trying to make a statement about what it must "feel like" to travel at near c, in the traditional sense of "feel". But in order to predict how it must feel, I first have to know exactly what they are actually experiencing. In other words: "Based on what we know is really happening to a person travelling at near c, what will they think is happening to them if they don't know any better?"

In that sense, I think it is entirely possible that if I were piloting that capsule and leaped across a lightyear in 15 days, when I got out of that capsule, I'd probably be saying "wow, that felt just like I was going 24c". Of course I would know better, and I could have shattered the illusion if I took the right kind of measurements along the way...

The reason that I was inquiring about all this to begin with, is that, well - if my understanding about what would really be happening at speeds near c is wrong, then I am going to be wrong about what it would feel like to do it. You cannot predict what a person is going to perceive unless you are very certain about what is actually going to happen to him. (Conversely, you cannot build a realistic flight simulator without knowing what it actually feels like to fly).

Thanks to daver pointing out that I failed to consider length contraction, I realized that my ideas about what the experience would "feel like" might have been wrong, but as the remainder of the thread illustrates, I think I still might be right, because the length contraction - in the absence of good reference points to judge against - is just going to feel like additional velocity.

Clear as mud?

Sheki

Wally
2004-Aug-06, 02:44 PM
Uhm. . . Ok daver. I know I'm an amateur here, but ya don't have to throw it in my face!

I was including myself in the amateur assessment.

Could you point out where I was being condescending?

Forget it Dave. I wrote that response after getting home from my golf league (aka. there was a few beers in me!). I just took your response as meaning sheki was wasting his time arguing SR with me et al here on the board, and that he could only gain knowledge from reading more advanced book on the subject.

In hindsight, I guess that wouldn't be condescending so much as a mini-slam against my lay-man's ability to describe SR. Regardless, I take it back!

worzel
2004-Aug-06, 04:15 PM
Thanks to daver pointing out that I failed to consider length contraction, I realized that my ideas about what the experience would "feel like" might have been wrong, but as the remainder of the thread illustrates, I think I still might be right, because the length contraction - in the absence of good reference points to judge against - is just going to feel like additional velocity.
What does velocity "feel" like? You can only feel the acceleration. Although we would observe you accelerate to near c I'm not sure what you would conclude your speed is due simpley to to your experienced acceleration (although I'm guessing near c too). Hopefully one of these knowledgable chaps will clear that up for us :)

Edited to add my guess.

Sheki
2004-Aug-06, 06:00 PM
Worzel,


What does velocity "feel" like? You can only feel the acceleration.

I knew I would not be able to get through that last spiel without hitting a bump. :(

It was a poor choice of words again. I switched over to using the word "feel" to replace "perceive" so as to avoid the difficulties of interpretation you mentioned earlier. Of course you cannot "feel" velocity in the sense that you mention, but you can certainly "perceive" velocity. You can perceive it in a number of ways:

Visual cues (I hope you can tell the difference between 10 kph and 100 kph when you are driving your car)
Logical cues (v=d/t)
Physiological cues (as you stated you can feel accelleration, and you cannot change velocity without +/- accelleration)

Travelling near c could "feel" like exceeding c primarily because of a failure of interpretation of the logical cues. v=d/t will not be valid (post hoc) because of the length contraction (and switching reference frames). Nevertheless it is pretty hard to shake v=d/t (it's pretty intuitive).

So much to say that when exiting the capsule, I would probably get out, look back in the general direction of earth, and say to myself "hee hee!! they are all over a light year away, but it only took me 15 days to get here! That's 24c! hee hee hee (I am guessing I would be pretty tickled about it) hee hee hee hee hee!!!" Afterall, in such a situation, why should I care about mixing up my reference frames!? (unless of course I want to go back home again - the two years that passed while I was gone will serve as a pretty straight-forward reminder that c is a hard and fast limit!)

Sheki

RoboSpy
2004-Aug-07, 08:23 AM
I've read this whole thread, and now I'm all into it! There's just one question that I'd like to address that was mentioned here, but was never really talked about in detail. I am referring, of course, to the twin paradox.

I hadn't considered it before, though now I can how obvious it is (due to the relativity of velocity) that both the guy in the spaceship and the guy on Earth would observe the clock of the OTHER guy as moving slower. Time dilation occurs for both of them, since we can't really say which of them is "actually" moving. Motion is relative, so either the spaceship is moving or the Earth is moving, depending on how you define the frame of reference. I suppose it would be possible to conceive of a frame of reference in which both were moving, but I have a feeling that would severely complicate things.

So, the guy on the spaceship sees his twin aging slower than he is, and the guy on Earth sees his twin aging slower than he is. The question is, if you were to bring them both together again, which would actually have aged more? I always assumed it would be the guy on the spaceship, but that's not necessarily true, since we can just as easily define the frame of reference as being centered on the spaceship as we can center it on Earth, and thus the Earth is moving rather than the spaceship. Which is moving at relativistic speeds, and which one is older as a result?

Cripes, it is WAY too late to try to think about this kind of stuff...someone help me please.

worzel
2004-Aug-07, 12:59 PM
The question is, if you were to bring them both together again, which would actually have aged more? I always assumed it would be the guy on the spaceship, but that's not necessarily true, since we can just as easily define the frame of reference as being centered on the spaceship as we can center it on Earth, and thus the Earth is moving rather than the spaceship. Which is moving at relativistic speeds, and which one is older as a result?
It's the one that turns around that ages slower. When he turns around his frame of reference changes.

As they are moving apart they see each other's clocks running slow. When they come together they see each other's clocks running slow. But when the twin turn's around his sudden change of frame causes him to see the other's clock suddenly leap forward whereas the twin that stays put just sees the other twin turn around. When you change frame, your notion of what is now over there changes.

Of course, the twin doesn't actually see the clock suddenly leap. But that is what he would deduce once he'd taken into account the delay of the light signals coming to him from earth. Because of the delay, he would have a period just after turning around where he sees the earth-bound twin's clock run fast whereas the earth-bound twin would never see the other's clock running fast.

That's how I figure it anyway, if any of that is wrong I'm sure someone here will correct me.

eburacum45
2004-Aug-07, 03:34 PM
Well, looking at this diagram, the moving twin sees the stay-at-home twin's clocks speed up for the entire duration of the return journey.
http://www.phys.unsw.edu.au/~jw/twin.html

Doesn't she?

RoboSpy
2004-Aug-07, 06:44 PM
It's the one that turns around that ages slower. When he turns around his frame of reference changes.

As they are moving apart they see each other's clocks running slow. When they come together they see each other's clocks running slow. But when the twin turn's around his sudden change of frame causes him to see the other's clock suddenly leap forward whereas the twin that stays put just sees the other twin turn around. When you change frame, your notion of what is now over there changes.

Right, right, but which twin turns around? Motion is all relative, so when the twin in the spaceship turns around to come back to Earth, who is to say that is it not in fact the Earth which turns around to return to the spaceship? Neither twin is really "staying put," at least not in relation to the other twin, so either twin could be said to "turn around." I guess what I'm getting at here is that when we're talking about a spaceships racing away from Earth and coming back, it's no different than if the Earth raced away from the spaceship and came back. In either instance their's time dilation, but who, if anyone, ends up on the short end of it?

One thought I had after I wrote last night's post was about a third frame of reference that I think might help me understand this. Let's presume that we are a third party observer on Earth, and the twins get into two different spaceships and race away at relativistic velocities in completely opposite directions. Let's say they travel with the same speed. Regardless of which twin we observe from Earth, time dilation for that twin is the same, so that when they both returned to Earth, the resulting gained or lost time would be the same for both of them. When they returned to Earth, they'd be the same age. If we then ask either twin what they observed, they would say that the clock onboard the other twin's ship AND the clock on Earth were moving slow, but with different dilations since the relative velocities are different. Now, we know from the observation at the third frame of reference that when both twins return, they should be the same age, even though while in transit they observe one another's clocks going slow. Does this, as you say, "leap forward", counter all the time dilation that took place during the trip such that when everyone returns to the same place they're all the same age again? Even the guy at the third frame of reference?

And if so, is time dilation simply a, I don't want to say illusion, but perhaps a warped perception as a result of moving near the velocity that all our observations must move at? In other words, are things really happening at the same rates, but simply observed differently from all these different frames of reference because light is having trouble keeping up with everyone?

Diamond
2004-Aug-07, 08:38 PM
Worzel,


What does velocity "feel" like? You can only feel the acceleration.

I knew I would not be able to get through that last spiel without hitting a bump. :(

It was a poor choice of words again. I switched over to using the word "feel" to replace "perceive" so as to avoid the difficulties of interpretation you mentioned earlier. Of course you cannot "feel" velocity in the sense that you mention, but you can certainly "perceive" velocity. You can perceive it in a number of ways:

Visual cues (I hope you can tell the difference between 10 kph and 100 kph when you are driving your car)
Logical cues (v=d/t)
Physiological cues (as you stated you can feel accelleration, and you cannot change velocity without +/- accelleration)

Woah!

Let's stop there and think about it. Forget Einstein and special relativity and just focus on what we mean by velocity and acceleration.

It was Galileo who established that if you were below decks in a ship that did not rock about, it would be impossible to tell whether the ship was "really" moving or not. This is the essence of Galilean relativity: that all velocities are relative, and that each observer could regard themselves as at rest, and everybody else moving.

Imagine you are in a rocket ship in deep space. Can you establish whether you are moving or not? Clearly the stars are a long way away and there are no road markers. In fact there are no experiments you could do that would establish whether you are moving at all. You are freely floating inside the rocket ship.

Suppose another rocket ship apparently passes directly by you which is also moving at a constant velocity relative to you: are you moving past a "stationary" rocket ship or is the other rocket ship moving and you are stationary? There's no way to tell - if you called up the astronaut on the other ship, he would be similarly baffled. He would say that he cannot tell whether he's moving or not - he's in free float and every experiment he can do suggests that he is at rest as well!

So the statement of Galilean relativity is: that all reference frames that are not accelerating are entitled to consider themselves at rest.

Now to accleration: It is perfectly possible to tell (other than the noise of the engines) whether you are accelerating or not. Simply put, the ship now causes you to apparently "stick" to one surface - you are no longer freely floating. Changing direction also does this because this is another form of acceleration. You don't need to look out of the window to see that you are accelerating - the effects are obvious - things thrown no longer go in a straight line - and everything appears to be attracted to one surface.

Thus acceleration is NOT relative but absolute. It's always possible to tell whether you, or someone else is accelerating.

As you say, you can "feel" acceleration. But as Newton stated, that a body remains at rest or continued in motion in a straight line unless acted upon by a force, that is, something which causes the body to accelerate either by changing speed or by changing direction. So you "feel" acceleration, but you do not "feel" velocity.

If we go on further, we would follow Einstain (and in fact people who informed Einstein of his opinion) that every person in a free-float situation should measure the laws of physics to be the same and that there is no preferred frame of reference, no absolute space from which everything is measured.

So in essence the first part of Einstein's Relativity is really an update of the relaitivity of Galileo and Newton, that all velocities are relative. The second part is that all non-accelerating frames of reference (you'll find they are sometimes called inertial or free-float frames) are equivalent and the laws of physics measured by each of them is the same, because observers in free-float are each entitled to consider themselves at rest.

Can I recommend a book, which takes this to the next step and explains the insight of Einstein's Relativity theory?

It's called "About Time" by Paul Davies (http://www.amazon.com/exec/obidos/tg/detail/-/0684818221/qid=1091910464/sr=1-1/ref=sr_1_1/104-9156733-4271941?v=glance&s=books)

The next step was from Einstein: that the laws of electromagnetism established by Maxwell (remember that Maxwell discovered that light is an electromagnetic wave which has a fixed speed) imply that EVERY free-float observer should measure the same speed of light. What that does, as Einstein showed in 1905 is that not only is velocity relative, but distance and time are as well. (This is what is covered so well in the book)

Grasp this (and I do recommend reading the book) and you begin to comprehend how Special Relativity is constructed and how time and space are not only not absolute, but are intimately related into something called "spacetime".

worzel
2004-Aug-08, 12:41 PM
Right, right, but which twin turns around? Motion is all relative, so when the twin in the spaceship turns around to come back to Earth, who is to say that is it not in fact the Earth which turns around to return to the spaceship?
Motion can only be measured relative to something else. Acceleration however is immediately apparent. The twin who turns around feels that acceleration. When you are in a lift you have no way of knowing when you are moving or not. It feels the same whether you are going up, down or standing still. But you can feel the change in velocity (acceleration) when you change from standing still to going up or down.


One thought I had after I wrote last night's post was about a third frame of reference that I think might help me understand this. Let's presume that we are a third party observer on Earth, and the twins get into two different spaceships and race away at relativistic velocities in completely opposite directions. Let's say they travel with the same speed. Regardless of which twin we observe from Earth, time dilation for that twin is the same, so that when they both returned to Earth, the resulting gained or lost time would be the same for both of them. When they returned to Earth, they'd be the same age.

And they'd both be younger the earth observer because they both changed their frame of reference when they turned around (accelerated).

Sheki
2004-Aug-08, 10:21 PM
Well, it is great to see some more people getting into the discussion.

Worzel:


Acceleration however is immediately apparent. The twin who turns around feels that acceleration.

This is easily the most fascinating concept to be discussed so far in this thread. It seems that you are basically saying that "the observer that experienced accelleration is considered differently than the unaccellerated observer". I find this interesting because on the one hand, it makes perfect sense to me, but on the other appears to conflict with the "all reference frames are equivalent concept".

If the accelleration due to turning allows us to consider one observer differently than another, then why doesn't the initial accelleration event have the same effect? I would posit that it does not!

Or to state it as clearly as I can:

We have two observers, each thinks the other is moving away from them at velocity x. Relativity tells us that each is perfectly valid in assuming that it is the other that is moving. However, one of them experienced accelleration, the other did not. Therefore, the two reference frames are not equal (or so it would appear based on the logical extention of how I have interpretted what you said).

daver: (if you are still around)

Although I have yet to take your advice and read any (more) books on relativity, I would nevertheless appreciate any light you might shed on the above.

Robospy:

Concerning the twins paradox, I am right there with you. If I have understood worzel correctly, then I would presume:

1. With respect to length contraction - The twin that did not accellerate will perceive the length of the other twin (his spaceship) to contract. The twin that did accellerate will perceive everything EXCEPT himself (his spaceship) to contract. Note: this part at least agrees with what I learned in undergrad physics - which is not to say that it is correct, but at least in agreement with what I was taught.

2. With respect to time dilation - Now this is the "iffy" part. Someone please correct me if my logic is wrong here! - Time dialtion should behave just like length contraction (afterall they are both just dimensions). ie. The twin that did not accellerate will perceive the other twin (his spaceship) to age more slowly (the clock onboard the spaceship will appear to move more slowly than the unaccellearted twin's reference clock). The twin that did accellerate will will perceive the other (the one back on earth) to age more quickly (the clock on earth will appear to move more quickly as compared to his reference onboard the spacecraft).

The net effect, if I am correct, is that regardless of whether or not anyone turned around, accelleration is the distinguishing point. The twin that experienced accelleration will be the younger. The one that did not accellerate will be the older.

Now I fully expect someone to come correct me, because this is obviously to simple to be correct. :D

Sheki

Lorentz
2004-Aug-08, 10:23 PM
And they'd both be younger the earth observer because they both changed their frame of reference when they turned around (accelerated).[/quote]

Einstein's original paper may have expressed relativity's underlying assumptions the best.

In "On the Dynamics of Moving Bodies," by Albert Einstein, translation of the 1905 German paper, Chapter I is the "Kinematic Part." The first paragraph is, "Let us take a system of coordinates in which the equations of Newton hold good. In order to render our presentation more concise and to distinguish this system of coordinates from others which will be introduced thereafter, we shall call it, "the stationary system." The stationary system is a reference frame in special relativity.

Newton, on his part, included equations based on the third law, which is in the "Principia." Law III is stated as, "To every action there is always opposed an equal reaction; or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts."

Just keep reading the two statements over and over. Newton's Third Law and the definition of stationary (i.e., reference) frame.

Neither of the space-moving observer during their turn around are in a frame "where Newton's equations hold good." The two bodies having a "mutual action" are the space ship and the astronaut. The astranaut couldn't accelerate if part of the space ship wasn't pushing him. The floor or couch the astronaut is on pushes him in the direction of the acceleration. The earth observer sees the astronaut (body 1) accelerate the space ship (body 2) in the opposite direction, toward the earth observer. The astronaut feels the force on him, but doesn't see the space ship accelerate relative to himself.

The astronaut feels force of the space ship (floor, couch, ceiling, etc.) on their bodies because of the acceleration. He does not measure the force he applies to the space ship. As far as he is concerned, the space ship is fixed in space and can't move. The earth man can do experiments to "measure" or observe the force on space ship and astronaut, once the light from the turn around reaches him. He can prove Newton's third law.

The space ship applies an action force to the astronaut (body 1). However, there is no "reaction force" to these forces (no body 2). The third law of Newton is violated. To the astronaut, there is a force that in some ways is similar to the gravitational force he grew up in. However, the astronaut can detect no "body" that is applying that force to him. He is being pulled to the floor by a force which in his frame does not obey Newton's third law.

This logic holds true whether or not the law of equaivalence holds true. The turn around astronaut, body 1, can not detect a body producing the force that pushes him against the spaceship. The spaceship, in his view, does not accelerate so the spaceship can't be body 2. Therefore, the principle of Lorentzian invariance doesn't apply at the turn around point to the astronaut. It does apply to the earth observer, who will eventually see the spaceship slow down.

The earth observer lives in a "stationary frame." The astronaut who turns around does not live in a "stationary frame." The astronaut during turn around doesn't have to see every beam of light in a vacuum going at the same speed. Analysis from the astronauts point of view during the turn around have to use a different set of equations than the ones for a "stationary frame." That is why SR is axiomatically correct.

Lorentz
2004-Aug-08, 10:53 PM
2. With respect to time dilation - Now this is the "iffy" part. Someone please correct me if my logic is wrong here! - Time dialtion should behave just like length contraction (afterall they are both just dimensions). ie. The twin that did not accellerate will perceive the other twin (his spaceship) to age more slowly (the clock onboard the spaceship will appear to move more slowly than the unaccellearted twin's reference clock). The twin that did accellerate will will perceive the other (the one back on earth) to age more quickly (the clock on earth will appear to move more quickly as compared to his reference onboard the spacecraft).

Sheki[/quote]

Yes, you are correct. The twin that did accelerate will eventually perceive the other (the one back on earth) age more quickly once forces from the earth twin, during turn around, reaches him. Light pressure would be an example of a force. Until the light reaches the astronaut from the earth twin's turn around point, the astronaut can not see the clocks speed up. He will then see clocks from all over the universe speed up at different rates. However, the astronaut is not in a stationary frame at that point.
To understand the dynamical part of the SR theory, the delay has to be clearly understood. There is a delay before the space ship twin sees the speed up. He is not going to see the relativistic speed up of clocks until the light from earth side twin, emitted when the earth twin accelerated, reaches the rocket man. The information that the earth observer's clock speeded up is not going to reach the astronaut until long after the turn around. This delay is important in understanding relativistic forces. Forces have to have a delay built into them in order to be consistent with special relativity. To understand how the forces cause time dilation and length contraction, you have to understand the basic assumption that forces as measured in the stationary frame can not be instantaneous.

worzel
2004-Aug-09, 09:52 AM
Well, looking at this diagram, the moving twin sees the stay-at-home twin's clocks speed up for the entire duration of the return journey.
http://www.phys.unsw.edu.au/~jw/twin.html

Doesn't she?

That's why I said "Of course, the twin doesn't actually see the clock suddenly leap. But that is what he would deduce once he'd taken into account the delay of the light signals."

If you look at stay-at-home twin's world line on the turn-around twin's diagram, the turn-around twin figures from his spacetime diagram that on the way out and on the way back the stay-at-home twin ages more slowly (and by the same amount the stay-at-home twin figures the turn-around twin ages more slowly). But the turn-around twin also figures that the stay-at-home twin suddenly jumps forward several years at the point he turns around.

worzel
2004-Aug-09, 10:16 AM
If the accelleration due to turning allows us to consider one observer differently than another, then why doesn't the initial accelleration event have the same effect? I would posit that it does not!

Or to state it as clearly as I can:

We have two observers, each thinks the other is moving away from them at velocity x. Relativity tells us that each is perfectly valid in assuming that it is the other that is moving. However, one of them experienced accelleration, the other did not. Therefore, the two reference frames are not equal (or so it would appear based on the logical extention of how I have interpretted what you said).
You have to be carefull here. SR doesn't deal with acceleration. The point about the turn-around twin accelerating is just to demonstrate that there is a difference in their experience and so the twins' experiences are not logicallly symmetrical.

The experiment can be set up such that there is no acceleration involved by having triplet A (earth bound) observe triplet B fly by when their clocks happened to be synchronized, then later triplet C fly by triplet B again with coincidentally synchronized clocks, then triplet C fly by triplet A. C's clock will be behind A's clock even though we only had non-accelerating clocks. The difference is caused by the switch in frame of reference from B's to C's.


1. With respect to length contraction - The twin that did not accellerate will perceive the length of the other twin (his spaceship) to contract. The twin that did accellerate will perceive everything EXCEPT himself (his spaceship) to contract.
Yes, everything moving relative to you contracts in its direction of motion relative to you.


2. With respect to time dilation - Now this is the "iffy" part. Someone please correct me if my logic is wrong here! - Time dialtion should behave just like length contraction (afterall they are both just dimensions). ie. The twin that did not accellerate will perceive the other twin (his spaceship) to age more slowly (the clock onboard the spaceship will appear to move more slowly than the unaccellearted twin's reference clock). The twin that did accellerate will will perceive the other (the one back on earth) to age more quickly (the clock on earth will appear to move more quickly as compared to his reference onboard the spacecraft).

The net effect, if I am correct, is that regardless of whether or not anyone turned around, accelleration is the distinguishing point. The twin that experienced accelleration will be the younger. The one that did not accellerate will be the older.

For years I thought it was the acceleration that made the difference. It isn't, not in SR anyway. While at a constant, non-zero, relative velocity both twins see each other aging slowly, they must, who's to say which one sees anything different. It is the change of frame (and therefore what is "now") for the turn around twin that accounts for his actual youth, depsite the fact that he sees his twin age more slowly on the way out and on the way back. (all assuming "see" means what they would figure once they'd taken into account the delay of the signals to each other)

eburacum45
2004-Aug-09, 11:15 AM
I think doppler effect should be taken into account too; if you look at the diagrams on that page I linked to
here it is again
http://www.phys.unsw.edu.au/~jw/twin.html

you will see that both parties see the other person's clocks speed up not slow down on the return journey- but this is due to Doppler effect, which must be accounted for.

worzel
2004-Aug-09, 11:54 AM
I think doppler effect should be taken into account too; if you look at the diagrams on that page I linked to
here it is again
http://www.phys.unsw.edu.au/~jw/twin.html

you will see that both parties see the other person's clocks speed up not slow down on the return journey- but this is due to Doppler effect, which must be accounted for.
True, but this is where a lot of confusion arises when trying to understand the problem - certainly was for me. It makes it look like it's some sort of optical illusion - the doppler effects would still be there (although slightly different) if the universe were Newtonian, but there would be no difference in their ages.

Using synchronized clocks at regular intervals in each frame of reference does away with the doppler effects and IMO really shows what's going on (which is a sudden jump of distant clocks when changing your inertial frame).

eburacum45
2004-Aug-09, 01:08 PM
Well it is the sudden jump that is causing the dilation effects; nothing can suddenly switch from
travelling away from you at relativistic speed
to
travelling toward you at relativistic speed

without a heck of a lot of acceleration...

worzel
2004-Aug-09, 01:22 PM
Well it is the sudden jump that is causing the dilation effects; nothing can suddenly switch from
travelling away from you at relativistic speed
to
travelling toward you at relativistic speed

without a heck of a lot of acceleration...
As I pointed out earlier, you can do it with three people, one for each frame, so there is no acceleration at all. The transformation from the co-ordinates of the outgoing to the incoming frame of reference (at the point where they co-incide) does entail a sudden jump of distant clocks. Their notion of what is "now over there" differs.

worzel
2004-Aug-09, 01:34 PM
Well it is the sudden jump that is causing the dilation effects; nothing can suddenly switch from
travelling away from you at relativistic speed
to
travelling toward you at relativistic speed

without a heck of a lot of acceleration...
Check out this link:

http://mentock.home.mindspring.com/twin2.htm

It explains the twin paradox from a GR perspective using the travelling twin's point of view. I'm not sure if the GR explanation from the earth bound twin's point of view would be the same as SR or different (dependent on the twin having to accelerate to turn around for instance). If the later then how would it explain the variant with no acceleration? And if the former then wouldn't the acceleration in the normal version also be a factor thus giving a different answer to SR? :-?

Lorentz
2004-Aug-09, 11:17 PM
[
You have to be carefull here. SR doesn't deal with acceleration. The point about the turn-around twin accelerating is just to demonstrate that there is a difference in their experience and so the twins' experiences are not logicallly symmetrical.
[/quote]

By that logic, there is no acceleration in Newton's Laws of motion. There are just a series of Galilean boosts which always happens in pairs (action-reaction). The point about bodies having different mass just explains why the boosts are not logically symmetrical.

You forgot all that work we had to do in calculus just to define derivative. The Lorentian boosts are just a variation on the Galilean "boosts" we had to do to define velocity and acceleration. The size of each step go to zero as a limit, and the number of steps increases to infinity. Saying there is "no" acceleration in SR can be confusing. The point about the acceleration of the turn around twin is that the forces can't be totally ignored in SR.

Acceleration is a mathematical concept, not a physical one. Its part of the kinematics. The physics part is the forces (or alternatively, the energies) that cause the acceleration. The assymmetry is part of the dynamics. Newton's Principia defines acceleration in terms of "Galilean boosts," which is why some of Newton's illustrations of orbits look like polygons.

Newton is considered by many the inventor of calculus. There was no formal definition of acceleration until he constructed one.

SR does deal with acceleration, as does Principia.

worzel
2004-Aug-10, 07:59 AM
By that logic, there is no acceleration in Newton's Laws of motion. There are just a series of Galilean boosts which always happens in pairs (action-reaction). The point about bodies having different mass just explains why the boosts are not logically symmetrical.

[snip]



Sorry. Should have said SR doesn't deal with relativistic effects due to acceleration. You can ignore acceleration in the TP and SR still resolves it.

worzel
2004-Aug-10, 11:57 AM
You forgot all that work we had to do in calculus just to define derivative. The Lorentian boosts are just a variation on the Galilean "boosts" we had to do to define velocity and acceleration. The size of each step go to zero as a limit, and the number of steps increases to infinity. Saying there is "no" acceleration in SR can be confusing. The point about the acceleration of the turn around twin is that the forces can't be totally ignored in SR.
Are you saying that if we approximate the twin turning around by taking just one instananeous change in intertial frame, then approximate it by two smaller changes, etc. etc. until we have an infinte number of infinitely small changes of intertial frame then the SR derivation can, in the limit, derive the GR acouunt due to the apparent gravitional field under acceleration?

From what I understand, the amount of time spent accelerating is cancelled out by the fact that you'd have to have a greater acceleration the shorter the period of acceleration so even an instaneneous change in direction should give the same answer.

Wally
2004-Aug-11, 03:20 PM
Well it is the sudden jump that is causing the dilation effects; nothing can suddenly switch from
travelling away from you at relativistic speed
to
travelling toward you at relativistic speed

without a heck of a lot of acceleration...
As I pointed out earlier, you can do it with three people, one for each frame, so there is no acceleration at all. The transformation from the co-ordinates of the outgoing to the incoming frame of reference (at the point where they co-incide) does entail a sudden jump of distant clocks. Their notion of what is "now over there" differs.

Well said Worzel. It all comes back to perception of simultaneous events. While triplet C and B will agree their clocks are in sync when they pass by each other, they will NOT agree as to what the clock says back on Earth. B will say it's been running slow, and is behind his "normal" time, while C will say it's running slow, but is currently years ahead of B's clock. Both would be right, from their respective FoR.

edited to add: Also B and C will disagree on exactly when B left Earth. This difference works out to explain why they perceive earth's time as different. i.e. B will say "I just left earth 15 days ago", while C will say "no, I saw you leave Earth years ago", thus it makes sense for C to see time on Earth as being years ahead of what B perceives. Again, both perceiptions are absolutely corrrect, from their own FoR.

Lorentz
2004-Aug-12, 01:14 AM
The Lorentian boosts are just a variation on the Galilean "boosts" we had to do to define velocity and acceleration. The size of each step go to zero as a limit, and the number of steps increases to infinity. The point about the acceleration of the turn around twin is that the forces can't be totally ignored in SR.

1) Are you saying that if we approximate the twin turning around by taking just one instananeous change in intertial frame, then approximate it by two smaller changes, etc. etc. until we have an infinte number of infinitely small changes of intertial frame then the SR derivation can, in the limit, derive the GR acouunt due to the apparent gravitional field under acceleration?
Pretty much I am saying that. That is how most scientists handle the acceleration. Einstein did that with a rotating "reference frame."


From what I understand, the amount of time spent accelerating is cancelled out by the fact that you'd have to have a greater acceleration the shorter the period of acceleration so even an instaneneous change in direction should give the same answer.
The length of time in the trip, as seen by the twins, ends up being independent of the values of acceleration in the limit of stepwise changes in velocity. That is, if the trip takes a year to the earth twin, but the turn around occurs in a second, it doesn't matter how the acceleration is distributed in that one second. The velocity profile for that second cancels out, two nearly equal quantities are subtracted, etc. However, it could be analyzed by breaking that step up in tiny Lorentz boosts.

GR can handle gravitational fields generated by "sources," by which mean masses. SR can't by itself handle gravity generated by masses, only acceleration generated gravitational fields. SR plus the law of equivalence equals GR.

Breaking down a velocity profile into a series of infinitesmal Lorentz boosts in SR is fully like breaking down a velocity profile into a series of infinitesmal Galilean boosts in Newtonian physics. And in both cases, one has to introduce the concept of force to arrive at a unique solution. Thus, you need dynamics when analyzing the turn around. Kinematics by itself is not sufficient.
Of course, people who don't understand forces isn't going to understand the dynamics of Principia or SR.

Bruce Dunn
2007-May-10, 05:55 PM
If I take the example of driving to work and only drive there at a speed approaching 'c' once, I am stuck wih the conclusion that on one day and one day only the distance was less than 40 km. Acually my wife dove that fast twicw so on one day it was a different distance for each of us. This can probably be nicely plotted geometrically using time as a geometrical dimension. I think there is a concept we might call modal time. That is your mosy frequent distance between home and work.