Time Dilation and Relative Time

[name123]

The prisoner example is a straw man. You can always take any solvable physical scenario and remove information until you can no longer solve the problem.

In the 3 sphere prisoner example which was analogous to your example and where you were told what was moving relative to what (unlike in the 2 sphere prisoner examples I've used), what problem did you need to solve that you weren't given enough information for?

Also the point of removing the information in the 2 sphere example, is to emphasis what matters when applying the equation, and that is done by realising you can't do it without the relative motion.

Also neither are straw men, as neither are an incorrect paraphrasing of a position on the subject.

 

[Dale]

The proper time along any path is ##\int \sqrt{g_{ab}dx^a dx^b}##

So you need to know the metric, g, and the path, dx. The metric is the Minkowski metric since this is a SR question. But if you don't know the path then you cannot calculate the time.

 

[PeterDonis]

Why do you think it matters in flat spacetime which felt acceleration

Because in flat spacetime, given two observers that both pass through the same pair of events (i.e., they start out together, separate, then come together again), the one who feels acceleration will always be the one who ages less. That's how the general rule I gave simplifies in flat spacetime.

if there was no absolute answer with regards to which was moving relative to the other

Velocity and felt acceleration are two different things. Velocity is not absolute. Felt acceleration is.

(since we aren't concerned with any time slow that may be due to acceleration)?

There is no "time slow due to acceleration" in general. Again, the general rule is that different paths through spacetime can result in different aging. There's nothing about acceleration in that rule. The difference in aging being due to felt acceleration in flat spacetime just happens to be the way the general rule simplifies for flat spacetime.

Can you think of a counter example (in flat spacetime) where it wouldn't be the one which was moving relative to the other that experienced the time dilation?

Um, what? If A is moving relative to B, B must be moving relative to A. It's a symmetric relationship. Once again, velocity and felt acceleration are two different things.

I can think of one in which the one that accelerated last wouldn't: a case where the other object had accelerated more earlier, you could imagine a few more steps in the prisoner for example.

If both prisoners feel acceleration, then the simplified rule I gave obviously doesn't work; you need to apply the more general rule, and look at the specific path each one follows through spacetime, and compute the elapsed proper time along each path. The profile of felt acceleration for each prisoner will affect the path they follow through spacetime, but it's the path that determines aging. Once again, that's the general rule: the general rule does not say it's "who is moving" that matters, and it does not say that it's felt acceleration that matters; it says that it's the path each observer takes through spacetime that matters. There is no other way to formulate the general rule. Any rule that mentions velocity or felt acceleration is only a simplified rule of thumb for certain cases.

It seems to me on each thought experiment, if they started off together, and then went off and came back, the one that underwent time dilation would be the one that was moved more during the experiment relative to the other

What does "moved more relative to the other" mean? Relative motion is a symmetric relationship. Once again, the general rule is what I stated above; there is no way to get around actually looking at the path through spacetime of each observer in the general case. You can't use "who is moving" as a general rule; it doesn't work.

(given the notion of a slowing of the laws of physics with motion)

The laws of physics don't slow down with motion; that doesn't even make sense.

 

[name123]

Velocity and felt acceleration are two different things. Velocity is not absolute. Felt acceleration is.

But we are talking about two velocities being compared, sure you might know that a billion years ago they were at rest together before one accelerated away before continuing at an relative accelerated velocity, and by that I mean that the velocity is absolutely faster than the other.

If both prisoners feel acceleration, then the simplified rule I gave obviously doesn't work; you need to apply the more general rule, and look at the specific path each one follows through spacetime, and compute the elapsed proper time along each path.

Well neither need be feeling accelerated during the period of time we concern ourselves with, we can imagine them to have different constant velocities. There is still the question about the relative time dilation during this period. Maybe in another example one was the last to accelerate or decelerate but maybe if you'd known more of the story you'd have considered the other to be moving faster (they were together, before one accelerated to a faster velocity).

The laws of physics don't slow down with motion; that doesn't even make sense.

It does to me, because time in physics is measured by using simultaneity in the rest frame. So if you were to imagine two parallel universes which had the same laws of physics, but in one the motion was slower than in the other, you could describe that as the laws of physics going slower in one than the other, not that it could be measured from within one, as measurements would be the same. From perspective which could view both universe though, one could say that the laws of physics ran slower in one than another. Another example would be a simulated physical universe on a computer, it could be run on a faster computer, and you could watch the physics going twice as fast, even though the computer generated characters with each simulation couldn't take a measurement to tell whether theirs was running faster or slower. I'm guessing Bergson made this type of point to Einstein, as Bergson had pointed it out in his writings.

 

[Simon Bridge]

What they said.

It is important to be clear when expressing your ideas, for eg.

It seems to me on each thought experiment, if they started off together, and then went off and came back, the one that underwent time dilation would be the one that was moved more during the experiment relative to the other

...define "moved more". How do you decide who moved more and who didn't? You say "relative to the other" but they move the same amount relative to each other.

Pay special attention to the comments regarding the space-time geometry.
You can take the space-time geometry and the path through it in any reference frame and come up with the same answer for the resulting time difference.
This is how you can get absolute time differences without absolute motion.

Your questions appear to have started from an assumption of absolute motion.
You need to discard this idea - it's hard I know: we all go through it.

 

[Simon Bridge]

But we are talking about two velocities being compared, sure you might know that a billion years ago they were at rest together before one accelerated away before continuing at an relative accelerated velocity, and by that I mean that the velocity is absolutely faster than the other.

... The relative velocity of two objects depends on the reference frame that the velocities are measured in.
There is no way to determine one's own absolute velocity - but you can tell how fast others are moving relative to you.
Put another way - you see another object wizz past you: you have no way to tell how much of it's speed comes from your motion and how much comes from it.
You are forced, empirically, to abandon the idea of absolute motion.

OTOH: you can measure your own acceleration - if you see an object accelerate past you, you can tell how much of the change in velocity you observe comes from something happening to it and how much due to something happening to you. This is something you should be familiar with from Galilean relativity and Newtonian mechanics.

Well neither need be feeling accelerated during the period of time we concern ourselves with, we can imagine them to have different constant velocities. There is still the question about the relative time dilation during this period.

This is usually just referred to as "time dilation" and is well covered in the links from post #5.
To each observer, the other observer's clock is ticking slower than theirs. What's wrong with that?

It does to me, because time in physics is measured by using simultaneity in the rest frame. So if you were to imagine two parallel universes which had the same laws of physics, but in one the motion was slower than in the other, you could describe that as the laws of physics going slower in one than the other, not that it could be measured from within one, as measurements would be the same.

What do you mean by motion being "slower"? How would you be able to tell?
Just being able to imagine something, and write it down, does not mean it makes sense: what you have imagined does not make sense.

In Different reference frames we can have communication between them - why all this talk about light pulses etc.
It means we can compare the rate that events happen in different frames.

From perspective which could view both universe though, one could say that the laws of physics ran slower in one than another. Another example would be a simulated physical universe on a computer, it could be run on a faster computer, and you could watch the physics going twice as fast, even though the computer generated characters with each simulation couldn't take a measurement to tell whether theirs was running faster or slower.

The computer speeds or slows the simulation by speeding or slowing the clocks - the laws of physics in the simulation don't have a speed. But this may help us understand what you are trying to say ... if we look into someone elses spaceship, we would see them carry out common activities in slow motion. This is normal time dilation.

I'm guessing Bergson made this type of point to Einstein, as Bergson had pointed it out in his writings.

Your guessing? You don't know? Did you try checking?

Anyway: Bergson was a philosopher - we are talking about physics here.
In particular, Bergson's philosophy was pretty much the opposite of science and physics.
He is not a useful source, therefore, for understanding science.

 

[PeterDonis]

by that I mean that the velocity is absolutely faster than the other

There is no such thing. As Simon Bridge says, you appear to have a mistaken concept of absolute velocity; that concept does not work.

neither need be feeling accelerated during the period of time we concern ourselves with, we can imagine them to have different constant velocities. There is still the question about the relative time dilation during this period

Yes, relative time dilation. If we are in flat spacetime, and neither one feels acceleration, and they are moving relative to each other, then there is no absolute fact of the matter about which one is "time dilated"; each one appears time dilated to the other. The only absolute comparison you can make is if the two of them separate and then come back together again; but in flat spacetime there is no way to do that without at least one of them feeling acceleration.

Anyway, you are still apparently not even reading what I wrote about the general rule: that it is the path each one takes through spacetime that matters. "Time dilation" is not a fundamental concept in relativity; it just isn't. Trying to use it as though it were a fundamental concept will not work.

It does to me, because time in physics is measured by using simultaneity in the rest frame

Correction: coordinate time is measured by using simultaneity. But coordinate time is relative, not absolute. The only absolute "time" in relativity is proper time--the time elapsed on a clock following a particular path through spacetime. If two observers are spatially separated, there is no absolute fact of the matter about "what time it is" for either observer relative to the other; it's a matter of convention--specifically, of which simultaneity convention you adopt. (Btw, the simultaneity convention of an inertial frame is not the only possibility, even in flat spacetime.)

 

[PeterDonis]

So if you were to imagine two parallel universes which had the same laws of physics, but in one the motion was slower than in the other, you could describe that as the laws of physics going slower in one than the other, not that it could be measured from within one, as measurements would be the same

If all the measurements in both universes are the same, there is no way to tell them apart physically, so your statement that "in one the motion was slower than in the other" has no meaning.

Another example would be a simulated physical universe on a computer, it could be run on a faster computer, and you could watch the physics going twice as fast

Twice as fast relative to the computer, not relative to the simulated universe. You are mixing up time in the "outer" universe, in which the computer exists, with time in the simulated universe. They are not the same, and while people have speculated about our own universe being a simulation, that is off topic for this thread. We are talking here about time within our universe and measurements that can be made within our universe.

 

[name123]

What they said.

It is important to be clear when expressing your ideas, for eg...define "moved more". How do you decide who moved more and who didn't? You say "relative to the other" but they move the same amount relative to each other.

Not with absolute motion they don't though. But why absolute motion? Because with it you have an explanation for why one thing moving relative to another will experience relative time dilation in flat space.

And it makes sense to that if two entities which are in the same rest frame and both accelerate relative to there initial rest frame using thrusters, but then at one point one accelerates even more (relative to their initial rest frame) and the other decreases (relative to their initial rest frame) then it makes sense to think that relative to the initial rest frame the one that has accelerated is moving faster than the one that decelerated relative to the initial rest frame. And you could do the same taking an imaginary marble at the point of the Big Bang and considering measuring motion relative to that (that being the initial rest frame). If the history of the motion doesn't matter then why would you need to know which one had accelerated perhaps a few billion years ago in order to work out which one would undergo the time dilation in flat space? With two bodies at motion relative to each other it just seems like your saying they could equally be considered the rest frame, but then admit that you can't actually just arbitrarily pick one as the rest frame if you'd want to match the actual results for which would undergo the time dilation.

 

[name123]

If all the measurements in both universes are the same, there is no way to tell them apart physically, so your statement that "in one the motion was slower than in the other" has no meaning.

Just because you couldn't tell them apart wouldn't mean that it had no meaning. You could understand the difference between them if you were outside of both. If you had a machine where you could go back and from either for example. They could each follow the same laws of physics as your own as far as you could tell, but maybe you notice that when coming back from one your clock has only moved on by half what the clock in the other universe had said, but when you go to the other universe and come back your clock has moved on twice as much as the clock in the visited universe would have led you to believe. In such a case it would be quite simple I would have thought to have understood the idea that in the first visited universe although the laws of physics appeared the same, they were actually running at twice the speed relative to those in your native universe, so 100 seconds in there was only 50 seconds in your native universe, but in the second visited universe although the laws of physics appeared the same, they were actually running at half the speed of those in your native universe, so 100 second in there would be 200 seconds in your native universe. It doesn't matter whether it corresponds to reality, to have a meaning you'd only need to understand the story.

 

[Drakkith]

Not with absolute motion they don't though. But why absolute motion? Because with it you have an explanation for why one thing moving relative to another will experience relative time dilation in flat space.

This explanation fails with a simple example. Consider 3 observers, A, B, and C. A and B are approaching each other at some velocity while C is stationary with respect to A and B. The amount of time dilation in A and B's frame, as measured by C, are equal, since both are approaching C at an equal velocity. However, from A's frame, B is experiencing more time dilation than C, since B is moving faster than C. B also measures more time dilation in A's frame than in C's, for the same reason. This always holds true as long as the three frames are inertial.

If there were absolute motion and a preferred frame of reference then there should be some situation where although the three observers are moving identically to the above situation with respect to each other, C would measure either A or B as having less time dilation than itself. In other words, there would be a situation where either A or B is moving slower than C with respect to this preferred frame and C would therefore see either A or B's clock as ticking faster than its own.

We've looked for this effect. It does not happen. There is no such thing as absolute motion.

And you could do the same taking an imaginary marble at the point of the Big Bang and considering measuring motion relative to that (that being the initial rest frame).

This is a misconception. The big bang occurred at every point in space at the same time. There was no 'initial rest frame'.

With two bodies at motion relative to each other it just seems like your saying they could equally be considered the rest frame, but then admit that you can't actually just arbitrarily pick one as the rest frame if you'd want to match the actual results for which would undergo the time dilation.

There is no 'actual' result. Both objects are experiencing time dilation when viewed from the other object. And both are equally valid in saying that the other is experiencing time dilation. After all, you cannot see yourself experiencing time dilation, you can only look at other frames of reference and compare yours to theirs.

Let me remind you that PF exists to teach people about mainstream science, not to argue about whether that science is right or wrong. If you wish to learn about special relativity, you are welcome here. If you want to argue that it doesn't make sense, then PF is not the place for you. Consider this your only warning before I lock this thread and issue an infraction.

 

[PeterDonis]

Just because you couldn't tell them apart wouldn't mean that it had no meaning. You could understand the difference between them if you were outside of both.

Which is off topic for both this thread and this forum. If you want to talk about speculations like this, please start a separate thread in an appropriate forum (the only one I can think of would be General Discussion).

 

[name123]

This explanation fails with a simple example. Consider 3 observers, A, B, and C. A and B are approaching each other at some velocity while C is stationary with respect to A and B. The amount of time dilation in A and B's frame, as measured by C, are equal, since both are approaching C at an equal velocity. However, from A's frame, B is experiencing more time dilation than C, since B is moving faster than C. B also measures more time dilation in A's frame than in C's, for the same reason. This always holds true as long as the three frames are inertial.

If there were absolute motion and a preferred frame of reference then there should be some situation where although the three observers are moving identically to the above situation with respect to each other, C would measure either A or B as having less time dilation than itself. In other words, there would be a situation where either A or B is moving slower than C with respect to this preferred frame and C would therefore see either A or B's clock as ticking faster than its own.

We've looked for this effect. It does not happen.

I'm not sure what you mean by C being stationary with respect to A and B. Do you mean that it is in the middle and the gap between it and each of them is decreasing at the same rate? As I understood it that you can't work out what the time dilation would be for anyone of them compared to another one of them other. We've been through this on this thread with the 2 sphere prisoner thought experiment. With any two of them you'd need to know which has accelerated was the understanding I was given by those on this forum on this thread.

You say we've looked for this effect, I was wondering if you have any references for any of the experiments, as I'm only aware of the plane one that I mentioned at the start of this thread.

I had said "With two bodies at motion relative to each other it just seems like your saying they could equally be considered the rest frame, but then admit that you can't actually just arbitrarily pick one as the rest frame if you'd want to match the actual results for which would undergo the time dilation."

To which you replied:

There is no 'actual' result. Both objects are experiencing time dilation when viewed from the other object. And both are equally valid in saying that the other is experiencing time dilation. After all, you cannot see yourself experiencing time dilation, you can only look at other frames of reference and compare yours to theirs.

Yes but in the plane experiment which I quoted in the original post there was supposed to be 'actual' time dilation in the sense that when they compared the clocks they were different, and some of the difference was reported as being down to time dilation due to SR. Could you perhaps explain to me why that measured difference didn't count as an actual result, because that would help me understand. But what I meant is that you can't just pick which one you like to be the rest frame if when you measure the time dilation in one of them (in plane case on the earth) one actually has a time difference. And it can't be that it just depends which frame you measured it in because for example there could be an example of a long spaceship with a clock on the front passing much shorter space ship. It could take a thousand years to pass, but it might not take the shorter ship long to get up to its speed and dock on the back (and so into its rest frame), and then check it by the ships internal video link.

 

[Drakkith]

I'm not sure what you mean by C being stationary with respect to A and B. Do you mean that it is in the middle and the gap between it and each of them is decreasing at the same rate? The point is that you can't work out what the time dilation would be for anyone of them compared to another one of them other. We've been through this on this thread.

I assume you are talking about posts 19-22? If so, then I think there's been a misunderstanding. Time dilation is indeed easily worked out in this example. I think you're getting confused over the difference in how much each twin has aged in the twin paradox and normal time dilation. Plain old time dilation occurs when any two or more observers are moving relative to each other. It deals with how quickly time is passing in one frame of reference as viewed from another.

You say we've looked for this effect, I was wondering if you have any references for any of the experiments, as I'm only aware of the plane one that I mentioned at the start of this thread.

The GPS satellite system is a good example. They are orbiting the Earth as the Earth orbits the Sun. Combined, these motions allow them to move in all three axes over time. If there were a preferred frame of reference, we should see a different rate of time passage in some satellites as our direction and speed along our orbit change. At some point two satellites would be traveling opposite directions, with one traveling slower relative to this preferred frame and other traveling faster. This would mean that the time dilation experience by each satellite would be different. But this never occurs. There is never a point where satellites moving in one direction experience more/less time dilation than the others.

In addition, many particle accelerator experiments deal with time dilation on a daily basis. Since they are rotating with the Earth's surface and are in orbit of the Sun, it should give an effect similar to the above example. However, we never see any discrepancies in these experiments that would suggest a preferred frame of reference. Decay rates do not change and the operation of the particle accelerators never require re-tuning to account for a variable amount of time dilation that would be experienced if there were a preferred frame.

Yes but in the plane experiment which I quoted in the original post there was supposed to be 'actual' time dilation in the sense that when they compared the clocks they were different, and some of the difference was reported as being down to time dilation due to SR. Could you perhaps explain to me why that difference didn't count as an actual result to help me understand.

Your using terminology incorrectly, which is leading to confusion. There is no such thing as 'actual time dilation'. Time dilation is not a difference how much something has aged, it is a difference in the rate that time passes. The former is a direct consequence of the latter, but means something different. The two clocks did indeed measure different amounts of time as having passed. However, while the plane was flying, an observer on the plane would have seen the same amount of time dilation in the Earth's frame that the observer on the Earth saw in the plane's frame, even though there is a difference in time passed when the plane lands.

I'm afraid I can't explain why this occurs, as my knowledge of the details of SR is not up to par. I just know it's all about which observer accelerates. Perhaps the wiki article can explain it better than I can: http://en.wikipedia.org/wiki/Twin_paradox#Resolution_of_the_paradox_in_special_relativity

 

[harrylin]

Some clarifications seem to be required here:

Not with absolute motion they don't [move the same amount relative to each other] though. But why absolute motion? Because with it you have an explanation for why one thing moving relative to another will experience relative time dilation in flat space.

That is correct: as a matter of fact, the Lorentz transformations were first derived based on the concept of absolute motion together with the relativity principle.
- https://en.wikisource.org/wiki/Translation:On_the_Dynamics_of_the_Electron_(June)

However, as Poincare explained in the introduction, the starting assumption was that such absolute motion cannot be detected. In other words: no preferred frame exists for the laws of motion. No matter what scenario you try to come up with, you can freely pretend that any inertial reference system is the "true rest frame" and make correct predictions.

[..] With two bodies at motion relative to each other it just seems like your saying they could equally be considered the rest frame, but then admit that you can't actually just arbitrarily pick one as the rest frame if you'd want to match the actual results for which would undergo the time dilation. [..]

It's a useful calculation exercise to check that for different inertial reference systems the same prediction is given for when two clocks are compared side by side.
Note that this is a necessary consequence of the fact that such was a starting assumption on which the Lorentz transformations were based!

Compare kinetic energy in classical mechanics, which uses Newton's "Galilean transformations": you can choose any inertial frame to calculate what happens at collision, and that fact is just as counter intuitive, as kinetic energy is similarly non-linear with speed. And still it works. :)

 

[Drakkith]

Hmm, Harry, you mind checking and making sure what I've explained regarding preferred frames is correct? After reading your post I'm not so sure anymore.

 

[harrylin]

Hmm, Harry, you mind checking and making sure what I've explained regarding preferred frames is correct? After reading your post I'm not so sure anymore.

I had the impression that it's incorrect, but instead of criticizing doubtful posts I decided to simply present a clarification to the OP that is correct beyond doubt. ;)

A main cause for confusions is the fact that in the literature "preferred frame" can be found to mean different, incompatible things. For example several people on this forum use it as synonym of "absolute", in direct contradiction with its meaning in the older literature.

Quick check:

This explanation fails with a simple example. Consider 3 observers, A, B, and C. A and B are approaching each other at some velocity while C is stationary with respect to A and B. The amount of time dilation in A and B's frame, as measured by C, are equal, since both are approaching C at an equal velocity. However, from A's frame, B is experiencing more time dilation than C, since B is moving faster than C. B also measures more time dilation in A's frame than in C's, for the same reason. This always holds true as long as the three frames are inertial.

OK

If there were absolute motion and a preferred frame of reference then there should be some situation where although the three observers are moving identically to the above situation with respect to each other, C would measure either A or B as having less time dilation than itself. In other words, there would be a situation where either A or B is moving slower than C with respect to this preferred frame and C would therefore see either A or B's clock as ticking faster than its own.

We've looked for this effect. It does not happen. There is no such thing as absolute motion. [..]

Here you equalized "absolute motion" with "preferred frame". But if there were a preferred frame for the laws of physics, then the Lorentz transformations would be wrong. Inertial motion is "relative" in the sense that absolute motion cannot be detected, if it exists or not; the same is true in Newtonian mechanics. SR says nothing about such metaphysical interpretations.

 

[Drakkith]

Here you equalized "absolute motion" with "preferred frame". But if there were a preferred frame for the laws of physics, then the Lorentz transformations would be wrong. Inertial motion is "relative" in the sense that absolute motion cannot be detected; the same is true in Newtonian mechanics.
As others have explained on this forum, one can choose any inertial frame and pretend it to be in reality an "absolute rest frame" with respect to which all motion "really" exists. That cannot change the predictions - and SR has nothing to say about it.

I was under the impression that if a preferred frame of reference existed, all lorentz transformations would be relative to that frame, making this preferred frame also the frame that absolute motion is measured relative to. Is that incorrect?

 

[harrylin]

I was under the impression that if a preferred frame of reference existed, all lorentz transformations would be relative to that frame, making this preferred frame also the frame that absolute motion is measured relative to. Is that incorrect?

It's a meaning of "preferred frame" that is indeed used in the literature, at odds with its original meaning. In fact, in what way would such a frame be "preferred", if we can take any other inertial frame and obtain the same results? Moreover, one would not be able to measure relative to it, since one cannot identify it...

 

[Drakkith]

It's a meaning of "preferred frame" that is indeed used in the literature, at odds with its original meaning. In fact, in what way would such a frame be "preferred", if we can take any other inertial frame and obtain the same results?

You couldn't in a world with absolute motion. That was my point.

 

[harrylin]

You couldn't in a world with absolute motion. That was my point.

SR says that we cannot observe absolute motion; it says nothing about the existence or not of absolute motion. See also the FAQ: https://www.physicsforums.com/threads/what-is-the-pfs-policy-on-lorentz-ether-theory-and-block-universe.772224/

 

[name123]

It's a useful calculation exercise to check that for different inertial reference systems the same prediction is given for when two clocks are compared side by side.

It sounds as though you are saying that with two bodies at motion relative to each other, either could be considered the rest frame when making the prediction for when they are compared side by side.

I don't understand how this can be the case and if you don't mind me recapping some of this thread, I'll explain why.
I was reading in Clifford M.Will's book "Was Einstein right? Putting General Relativity to the Test" that there was an experiment done where in October 1971 an experiment was done with radioactive clocks, and plane trips taken going with the spin of the earth, and against it. He reports: "The eastward trip took place between October 4 and 7 and included 41 hours in flight, while the westward trip took place between October 13 and 17, and included 49 hours in flight. For the westward flight the predicted gain in the flying clock was 275 nanoseconds (billionths of a second), of which two-thirds was due to gravitational blue shift; the observed gain was 273 nanoseconds. For the eastward flight, the time dilation was predicted to give a loss larger than the gain due to the gravitational blue shift, the net being a loss of 40 nanoseconds, the observed loss was 59 nanoseconds".

Now in the experiment there was the gravitational blue shift (where clocks 'tick' faster when not under gravity, so when flying the plane clock 'ticks' faster than the one on the Earth which is under a higher gravity), and the time dilation (where clocks 'tick' relatively slower with relative motion). The issue at the heart of this thread is how can you tell which clock would appear slower if the experiment were done in flat spacetime (where there is no gravitational blue shift). And here is a thought experiment:

Imagine a prisoner, prisoner A who is a physicist in prison sphere in a space. Prisoner A has a telescope, a clock, and a laser measuring device and can measure the distance to the back of another prison sphere that is in front of them (imagine prison spheres only have a glass front). Also imagine that these prison spheres are within a space within a dense asteroid formation, and that these prevent the stars from being seen. Imagine that Prisoner A then loses consciousness and wakes up to measure the distance between it and the other prison sphere increasing at a fixed rate. Prisoner A loses consciousness again and wakes up to measure that the distance between it and the other prison sphere is decreasing at a fixed rate. Prisoner A loses consciousness again and wakes up, with the other prison sphere back in front of its.

How could prisoner A tell if the clock in its prison sphere or the one in the sphere in front would be the one which had 'ticked' less? It has been said on this thread that you can't, that you'd need to know which had accelerated. If you disagree could you please let me know, if you agree, then we can imagine just a fragment of the prisoner thought experiment episode, say where the prisoner had woken up to see the distance between it and the other sphere closing. And let's re-examine the idea that that with two bodies at motion relative to each other, either could be considered the rest frame when making the prediction for when they are compared side by side. It seems that it doesn't work, one will have gone slower than the other and if you were prisoner A you couldn't tell which it would be.

The answer can't be that it all depends on which rest frame the clocks are compared in because there could be an example of a long spaceship with a clock on the front passing much shorter space ship. It could take a thousand years to pass, but it might not take the shorter ship long to get up to its speed and dock on the back (and so into its rest frame), and then check it by the ships internal video link.

Another issue, though related, is that you said in another post (which shows on mine as #56) that "SR says that we cannot observe absolute motion; it says nothing about the existence or not of absolute motion." What I'm not sure one is why it couldn't be said that the one that actually ends up with slower clock due to SR time dilation when compared was the one with the greater absolute motion?

 

[PeterDonis]

I don't understand how this can be the case

This is a basic feature of SR. It has been explained repeatedly in this thread.

How could prisoner A tell if the clock in its prison sphere or the one in the sphere in front would be the one which had 'ticked' less?

On the information given, he can't, because he can't see the other prisoner's clock. So he needs more information to draw any conclusion. That answer has been given to you repeatedly in this thread.

we can imagine just a fragment of the prisoner thought experiment episode

But for just this fragment, we lose the key feature of the scenario, which is that the prisoners start out together, separate, and then come back together again. Only if that is true is there any absolute fact of the matter about which one ages less. If we just look at one segment of the scenario, where the two prisoners are moving relative to each other and neither one is accelerating, then there is no absolute fact of the matter about which one's clock is running slower; it depends on the frame you choose. That has been explained repeatedly in this thread.

It has been said on this thread that you can't, that you'd need to know which had accelerated.

Because, as has been explained repeatedly in this thread, in flat spacetime, that is the simplest piece of additional information that would allow him to draw a conclusion.

At this point we're just going around in circles. Thread closed.