# Time Dilation and Relative Time

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".

I understood him to have explained previously that with special relativity things moving relative to you (or any other frame of reference) will undergo time dilation relative to that reference. That the reference used was an imaginary clock in the centre of the earth, and the time dilation for the clock on the earth, and the clock in the plane being calculated relative to it. When going with the spin of the earth, the clock on the plane is moving faster relative to the imagined stationary clock in the centre of the world, than it is when it flies against the spin of the earth. So the eastward trip would show more of a time slow for the plane relative to the earth (which moves the same speed relative to the centre of the earth in both trips), and in the experiment while travelling against the spin time was gained (time was going faster), when travelling with it time dilation incurred countered the gain from less gravity to give an observed loss (the time dilation was seen).

What I don't understand is this can happen and time be relative. To hopefully make the problem in understanding it that I have more clear, imagine we performed 2 thought experiments, and in each we removed the planet, so we could ignore general relativity and just look at the special relativity aspect. Imagine that we just had the clock that was previously in the plane and the clock that was previously on the ground. Now relative to each other they could move as they did in the experiment in the with the spin leg. Now if things could be looked at relatively, I'd be assuming that in the first thought experiment we could imagine that the stationary point of reference was the clock that was on the ground in the experiment. We could see the two clocks together at the start, the 2nd clock leave the frame of reference and move relative to it before returning to the same frame of reference. I was thinking that since the 2nd clock would be moving relative to the first, actual time dilation for it would be expected. So it would lose time relative to the clock that was being considered to the first clock that we are imagining to be stationary. However I'm not sure why we couldn't we also have considered a different thought experiment in which we consider the 2nd clock to be the stationary frame of reference, and there the 1st clock would move relative to it, and there would be time dilation for the 1st clock, and so at the end the 1st clock would have lost time relative to the stationary 2nd clock. I guess I'm wrong because otherwise it would seem to me that the time dilation in the plane experiment showed which clock was moving relative to which (the clock in the plane underwent the time dilation relative to the clock on the Earth's surface because it was moving relatively faster), and therefore motion wouldn't be relative, and therefore nor would the time dilation.

As you can probably see, I'm slightly confused on the issue, and would appreciate any help on the matter.

## Answers and Replies

A.T.
Search for "Twin Paradox".

Simon Bridge
Homework Helper
What you have described is called the Twins Paradox.
Put more simply, consider two observers moving with respect to each other.
Each observer looks at the other's clock and observes the other clock is slow.
This is not a problem... it is similar to how two observers separated by a distance each observe the other to be short.
We call this second thing "perspective", and we are used to it so it does not seem strange.

I've taken a quick look at the twin paradox, http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_intro.html, but am unfortunately still having problems understanding it. In the intro it seems already to be settled that it Stella that was moving because of the acceleration, but that would mean that it isn't relative which one was moving. It says:

"When our heroes meet again, what do they find? Did time slow down for Stella, making her years younger than her home-bound brother? Or can Stella declare that the Earth did the travelling, so Terence is the younger?

Not to keep anyone in suspense, Special Relativity (SR for short) plumps unequivocally for the first answer: Stella ages less than Terence between the departure and the reunion.

Perhaps we can make short work of the "travelling Earth" argument. SR does not declare that all frames of reference are equivalent, only so-calledinertial frames. Stella's frame is not inertial while she is accelerating. And this is observationally detectable: Stella had to fire her thrusters midway through her trip; Terence did nothing of the sort. The Ming vase she had borrowed from Terence fell over and cracked. She struggled to maintain her balance, like the crew of Star Trek. In short, she felt the acceleration, while Terence felt nothing.

Whew! One short paragraph, and we've polished off the twin paradox. Is that really all there is to it? Well, not quite. There's nothing wrong with what we've said so far, but we've left out a lot. There are reasons for the popular confusion."

Then it goes onto declare that according to Terrance the thing took 14 years and a day, and according to Stella 2 years, but I'm not sure how they got there.

Say there is A and B, they move apart and come back again, A claims that B was moving and that A was stationary, B claims that A was moving and B was stationary. How to tell which one was right, and which gets the slower clock is what I'm not sure about. I mean I can understand being able to say which one gets the time dilation if you knew whether either A or B's claim was right, but without knowing it (if both claims could be said to be equally as valid), how can you tell?

Simon Bridge
Homework Helper
Twins paradox is the special case where the two observers meet again.
To do that, there must have been some accelerating... which means that SR no longer applies.
However it is possible to make headway using the tools of SR.

Basically: it is not a matter of who was really moving... such questions are meaningless.

Try...
http://www.physicsguy.com/ftl/html/FTL_intro.html
... go through the 1st two chapters.

Basically, Alice and Bob will agree about the final outcome, but disagree about hoe it came about. (Though they can resolve their differences by applying some relativity.)

Lets say Alice sees Bob zip by, travel some disrance, turn around and come back. Bobs clock is slow, so it is no surprise that Bob returns younger.

What Bob sees is this: Alice zips by, travels for some distance, then Bob exerts himself for a bit so that Alice turns around, and comes back.
The bit where Bob is using energy is where the outcome is decided for Bob.
On the outbound and inbound legs, Alice's clock is slow, but while turning around, her clock goes really fast.

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I'll take a look at the paper thank you. Though your answer had some points that looked interesting.

Say there is A and B and they separate and come back again. Let us say that the gap between them increases exponentially by one hundredth the distance light would have travelled in a second, each second, for 5 seconds, so that the gap is 0.15 of a light second before continuing to increase at 0.5 of a light second for 3 seconds (I don't think this 3 seconds wouldn't require an accelerating frame), before increasing at 0.25 of a light second for 1 second, then decreasing by 0.25 of a light second (possibly a turn around like in the twin paradox), and continuing to decrease in a fashion opposite to the increase until they are at rest with one another again.. Now during any acceleration I understand that you're saying that SR wouldn't be appropriate, and I'd read on the twin paradox page I quoted earlier that for acceleration a psuedo magnetic field is added, and presumably this slows time as gravity does in general relativity. Though would you be saying that with the plane experiment, the slowing of time was done only during the moments of acceleration, because I was thinking that they were saying that some of the difference in the clocks was due to time dilation. If so then there would be some slowing of time in the period in between the acceleration(s) and deceleration(s). But which would get it A or B? Because when the clocks met up in the actual plane experiment one had it and the other didn't and in the book it was saying that SR was responsible for some of the difference. But if all frames of reference are equally valid, how can you tell whether A or B would get the type of time dilation they are saying they measured in the plane experiment. I was wondering if you could let me know what extra information you'd need to know before you could tell me whether A or B would have undergone the relative slowing of time because I can't see how you could do it from the information I have given you about A and B so far.

Nugatory
Mentor
I've taken a quick look at the twin paradox, http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_intro.html, but am unfortunately still having problems understanding it. In the intro it seems already to be settled that it Stella that was moving because of the acceleration, but that would mean that it isn't relative which one was moving. It says:
"When our heroes meet again, what do they find? Did time slow down for Stella, making her years younger than her home-bound brother? Or can Stella declare that the Earth did the travelling, so Terence is the younger?

Not to keep anyone in suspense, Special Relativity (SR for short) plumps unequivocally for the first answer: Stella ages less than Terence between the departure and the reunion.

You are misunderstanding the explanation. The unequivocal answer is that Stella ages less than Terence. That's not the same thing as saying that she is "really" moving. We can construct variants of the twin paradox in which both twins accelerate (the Hafele-Keating experiment you're asking about is like that) and ones in which neither twin accelerates. All of these variants work the same way: If you analyze them correctly using either the space-time diagram approach or the Doppler approach, you will find that in general the twins age by different amounts between their separation and their reunion.

Nugatory
Mentor
To do that, there must have been some accelerating... which means that SR no longer applies.

This is a very common misunderstanding. Special relativity works just fine in the presence of acceleration - google for "Rindler coordinates" for an example, and "relativistic rocket" for another.

Special relativity does not work in curved spacetime, which is to say in the presence of non-negligible tidal gravitational effects. That's what makes it "special" - it applies only to the special case of flat spacetime, whereas general relativity applies in the general case of flat or non-flat space-time. They're both perfectly comfortable with accelerations.

Simon Bridge
Homework Helper
Well, the standard high school handwavey SR does not work for accelerating frames. You have to do something extra.
Rindler coords and such would, above, fall under "However it is possible to make headway using the tools of SR".
Its the sort of thing that tends to further confuse beginners... and we dont need it for the expaination above.

I the link that you gave I've read "Remember that relativity involves figuring out what an observation would seem like to one observer once you knew what it looked like to another observer who is moving with respect to the first" and that is something I haven't said in the A and B scenario. I assume A could say that B's sphere went away and came back, and that B could say that A's sphere went away and came back (maybe they are prisoners in spheres in space).

I wouldn't have thought it could be done from there either though, because if one report would be different from the other then how could they equally represent the non-moving frame. But maybe I'm missing something, or would more information be required?

Simon Bridge
Homework Helper
Say there is A and B and they separate and come back again. Let us say that the gap between them increases exponentially by one hundredth the distance light would have travelled in a second, each second, for 5 seconds, so that the gap is 0.15 of a light second before continuing to increase at 0.5 of a light second for 3 seconds (I don't think this 3 seconds wouldn't require an accelerating frame), before increasing at 0.25 of a light second for 1 second, then decreasing by 0.25 of a light second (possibly a turn around like in the twin paradox), and continuing to decrease in a fashion opposite to the increase until they are at rest with one another again.. Now during any acceleration I understand that you're saying that SR wouldn't be appropriate,
The usual SR arguments you have been trying to use dont work during the acceleration.
The usual approach it to treat each velocity change as a shift from one inertial frame into another.
You example above just overcomplicates things. To see the details, simplify.

and I'd read on the twin paradox page I quoted earlier that for acceleration a psuedo magnetic field is added, and presumably this slows time as gravity does in general relativity.
Um.. whaa... off that I would recommend not using that page ever again. Just ignore it.

The link you posted talks about "a pseudo gravitational field"... not magnetic.
It invokes the equivalence principle in GR, where uniform acceleration is indistinguishable from gravity. The author basically says that one party also undergoes a gravitational time dilation in addition to the usual one in SR. Since only one party accelerates, there is a difference in age.

Though would you be saying that with the plane experiment, the slowing of time was done only during the moments of acceleration,
No. Time does not slow down any more than distant objects get smaller.
Time dilation is a geometric effect that always happens.
Im saying that what determines the final outcome is the moments of acceleration.

there would be some slowing of time in the period in between the acceleration(s) and deceleration(s). But which would get it A or B?
Neither party gets slower time.
The party that ends up younger is the one that has the acceleration.

Because when the clocks met up in the actual plane experiment one had it and the other didn't and in the book it was saying that SR was responsible for some of the difference. But if all frames of reference are equally valid, how can you tell whether A or B would get the type of time dilation they are saying they measured in the plane experiment.
In the standard examples one of the parties has undergone an acceleration. Thats how you tell.

I was wondering if you could let me know what extra information you'd need to know before you could tell me whether A or B would have undergone the relative slowing of time because I can't see how you could do it from the information I have given you about A and B so far.
You mean, which one ends up younger... time does not slow down for either of them... you are right, in your original example, you did not specify who did the accelerating. If you mean to describe a situation where A and B follow exactly symmetrical motions, then there will be no difference in their ages when they meet up.

Reread my description for Alice and Bob before... see how Bob has a different experience to Alice?

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You are misunderstanding the explanation. The unequivocal answer is that Stella ages less than Terence. That's not the same thing as saying that she is "really" moving. We can construct variants of the twin paradox in which both twins accelerate (the Hafele-Keating experiment you're asking about is like that) and ones in which neither twin accelerates. All of these variants work the same way: If you analyze them correctly using either the space-time diagram approach or the Doppler approach, you will find that in general the twins age by different amounts between their separation and their reunion.

Thank you for your help. Though and while I'm still confused, perhaps you could help me clear up my misunderstanding.

Imagine that there were two prisoners, prisoner A and prisoner B, both physicists. They are both in prison spheres which are equipped with telescopes, they are in the same rest frame and can see each other, but a gas is released from within the spheres, and they lose consciousness. When they wake up, using their telescopes they see that the distance between them is increasing at a fixed rate. They are gassed again, and when they wake up they see that they are travelling towards each other at a fixed rate. They are gassed again. And when they wake up, they are back next to each other again. How could they use SR to tell which of them had would undergo time dilation relative to the other, or would they need more information?

Simon Bridge
Homework Helper
Imagine that there were two prisoners, prisoner A and prisoner B, both physicists. They are both in prison spheres which are equipped with telescopes, they are in the same rest frame and can see each other, but a gas is released from within the spheres, and they lose consciousness. When they wake up, using their telescopes they see that the distance between them is increasing at a fixed rate. They are gassed again, and when they wake up they see that they are travelling towards each other at a fixed rate. They are gassed again. And when they wake up, they are back next to each other again. How could they use SR to tell which of them had would undergo time dilation relative to the other, or would they need more information?
On the return journey they can tell which will end up younger... the one who accelerated while unconscious will be younger. This answer has already been provided in post #5... please reread, and check the reference I gave you... its a bit clearer than the references youve been using.
Note... both prisoners will observe time dilation. Neither will experience it.
"Time dilation" is the name given to the effect where observers in relative motion observe each other's clocks to run slow.

Concentrate on the simple situation in post #5 where one observer is accelerating.... can you not see that the two experiences are physically different?

In the standard examples one of the parties has undergone an acceleration. Thats how you tell.

So when there are two bodies in flat space time moving relative to each other, you need to know the history in order to know which one would undergo relative time dilation as described by SR?

pervect
Staff Emeritus
There are multiple ways of "explaining" the twin paradox. I'll try one approach that I think might be helpful here. It considers an analog of the twin paradox, the "odometer paradox".

We know that a clock, moving a long a world-line, keeps a sort of time known as "proper time". And the "paradox" is that two clocks, taking different routes, show different readings when they meet up.

Let's consider the situation where we have, not clocks, but odometers, and the odometers move not through space-time, but through space. Then we know that the odometer measures the "length" of a path travelled through space.

We then construct the following "paradox". We have three points, A, B, and C. If you go from A to C, directly, you get one reading on your odometer, but if you go from A to B to C, you get a different reading. How is this possible?

Well, you probably don't even think there is a "paradox" there at all. But you can translate things that are confusing you about the Twin Paradox into the Odometer paradox, and gain some insight.

For instance, someone might ask "what is the mechanism that makes the path from A to C shorter than the path from A to B to C". You'd probably answer that the mechanism is geometry, or maybe more specifically, the triangle inequality.

Suppose someone asks "If you go from A to B to C, it's longer than going from A to C. How do you explain that if you go from A to C to B, that that is longer than going from A to B". You might say "It's the straight line distance that's always the shortest, and this is due to geometry".

Suppose someone has doubts that odometers are consistent, because they come up with different answers to distance depending on the path you take? You might reply - "well, that's just how they work, they behave in a consistent manner, you just have to understand them." The translation of this would be "The way time works in relativity is that clocks travelling along different paths read differently when the reunite, that's just how they work, they behave in a consistent manner, you just have to understand them".

I can't possibly come up with all possible objections one might have to clocks in relativity, but I've translated what I think is a reasonable sample into objections about clocks into objections about the behaviors odometers.

The abstract elements common to both odometers and clocks (which is the notion of curves , curves which have lengths) allow one to create useful analogies. One key element here is to point out that time and space are closely related in relativity, and that thinking about time in the way that one used to think about space can be productive.

.

You lost me there a bit, I wasn't thinking there was a curve between A and C I was thinking it was a straight line, the one with the curve (B was a curve on the A B C route) was longer. Also I'm not too clear on geometry even the 2D examples on surfaces seem to me to be 3d examples, where the extra dimensional information is held in the surface. I tend to think of it as Cartesian space, though I can understand that there is the idea that another spacial dimension exists the information about which is held in the 4D surface. But I find it hard to imagine. I appreciate all the effort, but it if you want to help if you could just explain this for me.

Imagine that there were two prisoners, prisoner A and prisoner B, both physicists. They are both in prison spheres which are equipped with telescopes, they are in the same rest frame and can see each other, but a gas is released from within the spheres, and they lose consciousness. When they wake up, using their telescopes they see that the distance between them is increasing at a fixed rate. They are gassed again, and when they wake up they see that they are travelling towards each other at a fixed rate. They are gassed again. And when they wake up, they are back next to each other again. How could they use SR to tell which of them had would undergo time dilation relative to the other, or would they need more information? Perhaps when there are two bodies in flat space time moving relative to each other, you need to know the history in order to know which one would undergo relative time dilation as described by SR? Or perhaps there would be certain geometry readings you would be looking for?

russ_watters
Mentor
In the intro it seems already to be settled that it Stella that was moving because of the acceleration, but that would mean that it isn't relative which one was moving.
You got it! Acceleration is not relative, so the twin that accelerates is the one that is "really" moving. Think about it this way: the one that accelerated had to fire-up a big rocket to do that. It doesn't make sense to say that you can fire a rocket engine and everyone else in the universe accelerates away from you as a result.

You got it! Acceleration is not relative, so the twin that accelerates is the one that is "really" moving. Think about it this way: the one that accelerated had to fire-up a big rocket to do that. It doesn't make sense to say that you can fire a rocket engine and everyone else in the universe accelerates away from you as a result.

Would thinking of it that way mean that motion may have a history involving acceleration, and that if so then it would have to be taken into account? If so then I guess that sorts out what your answer would be to the following: Imagine that there were two prisoners, prisoner A and prisoner B, both physicists. They are both in prison spheres which are equipped with telescopes, they are in the same rest frame and can see each other, but a gas is released from within the spheres, and they lose consciousness. When they wake up, using their telescopes they see that the distance between them is increasing at a fixed rate. They are gassed again, and when they wake up they see that they are travelling towards each other at a fixed rate. They are gassed again. And when they wake up, they are back next to each other again. How could they use SR to tell which of them had would undergo time dilation relative to the other, or would they need more information? When there are two bodies in flat space time moving relative to each other, do you need to know the history in order to know which one would undergo relative time dilation as described by SR?

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russ_watters
Mentor
How could they use SR to tell which of them had would undergo time dilation relative to the other, or would they need more information?
If they aren't provided with information on who did the accelerating, they would not know.

If they aren't provided with information on who did the accelerating, they would not know.
So when there are two bodies in flat space time moving relative to each other, you'd need to know the history in order to know which one would undergo relative time dilation as described by SR.

Yes.
Well that clears that up then I guess, thanks for all the help :)

Simon Bridge
Homework Helper
So when there are two bodies in flat space time moving relative to each other, you need to know the history in order to know which one would undergo relative time dilation as described by SR?
In the prisoner example, at all times that they can watch each other, they both see the other's clock running slow.
i.e. Both prisoners observe the time dilation - which is just a description of how perspective works at different speeds.
Does it make sense to talk about them "undergoing" time dilation?

The twin's paradox is a result of the different histories ... I think this is what you are trying to ask about ... how one ends up younger than the other? In which case - yes: you need to know their histories to make predictions.

Naturally the prisoners in the example need only look at each other.

Just a few more precisions:
Would thinking of it that way mean that motion may have a history involving acceleration, and that if so then it would have to be taken into account?
Clock rate and the length of a ruler only depend on the current state, as long as they were not permanently affected (deformed/broken/deregulated) by earlier accelerations. What depends on history however, is the accumulated number of seconds that a clock displays.
[..] Imagine that there were two prisoners, prisoner A and prisoner B, both physicists. They are both in prison spheres which are equipped with telescopes, they are in the same rest frame and can see each other, but a gas is released from within the spheres, and they lose consciousness. When they wake up, using their telescopes they see that the distance between them is increasing at a fixed rate. They are gassed again, and when they wake up they see that they are travelling towards each other at a fixed rate. They are gassed again. And when they wake up, they are back next to each other again. How could they use SR to tell which of them had would undergo time dilation relative to the other, or would they need more information?
Please allow first a little nitpicking (however it is important for correct understanding): In SR, everyone and everything is in the same rest frame. What you surely mean with that someone is "in a rest frame", is that someone is "at rest in" a certain inertial reference system ("frame" in usual jargon) which you call "rest frame".

Now, clearly, from the symmetrical way that you phrased your question, they would need more information, as the accumulated clock times on both watches depends on their velocities as function of time, as determined with any inertial reference system.
When there are two bodies in flat space time moving relative to each other, do you need to know the history in order to know which one would undergo relative time dilation as described by SR?
Yes, you do need to know the speed as function of time to predict the accumulated proper clock time. On the other hand, if you know that for the time under consideration they are both in purely inertial motion, then relative time dilation as described by SR is simply a function of measured relative speed, as you can see from the "time dilation" formula.

All this was already explained in Einstein's 1905 paper: scroll to § 4 of http://fourmilab.ch/etexts/einstein/specrel/www/

He there also introduced what is called the "clock hypothesis": it is assumed that acceleration has in itself no effect on clock rate, and that turned out to be correct for atomic processes. Note however that there he also ignored a possible effect from gravitation on clock rate; in practice that cannot be ignored ("otherwise identical conditions" should include the same gravitational potential).

PS you also asked "How could they use SR". There are different ways to discern non-inertial motion according to SR, such as by watching the stars with a telescope. From that they could figure out each others' v(t) history.

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In the prisoner example, at all times that they can watch each other, they both see the other's clock running slow.
i.e. Both prisoners observe the time dilation - which is just a description of how perspective works at different speeds.
Does it make sense to talk about them "undergoing" time dilation?

The twin's paradox is a result of the different histories ... I think this is what you are trying to ask about ... how one ends up younger than the other? In which case - yes: you need to know their histories to make predictions.

Naturally the prisoners in the example need only look at each other.

I thought it did make sense that they underwent time dilation, because in the plane experiment that this thread started with, some of the time difference was put down to SR (it wasn't all due to gravity).

Here is a different version of the prisoner 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 use SR to tell which sphere had undergone time dilation relative to the other or would it need more information? When there are two bodies in flat space time moving relative to each other, do you need to know the history in order to know which one would undergo relative time dilation as described by SR and reportedly measured in the plane experiment (mentioned in the original post on the thread)?

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Just a few more precisions:

Clock rate and the length of a ruler only depend on the current state, as long as they were not permanently affected (deformed/broken/deregulated) by earlier accelerations. What depends on history however, is the accumulated number of seconds that a clock displays.

I thought on the plane experiment (which is a bit like the twin experiment), that some of time difference was due to gravity, and some due to SR. And with the twin experiment, people said that you'd need to know which one accelerated to know which one would get the time dilation due to SR.

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 use SR to tell which sphere had undergone time dilation relative to the other or would it need more information? When there are two bodies in flat space time moving relative to each other, do you need to know the history in order to know which one would undergo relative time dilation as described by SR and reportedly measured in the plane experiment (mentioned in the original post on the thread)?

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Simon Bridge
Homework Helper
I thought it did make sense that they underwent time dilation, because in the plane experiment that this thread started with, some of the time difference was put down to SR (it wasn't all due to gravity).
The thing to realize is that the term "time dilation" does not properly refer to any of the difference in times that you are talking about here.

Time dilation (in SR) is a technical term that refers to the effect that moving clocks run slow.
This happens equally for each pair of observers: Bob and Alice each see the others clock run slow by the same amount.

The Twin's paradox effect is where two observers disagree about the elapsed time for the same journey.
This is often introduced (as in this case) as a consequence of time dilation - but it is not properly referred to by that term.

If you take care to use the correct terms, things are more likely to end up clearer.

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). 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 use SR to tell which sphere [ended up younger] relative to the other or would it need more information?

The thing to realize is that the term "time dilation" does not properly refer to any of the difference in times that you are talking about here.

But if I could just quote the 1st paragraph of the original post:
---
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".
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Notice that in the experiment they are saying that the clocks on the plane and the ground really were different and that for the eastward flight, the time dilation due to SR was greater than the gravitational blue shift, and that this caused a loss of time (whereas with the journey against the planet spin when the SR time dilation (time loss) < gravitational blue shift (time gain) there was a gain). And it is this reported difference in time due to SR that I am talking about.

Regarding whether the physicist in the thought experiment could tell which prison sphere clock would be slower, you said:

Which is fine, but if there is an absolute answer with regards to which one was moving relative to the other (the one with the relative time dilation), then how is it (or time) truly relative (as opposed to just being ignorant as to the absolute motion (or time)), since it isn't arbitrary which one can correctly be considered to be moving relative to the other one?

As I currently understand it, the laws of physics going slower for the object the faster the object moves though space (not that the slowing could be measured within a rest frame because in a rest frame the clocks would be governed by those laws, and since time in physics is based on the simultaneity of events in the rest frame, there wouldn't be any slowing measured by physics in the rest frame, it could only be observed when viewing a rest frame in motion relative to your's) when things are under a gravitational force or moving through space wouldn't make things truly relative (the motion isn't as you can see when you take the plane experiment and the single prison sphere thought experiment together). I presume the slowing of the laws of physics measured as being due to motion through space is linear to allow for it to be calculated using the attributable relative motion, and by that I mean you'd need to know not just the rate at which they were parting (the relative motion), but how much each was responsible for the rate (the attributable relative motion). The one the most responsible for the rate I assume would undergo the time dilation relative to the other, and if they were equally responsible they'd undergo equal time dilation (the laws of physics would have slowed equally for both of them if they weren't at absolute rest).

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PeterDonis
Mentor
if there is an absolute answer with regards to which one was moving relative to the other

There isn't. But if the two meet up again (which the two prisoners do in your scenario, and which the clocks that were taken on airplanes did in the Hafele-Keating experiment described in what you quoted from Will), there is an absolute answer with regards to which one aged more--you just compare their clock readings.

The key thing to realize is that attributing the difference in aging, between the prisoners or between the airplane clocks, to "motion" (either all of it, as in the prisoner case, or part of it, as in the airplane case) is not a law of physics; it's a rule of thumb. The law of physics is that objects that take different paths through spacetime might have aged differently when they meet up again. To know, in general, how differently they age, you have to know the geometry of the spacetime and the path each one takes through that geometry. That's the general law of physics, and it works for any scenario whatsoever.

But there are some scenarios where the geometry of the spacetime, or the kinds of paths being followed, have particular properties that let you simplify the analysis. In the prisoner case, spacetime is flat, so the analysis simplifies to: whichever prisoner felt acceleration will have aged less when they meet again. In the airplane case, the spacetime geometry is a little more complicated, but it still has important symmetries that let you split up the effects on aging into a "gravitational" piece (due to altitude above the center of the gravitating mass) and a "motion" piece (due to motion relative to a non-rotating frame centered on the gravitating mass). So instead of having to go through the full computation of aging along each airplane's path through spacetime, you can do a simpler calculation using the altitude change and the motion. But this is not the general law; it's just a simplified version that happens to work in this particular scenario. If you're really trying to understand the physics, you need to understand the general law, that it's taking different paths through spacetime between the same two events (where the two observers or clocks split up and then meet again) that causes differential aging.

You quoted where I had said "if there is an absolute answer with regards to which one was moving relative to the other" and replied:

There isn't. But if the two meet up again (which the two prisoners do in your scenario, and which the clocks that were taken on airplanes did in the Hafele-Keating experiment described in what you quoted from Will), there is an absolute answer with regards to which one aged more--you just compare their clock readings.

You also said:
In the prisoner case, spacetime is flat, so the analysis simplifies to: whichever prisoner felt acceleration will have aged less when they meet again.

Why do you think it matters in flat spacetime which felt acceleration if there was no absolute answer with regards to which was moving relative to the other (since we aren't concerned with any time slow that may be due to acceleration)? 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? 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. 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, no matter how long the thought experiment took place over, or how many accelerations or decelerations took place. Which seems to me to be a strong argument for saying that there is an absolute answer with regards to which one moved more, and it is given by which one experienced the time dilation according to SR, and explained by it (given the notion of a slowing of the laws of physics with motion).