Could there be an absolute 'state of reference?'

[mrnike992]

Could there be an absolute 'state of reference' somewhere in the universe, perhaps at the location of the original center? If so, would it have to hold the same frame of reference in each dimension, including time? How would it do so?

Looking at the Hafele-Keating Experiment in particular, the atomic clocks were affected in different ways due to different positions and velocities. The velocities/positions of course would be relative to the observer, however is it possible that there is a "correct" spot in which to observe the universe?

I apologize if this is in the wrong location, a stupid question, confusing, or if this has been discussed before. This is my first post here at Physics Forums.

 

[PeterDonis]

Hi, mrnike992, and welcome to PF!

Could there be an absolute 'state of reference' somewhere in the universe, perhaps at the location of the original center?

No. There is no "original center" to begin with. But in any case, there isn't any absolute "state of reference" (by which I assume you mean a frame of reference from which to make observations); all frames of reference are on an equal footing in principle. Different frames of reference may be more convenient for making certain observations, but that's all.

That doesn't mean there aren't any absolutes at all; see below.

Looking at the Hafele-Keating Experiment in particular, the atomic clocks were affected in different ways due to different positions and velocities. The velocities/positions of course would be relative to the observer

No, they're relative to *each other*. The difference in clock readings observed in the experiment is invariant; it will be the same regardless of which frame of reference you use to observe it. And that difference is caused by differences in the paths that the clocks take through spacetime; those differences in paths are also invariant.

So even though there are no absolute frames of reference, there are still absolutes, in the sense of actual measured quantities, like the difference in clock readings in the H-K experiment, being invariant, independent of your frame of reference.

however is it possible that there is a "correct" spot in which to observe the universe?

I'm not sure what you mean by "correct". Some spots may be more convenient than others for making certain observations, as I said above. But that's a matter of practical convenience; there is no frame of reference that is privileged in principle.

 

[ghwellsjr]

Could there be an absolute 'state of reference' somewhere in the universe, perhaps at the location of the original center? If so, would it have to hold the same frame of reference in each dimension, including time? How would it do so?

Looking at the Hafele-Keating Experiment in particular, the atomic clocks were affected in different ways due to different positions and velocities. The velocities/positions of course would be relative to the observer, however is it possible that there is a "correct" spot in which to observe the universe?

I apologize if this is in the wrong location, a stupid question, confusing, or if this has been discussed before. This is my first post here at Physics Forums.

Even if it were possible that there exists an absolute "state of reference", there is no way to identify it. As a matter of fact, every inertial reference frame would look just like the absolute "state of reference", so how would you know which one it was?

 

[pervect]

Could there be an absolute 'state of reference' somewhere in the universe, perhaps at the location of the original center?

If you're asking in the context of general relativity, no. Non-GR theories might allow such a thing to exist, but I'm not aware of any with any experimental support. Non-GR theories would best be addressed in a different group, anyway.

 

[mrnike992]

No. There is no "original center" to begin with.

If the universe began at one point, and expands infinitely in every direction, would there not still be a 'starting point' at the center of the expanding universes?

No, they're relative to *each other*.

Was I mistaken in believing that clock A and clock B would not be the same if the experiment took place somewhere else? I thought I remembered reading that gravitational potential also affected the time of the clocks. This would mean that the two clocks could not be looked at solely as being relative to each other, if an outside system is affecting them differently.

And I guess I don't understand this part here:

So even though there are no absolute frames of reference, there are still absolutes, in the sense of actual measured quantities, like the difference in clock readings in the H-K experiment, being invariant, independent of your frame of reference.

How can the clocks be absolutes if the same clocks read different times (Even after starting synchronized)?

I'm not sure what you mean by "correct".

Well, if there are discrepancies in the data recorded by the clocks representing time, then could there be a spot in which everything else is the same in relation to this spot?

I'm sorry, I'm having trouble bringing words to what I'm thinking.

 

[ZapperZ]

If the universe began at one point, and expands infinitely in every direction, would there not still be a 'starting point' at the center of the expanding universes?

This is wrong.

There was no "point" at the beginning of the universe. You are thinking of something that already existed in some space and time frame, and then expanding. This is the wrong view of the beginning of the universe. The beginning of the universe isn't just the beginning of some "thing". It is also the being of the expansion and formation of spacetime! A "center" or location just didn't exist when the universe began!

Zz.

 

[PeterDonis]

If the universe began at one point

It didn't. As ZapperZ said, the universe did not start at a point and expand into a pre-existing space.

I thought I remembered reading that gravitational potential also affected the time of the clocks.

You're right, it does; so I shouldn't have said the velocities are purely relative to each other. They're also relative to the gravitational field. But that's still not the same as them being relative to "the observer". The gravitational field itself can be described in a way that is independent of observers or frames or coordinates.

How can the clocks be absolutes if the same clocks read different times (Even after starting synchronized)?

That's why I was careful to define how I was using the term "absolute". The difference in the clock readings when the clocks come back together is the same regardless of which frame of reference you use; it's invariant. Invariant quantities are very important in relativity; in fact, Einstein once said that his theory was misnamed, and it should really be called the theory of invariants. Invariant quantities may not be "absolute" in the pre-relativistic sense, but that's because there really isn't anything that's "absolute" in the pre-relativistic sense.

Well, if there are discrepancies in the data recorded by the clocks representing time, then could there be a spot in which everything else is the same in relation to this spot?

I'm not entirely sure what you mean by this, but I think the answer is "no".

 

[mrnike992]

Alright, that really helps, thanks to everybody that contributed!

 

[Layman]

Even if it were possible that there exists an absolute "state of reference", there is no way to identify it. As a matter of fact, every inertial reference frame would look just like the absolute "state of reference", so how would you know which one it was?

Why are you saying it's "impossible?' Are you equating "impossible to detect" (CMBR notwithstanding) with "physically impossible?"

 

[PAllen]

Why are you saying it's "impossible?' Are you equating "impossible to detect" (CMBR notwithstanding) with "physically impossible?"

CMBR allows you to identify a locally inertial frame with the property that the CMBR is isotropic. This is not different from the air on Earth allowing you to identify a state of motion in which there is locally no wind. Neither is fundamental. The key word is local. There is no globally inertial frame at all that is possible over cosmological distances because local frames each 'at rest' per CMBR isotropy are separating from each other, so you clearly do not have a single inertial frame.

 

[ghwellsjr]

Even if it were possible that there exists an absolute "state of reference", there is no way to identify it. As a matter of fact, every inertial reference frame would look just like the absolute "state of reference", so how would you know which one it was?

Why are you saying it's "impossible?' Are you equating "impossible to detect" (CMBR notwithstanding) with "physically impossible?"

No (to your second question), I thought my post made that clear.

If you understand Special Relativity, you will know that attempting to promote an absolute "state of reference" is a pointless pursuit.

The question is: do you want to understand Special Relativity? If not, then you shouldn't be posting on this forum as that is that stated purpose of this forum and continually violating that purpose will get you banned.

 

[Nugatory]

Why are you saying it's "impossible?' Are you equating "impossible to detect" (CMBR notwithstanding) with "physically impossible?"

Impossible, because it would require detecting a difference that cannot exist.

The laws of physics are the same in all inertial frames, meaning that the speed of the inertial frame doesn't appear anywhere in these laws (it does appear in the coordinate transforms between inertial frames, but that is by definition relative motion not absolute). Therefore the result of any experiment carried out in any inertial frame will be the same no matter what speed you choose to assign to the frame.

This is why ghwellsjr says that it is impossible to identify the hypothetical absolute frame; it cannot be distinguishable in any way from any other inertial frame.

 

[Dale]

Impossible, because it would require detecting a difference that cannot exist.

The laws of physics are the same in all inertial frames

Hmm, I think that I understand what you are trying to say, but I am not sure that I fully agree. I think that what you are stating is a logical impossibility based on a specific definition of "inertial frames" that you have in mind. Under that definition for a frame to qualify as "inertial" all of the laws of physics must be identical, so if a difference between two frames is detected then the logically the frame cannot be "inertial".

I think that even with such a definition there remains an experimental question, which is about how many inertial frames there are and what are the admissible transformations between inertial frames. We know from experiments that there are an infinite number of inertial frames, and that the admissible transformations are the Poincare group.

If the laws of physics were different than they are, then it could be that there were only 1 inertial frame, or that inertial frames were related by the Gailiean transform, or that the admissible transformations did not contain boosts, and so forth. Such transforms are contrary to available evidence, and therefore physically impossible, but not logically impossible.

Layman, please don't mistake this as a vindication of your position. Nugatory and I agree on the facts, this is just a minor comment on terminology.

 

[Layman]

.Layman, please don't mistake this as a vindication of your position. Nugatory and I agree on the facts, this is just a minor comment on terminology.

DaleSpam, may I ask what you presume "my position" to be? Have you made your inferences about "my position" from the question I asked in this thread (and it was merely a question, not a statement of position) or something I said elsewhere?

I happen to agree completely with what you just said about there being a distinction between logical and practical impossibility. I actually thought that was the question I was asking of ghwells: "Are you equating "impossible to detect" (CMBR notwithstanding) with "physically impossible?"

He said he was not doing that, as I understood him, so I think we all agree. It's just that he conjoined the ontological and epistemological aspects in a way that made me unsure of what he was saying.

 

[Layman]

If you understand Special Relativity, you will know that attempting to promote an absolute "state of reference" is a pointless pursuit.

The question is: do you want to understand Special Relativity? If not, then you shouldn't be posting on this forum as that is that stated purpose of this forum and continually violating that purpose will get you banned.

I started a thread in this forum that was first moved to the general physics forum, then closed. Now I am being threatened with banishment. As I recall, in the guidelines there was mention of "civil debate." Was that misleading? Is debate prohibited? If I don't understand, or agree with, a statement about SRT made by another poster in this forum, am I supposed to refrain from expressing disagreement?

I guess I really don't understand the "forum rules."

What do you mean by "attempting to promote?" Making a reference to test theory studies, like those conducted by Sexl and Mansur, is that it?

Maybe it's just me, but I see those studies as being absolutely crucial to any in-depth understanding of the theory of special relativity. Understanding the theory, qua theory, is different than merely understanding the mathematical rules you are directed to follow by SRT, isn't it?

 

[Dale]

DaleSpam, may I ask what you presume "my position" to be? Have you made your inferences about "my position" from the question I asked in this thread (and it was merely a question, not a statement of position) or something I said elsewhere?

Based on your comments and questions both here and in other threads you appear to be a LET proponent. If that is not the case then you should be aware that you give that impression rather strongly.

 

[PeterDonis]

If I don't understand, or agree with, a statement about SRT made by another poster in this forum, am I supposed to refrain from expressing disagreement?

It depends on why you disagree, and how you express the disagreement.

For example, if someone were to say on these forums that "special relativity uses Galilean transformations to go from one inertial frame to another", you would be quite justified in pointing out that that's false; SR uses Lorentz transformations, not Galilean ones.

But if someone says that, in SR, the concept of an "absolute frame of reference" is not valid, and you disagreed with that, you would have to be careful how you expressed that disagreement, because your disagreement would be wrong: SR *does* say that the concept of an "absolute frame of reference" is not valid (more precisely, it's not valid within the context of SR as a theory; SR as a theory has no room for it, doesn't use it, and doesn't assign any meaning or weight to it). All inertial frames are equivalent in SR, in the sense that they are all equally valid for expressing physical laws. Disagreeing with that statement, or even appearing to disagree with it, just leads to pointless threads that go on forever; those of us who have been here on PF for a while have seen it happen all too many times, which is why we try pretty hard to nip it in the bud if it looks like it's happening again.

In your case, you implicitly equated measuring the CMBR with measuring an "absolute frame of reference". What you should have done, IMO, was to ask a question something like this: "I can measure the CMBR, and that measurement picks out a particular frame of reference: the one in which the CMBR is isotropic. How does relativity reconcile that with the principle that all inertial frames are equivalent?" That would have made it clearer that you were not trying to claim that SR was wrong; you were just trying to understand how SR reconciles two things that look, on the surface, like they don't fit together. (There are a *lot* of examples in relativity where things look, on the surface, like they don't fit together, but can be reconciled perfectly well; so when you see things in relativity that look, on the surface, like they don't fit together, it's always a good idea to assume, or at least behave as if you assume, that there *is* a reconciliation at a deeper level and ask what it is.)

PAllen went ahead and gave a partial response to that question, even though you didn't ask it. A further response would be to say that inertial frames are equivalent for expressing physical laws, but obviously that doesn't mean that all inertial frames look the same in every respect. The physical laws say things like: the frequency you will measure for a particular photon (such as one in the CMBR) depends on your 4-velocity and the photon's 4-momentum. You can assess that in any inertial frame; the calculation may be simpler to do in the frame in which the CMBR is isotropic, but the same physical law can be expressed in any frame, and is equally valid in all of them. The experimental fact that the CMBR exists shows that the universe is filled with photons that have particular properties; but that in no way privileges the frame in which those photons look isotropic, from the standpoint of physical laws.

In the other thread you refer to, while the test theory studies you mention may have established that assuming that there is absolute motion can be reconciled with experiment (I'm not familiar enough with the studies to know whether they actually did that), you appear to me to have been making a stronger claim: that *Special Relativity*, that specific theory (as opposed to some generalized test theory of which SR is one special case), allows one to assume absolute motion. That's not correct; SR, the specific theory, has no room for a concept of absolute motion, any more than for a concept of an absolute reference frame. You also appeared to continue to insist that SR requires everyone to assume that they are "not moving", i.e., to always adopt an inertial frame in which they are at rest, even after at least two posters in that thread pointed out to you that SR doesn't require that.

Once again, I understand that these are things that look, on the surface, like they are difficult to reconcile; but your response should be to ask what the reconciliation is, not to repeat claims that you have already been told are wrong.

 

[WannabeNewton]

Understanding the theory, qua theory, is different than merely understanding the mathematical rules you are directed to follow by SRT, isn't it?

A statement of pithy indeed-if only this could be written across the cover of every modern physics textbook ever written...

 

[ghwellsjr]

If you understand Special Relativity, you will know that attempting to promote an absolute "state of reference" is a pointless pursuit.

The question is: do you want to understand Special Relativity? If not, then you shouldn't be posting on this forum as that is that stated purpose of this forum and continually violating that purpose will get you banned.

I started a thread in this forum that was first moved to the general physics forum, then closed.

Getting your first thread closed within 4 hours of opening should be a warning to you.

Now I am being threatened with banishment..

I have no ability to banish you, I'm just warning you from past experience on this forum.

As I recall, in the guidelines there was mention of "civil debate." Was that misleading? Is debate prohibited? If I don't understand, or agree with, a statement about SRT made by another poster in this forum, am I supposed to refrain from expressing disagreement?.

I am not aware of anything uncivil going on here. There's lot a debate happening on this forum but it should all be directed at increasing understanding.

I guess I really don't understand the "forum rules."

What do you mean by "attempting to promote?" Making a reference to test theory studies, like those conducted by Sexl and Mansur, is that it?

Here are two of the rules that I was referring to:

•Challenges to mainstream theories (relativity, the Big Bang, etc.) that go beyond current professional discussion
•Attempts to promote or resuscitate theories that have been discredited or superseded (e.g. Lorentz ether theory)

Maybe it's just me, but I see those studies as being absolutely crucial to any in-depth understanding of the theory of special relativity. Understanding the theory, qua theory, is different than merely understanding the mathematical rules you are directed to follow by SRT, isn't it?

This forum is to help people learn and understand relativity. Do you consider yourself to be at the level of a teacher or are you trying to learn?

 

[Layman]

Based on your comments and questions both here and in other threads you appear to be a LET proponent. If that is not the case then you should be aware that you give that impression rather strongly.

Dale, I wouldn't say I'm an LET "proponent." I do think it has been well established that theories which posit absolute simultaneity are consistent with all experimental evidence. In the other thread, I took the poster I was responding to to be claiming otherwise (i.e., that ONLY SRT was consistent with the empirical data), and I disagreed with that.

The other thread made specific reference to an example Einstein used to "promote" the "relativity of simultaneity." I personally found that explanation to be questionable, since it requires, as does the theory as a whole, all observers to assume that they can't be moving, and that only the "other guy" can be moving.

Let me give an example of what puzzles me. Maybe someone can explain why it is more reasonable than it appears to me to be:

Let's say I'm an astronaut who has prepared to years to take an inter-stellar space flight. I get on board my rocket. I blast off. Thereafter, for days, weeks, and months I feel a constant acceleration, and then, one day, the acceleration stops. I am now in an inertial state of, let's say, .9c (relative to earth).

Would I, as an astronaut with all that knowledge, actually assume that I am motionless? Would I assume that the Earth is moving away from me, and not vice versa? I don't think so. And yet, as I understand it, that's what SRT would require me to assume, if everything is to work out "right' (per SR) mathematically.

This seems to contradict reason, to me.

 

[Dale]

as I understand it, that's what SRT would require me to assume,

Your understanding is incorrect, as was already clearly explained to you in the other thread.

Any inertial frame is as good as any other, that is what the first postulate asserts. Therefore there is no requirement to use one over another. The astronaut may use any inertial frame, the one where he was initially at rest, or the one where he ends at rest, or any other that he likes including ones where he is never at rest.

 

[PeterDonis]

Let's say I'm an astronaut who has prepared to years to take an inter-stellar space flight. I get on board my rocket. For days, weeks, and months I feel a constant acceleration, and then, one day, the acceleration stops. I am now in an inertial state of, let's say, .9c (relative to earth).

Ok.

Would I, as an astronaut with all that knowledge, actually assume that I am motionless.

It would depend on why you were making the assumption, wouldn't it? If you are floating in the center of the ship's cabin and you reach for a pen in front of you, are you moving the pen to you, who are motionless, or are you deflecting it just a bit from its course away from the Earth at nearly light speed? Isn't it obvious that, in this situation, you *would* assume you were motionless?

In other words, there is nothing that *requires* you to assume that you are motionless *or* to assume that you are moving. It depends on the situation. Physics doesn't care. These assumptions are pragmatic ones, not fundamental ones; you make whatever assumption is convenient for the problem at hand, and you can make different assumptions in different situations.

And yet, as I understand it, that's what SRT would require me to assume, if everything is to work out "right' (per SR) mathematically.

What has led you to this understanding? Can you give some references, or some examples, of how SR appears to you, *mathematically*, to require that you must assume you are motionless? I emphasize the word "mathematically" because I'm not asking about ordinary-language discussions for a non-technical audience. I'm asking about actual math used to make actual physical predictions using the actual theory of SR. My understanding is that that math allows you to use any reference frame you like, regardless of your state of motion; so the astronaut in your example could use a frame in which he is at rest, a frame in which the Earth is at rest, or even a frame in which both of them were moving, if that was what was most convenient for doing a particular calculation. If your understanding is different, you're going to have to show us specific *mathematical* examples of why, and where those examples are coming from.

 

[Layman]

Your understanding is incorrect, as was already clearly explained to you in the other thread.

Any inertial frame is as good as any other, that is what the first postulate asserts. Therefore there is no requirement to use one over another. The astronaut may use any inertial frame, the one where he was initially at rest, or the one where he ends at rest, or any other that he likes including ones where he is never at rest.

Well, Dale, from my point of view, that is not an "explanation," it is an assertion. Can you actually "explain" it?

I commented that IF both the person on the train and the person on the embankment assumed that the train was moving, and not the earth, then they would not calculate the speed of light to be isotropic, would agree on simultaneity, etc. Why is this wrong?

It's been a while since I read authorities on the topic, but this is just mainstream physics and common sense, isn't it?

The history of physics demonstates this (thinking of Lorentz, Poincaire, and Einstein here) as I understand it. If we disagree on this then it could lead to a lengthy "debate" I suppose, and (perhaps) with me being banned for debating it.

 

[PeterDonis]

I commented that IF both the person on the train and the person on the embankment assumed that the train was moving, and not the earth, then they would not calculate the speed of light to be isotropic, would agree on simultaneity, etc.

Show your work, please. That is, show us the actual *math* that you are using to justify this claim.

 

[Layman]

Ok.What has led you to this understanding? Can you give some references, or some examples, of how SR appears to you, *mathematically*, to require that you must assume you are motionless? I emphasize the word "mathematically" because I'm not asking about ordinary-language discussions for a non-technical audience. I'm asking about actual math used to make actual physical predictions using the actual theory of SR. My understanding is that that math allows you to use any reference frame you like, regardless of your state of motion; so the astronaut in your example could use a frame in which he is at rest, a frame in which the Earth is at rest, or even a frame in which both of them were moving, if that was what was most convenient for doing a particular calculation. If your understanding is different, you're going to have to show us specific *mathematical* examples of why, and where those examples are coming from.

Peter, I'll try to answer this the best I can, but I'm not a mathematician. I'll have to use a different methods. According to Einstien (actually the Lorentz transformations) a moving clock runs slower than one that isn't moving, right?

The LT tells you that, right? What the LT does NOT, and CAN NOT, tell you is which of two objects is relatively motionless. The math can't tell you that.

But, either way, one clock will be slower than the other. If the guy on the train is moving, his clock will be slower. If the guy on the embankment is moving, then, per the LT, his clock will be slower. No physicist that I know claims that each clock is moving slower than the other. Which one is slower? The one which is moving. To me, that is a question of physics, not mathematics.

What I'm saying is that the point I am making has nothing to do with the mathematics, as such. It is the APPLICATION of the math which determines these things, not the math itself.

 

[WannabeNewton]

According to Einstien (actually the Lorentz transformations) a moving clock runs slower than one that isn't moving, right?

Relative to the rest frame of one of the clocks, yes.

If the guy on the train is moving, his clock will be slower. If the guy on the embankment is moving, then, per the LT, his clock will be slower.

Again, only relative to the respective rest frames of the clocks-without this qualification your statements are meaningless.

No physicist that I know claims that each clock is moving slower than the other.

You haven't been talking to physicists then.

 

[A.T.]

that is not an "explanation," it is an assertion.

Yes it is a postulate. One much older than SRT.

 

[Doc Al]

Peter, I'll try to answer this the best I can, but I'm not a mathematician. I'll have to use a different methods. According to Einstien (actually the Lorentz transformations) a moving clock runs slower than one that isn't moving, right?

The LT tells you that, right? What the LT does NOT, and CAN NOT, tell you is which of two objects is relatively motionless. The math can't tell you that.

What you seem to be stuck on has nothing really to do with SRT; you need to review Galilean relativity.

But, either way, one clock will be slower than the other. If the guy on the train is moving, his clock will be slower.

Relative to the embankment observer, the train is moving. So the embankment observer sees the train clocks run slow (compared to his).

If the guy on the embankment is moving, then, per the LT, his clock will be slower.

Relative to the train observer, the embankment is moving. So the train observer sees the embankment clocks run slow (compared to his).

No physicist that I know claims that each clock is moving slower than the other.

Time to meet some real physicists! The effects of time dilation are completely symmetric. They each see the other's clocks as running slow.

 

[A.T.]

DaleSpam, may I ask what you presume "my position" to be?

Well, in the other thread you said that the Earth is obviously at absolute rest. Sounds like pre-Galilean and pre-Copernican ideas.

 

[Layman]

Well, in the other thread you said that the Earth is obviously at absolute rest. Sounds like pre-Galilean and pre-Copernican ideas.

I don't recall saying any such thing, A.T.

 

[PeterDonis]

Peter, I'll try to answer this the best I can, but I'm not a mathematician.

Then you shouldn't be making claims about what the math of SR says or doesn't say.

According to Einstien (actually the Lorentz transformations) a moving clock runs slower than one that isn't moving, right?

This is the way it's often described, yes, but IMO it's a bad description, because it leaves out too much information.

Also, it's not a good idea to talk about some vague, unspecified scenario. Let's talk instead about a concrete scenario: the train and the embankment. In the Einstein example that I think you were referring to in the other thread, we had the following, IIRC:

(1) An observer at the center of the train, which is moving along a track parallel to the embankment.

(2) An observer standing on the embankment. The two observers pass each other (i.e., they are co-located, since we are ignoring all but one spatial dimension) at some particular instant.

(3) Two lightning strikes that hit particular points on the embankment at particular instants.

(4) Light from those two lightning strikes travels to the observer on the embankment; the light from both strikes reaches him at the same instant. This happens *after* the two observers pass each other.

So we have four events of interest: event A, the first lightning strike hitting the embankment; event B, the second lightning strike hitting the embankment; event O, the two observers passing each other; and event L, the light from the two lightning strikes reaching the observer on the embankment.

Mathematically, the way we model this is to first pick a frame of reference, and then assign each event of interest coordinates in that frame of reference. I'll do that below.

The LT tells you that, right? What the LT does NOT, and CAN NOT, tell you is which of two objects is relatively motionless. The math can't tell you that.

I'm not sure what this means. There will be some velocity $v$ in the math, which represents the relative velocity of two observers or objects. In our train-embankment scenario, it represents the relative velocity of the train and the embankment; and we would use that $v$ in the Lorentz transformation formulas to convert coordinates of events in the embankment frame to coordinates of events in the train frame. If you are saying that that process does not pick out either frame as "motionless", you are correct. If you're saying something else, you'll need to clarify what it is before I can respond to it.

either way, one clock will be slower than the other.

But which clock it will be depends on which frame you choose. More precisely, that's true as long as the relative motion between the two frames is the same, which is the case for our train-embankment scenario. In other scenarios, where that's not the case, there might be an invariant sense in which one clock runs slower than the other. It depends on the scenario.

If the guy on the train is moving, his clock will be slower. If the guy on the embankment is moving, then, per the LT, his clock will be slower.

This is just another way of saying what I said just now, that which clock runs slower depends on which frame you choose. Choosing a frame amounts to choosing which object you are going to assume to be "motionless" for purposes of your calculation. But the physics doesn't care which frame you choose; they're all equivalent. The only reason to choose one at all is to do a particular calculation. See below.

Which one is slower? The one which is moving. To me, that is a question of physics, not mathematics.

No, it's a question of properly understanding what "moving" means.

Let me work through the train-embankment example more explicitly, to illustrate what I said above. Suppose that we know, from actual measurements made by the observer on the embankment, that the coordinates of the four events of interest, in the embankment frame (i.e., the frame in which the embankment is motionless) are:

Event O: $(t, x) = (0, 0)$

Event A: $(t, x) = (0, -1)$

Event B: $(t, x) = (0, 1)$

Event L: $(t, x) = (1, 0)$

Note that I am using units in which the speed of light is 1; for example, distance could be in feet and time in nanoseconds, or distance in kilometers and time in light-kilometers (the time it takes light to travel 1 kilometer, or 1/300,000 of a second), or whatever. The specific units don't matter for this discussion; I'll just call them "units".

Note also that, as you can see from the above, 1 unit of time elapses in the embankment frame between event O and event L. Physically, this means that 1 unit of time elapses on the embankment observer's clock between the train observer passing him and the light from the two lightning strikes reaching him.

Now, if we know the velocity $v$ of the train relative to the embankment, we can use the Lorentz transformation to obtain the coordinates of these three events in the train frame (i.e., the frame in which the train is motionless). The transformation equations are:

$$
t' = \gamma \left( t - v x \right)
$$

$$
x' = \gamma \left( x - v t \right)
$$

where $\gamma = 1 / \sqrt{ 1 - v^2 }$.

Applying these to the above coordinates gives:

Event O: $(t', x') = (0, 0)$

Event A: $(t', x') = (\gamma v, \gamma)$

Event B: $(t', x') = (- \gamma v, \gamma)$

Event L: $(t', x') = (\gamma, - \gamma v)$

To see how these numbers show that "moving clocks run slower", observe that, in the train frame, the observer on the embankment is moving, so the elapsed time by his clock (1 unit) between event O and event L is less than the coordinate time between those two events in the train frame ($\gamma$ units). So, relative to the train, the embankment clock does indeed show "time dilation". (And notice how I reversed things, by showing how the *embankment* clock runs slow relative to the train frame, rather than how the train clock runs slow relative to the embankment frame? That was to illustrate that which clock is "moving" and runs slow is a matter of choice of frame; the physics is the same either way.)

But notice how much that description leaves out. First, it leaves out the fact that event L has a different *spatial location*, in the train frame, than event O (because in the train frame, the embankment is moving). Second, it leaves out relativity of simultaneity: notice that events A and B have *different* time coordinates, in the train frame, whereas they have the same time coordinate (they are simultaneous) in the embankment frame. (Physically, this is because we specified that light from the two lightning strikes reach the observer on the *embankment* at the same instant. If we had specified that light from the two lightning strikes reached the observer on the *train* at the same instant, we would have obtained different coordinates for events A and B.) To really understand what's going on, you have to include *all* the physics, not just time dilation.

 

[Layman]

Time to meet some real physicists! The effects of time dilation are completely symmetric. They each see the other's clocks as running slow.

I completely agree that each will "see" the other's clock as running slow, IF, and only if, each assumes that he is motionless and the other is moving. Otherwise, no.

But questions still exist apart from what a person will "see." I put "see" in scarequotes because we are not talking about actual observation. We are talking about calculations BASED ON certain given permises (which may or may not be true).

Take the global positioning system. Ignoring the distorted time effects created by gravity, we ASSUME that a clock on the satellite will run slower because we assume that it is moving relative to us (and NOT that we are moving relative to it). As it turns out, our assumptions are right. The clock on the satellite DOES, in fact, run slower. Why? Presumably because it is moving. It has the "moving clock," not us.

 

[WannabeNewton]

Why? Presumably because it is moving. It has the "moving clock," not us.

You do realize if you boost to the rest frame of the clock in orbit, the central clock will now be in orbit and it will have a time dilation factor attached to it right? So your argument makes no sense. The only thing absolute in your scenario is the fact that one clock accelerates whereas the other is inertial. This doesn't affect the kinematical time dilation which only depends on relative velocity.

 

[PeterDonis]

Ignoring the distorted time effects created by gravity, we ASSUME that a clock on the satellite will run slower because we assume that it is moving relative to us (and NOT that we are moving relative to it). As it turns out, our assumptions are right. The clock on the satellite DOES, in fact, run slower. Why? Presumably because it is moving. It has the "moving clock," not us.

This is a different sense of "moving" than the train and embankment example. The GPS satellites are in closed orbits; they return to the same position, relative to someone on the surface of the Earth, periodically. That gives a common reference from which to measure elapsed time, by measuring elapsed time between one time the satellite passes and the next; it's not the same as the train and the embankment, where the two observers only pass each other once. In cases like GPS (or the "twin paradox"), where the two observers meet more than once, you can use the elapsed time between meetings as an invariant measure of which clock "runs slower". But you can't do that if the observers only meet up once.

 

[A.T.]

I don't recall saying any such thing, A.T.

It was just a few hours ago:

My question was merely addressing a guy on a moving train, on earth, claiming that he was motionless. In that case, the "absolute" frame is obviously the surface of the earth.

So, our Earth defines the absolute frame?