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A discussion on this question on 'grounding absolute time' prompted the following possibly clarifying, possibly unclarifying thought:

In Newtons Principia, he defined two concepts of objective time:

absolute, true and mathematical time, of itself, and from its own nature, flows equably in itself and without regard to anything external.

And he adds:

relative, apparent and common time, is some sensible and external measure of duration by means of motion

How do these two concepts alter in SR; if in fact they do, which post-hoc, we know they must?

Now the concept of relative time must change in SR, because it is explicitly, as Newton defines it, dependent on the concept of motion; and it is this concept that is altered in SR: ie the motion of light is not Galilean - being always constant.

And an argument first presented by a Einstein (using the motion of light as a clock - this is his version of Galileos pendulum) shows that in fact this is the case.

I would suggest, however, that the absolute concept does not alter, as it does not refer to anything external; thus how a particle moves in space does not affect this concept of time; thus proper time in SR ought to be that of absolute time in Classical Mechanics.

But is there a good heuristic argument that shows that this is in fact the case?

This a problematic since only when two particles are at the same place can we directly compare their proper times, and see that they flow at the same rate; when separated we cannot compare directly.

The following argument suggests itself:

Consider two particles at the same place in space; they then move away from each other in opposite directions at the same speed and in a straight line.

Taking an inertial frame with particle A, we see that the clock held by B has slowed; analogously when taking an inertial frame with particle B, the clock held by A slows; these are in fact symmetric situations - and though we cannot compare the proper times of A and B directly, we see that by symmetry that they must flow at the same rate.

But this was a special situation; what if, say the two particles are moving with uniform but arbitrary linear speeds? Then, I would suggest that there is an inertial frame that resolves this situation to the situation above.

Thus proper time, I would suggest is absolute time; even though the concepts objectively belong to two different physical theories.

Further, one can consider GR; recalling the elevator Gedanken-experiment which free-falls; and when within and without probing externally - ie there are no windows - one cannot tell whether one is within a free-falling elevator or not.

Again, recalling Newtons definition of absolute time, which flows without reference to anything externally, we see that the proper time within the elevator can be legitimately called absolute time - even if it is not.

The concept that connects all these situations, I would suggest, is that all inertial frames everywhere and at all times are the same - so proper time again can be legitimately connected with absolute time.

Finally is this usefully correct or unusably and unusefully uncorrect?

  • I think there is a basic error in "Then, I would suggest that there is an inertial frame that resolves this situation to the situation above". Neither person would use this frame's time, simultaneity in this frame would not be simultaneity for their frames, etc. Shifting to 'neutral ground' does not do the same thing here that it does in classical mechanics. – user9166 Aug 28 '15 at 16:31
  • @jobermark: shifting to this 'neutral frame' isn't to establish simultaneity, but to reduce the general case of two frames in general linear motion to the first special case, where it's established that the proper time of each frame flow at the same rate, by symmetry. That's what's the move for: to make the general situation symmetric. – Mozibur Ullah Aug 28 '15 at 16:38
  • So the proper time for a third party would not exist. Establishing something pairwise accomplishes nothing without transitivity. And that kind of points up how silly the pairwise case actually is. If you want to say every system has a center of motion. OK, nothing happens there that is of any use. The time at the center of motion is a useless abstract concept. Mapping everyone's time to that of the center still resolves no aspect of the problems that make establishing common time impossible, because each individuals time maps there differently. – user9166 Aug 28 '15 at 16:43
  • Let's take a concrete situation ie on earth: take two guys on motorbikes, starting at the same place, they rev up their engines and set off in different directions at the same time, and at different speeds; there should be a frame where they're moving in opposite directions at the same rate. That's the neutral frame I'm after. – Mozibur Ullah Aug 28 '15 at 16:43
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    Involve the third person, as suggested in the long comment, and see if you don't end up considering this time-flow pointless without a center to the universe. – user9166 Aug 28 '15 at 17:25
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You ask a series of questions, sometimes expressed separately and other times embedded in your theses. I pick up some questions which I can isolate:

  1. How does Newton's concept of absolute time change in SR? Answer: Absolute time is abolished, there is no absolute time in SR. The main reason is the contradictory concept of global simultaneoussness. In GR Einstein also votes against an entity which influences other entities, but does not experience itself any impact from other entities: Not only does spacetime prescribe via geodesics the trajectories of material objects. Spacetime itself is curved by the mass distribution.

  2. How does Newton's concept of relative time change in SR? Answer: One can substitute the proper time along a trajectory for Newton's concept of relative time.

  3. Is it correct that all inertial frames everywhere and at all times are the same? Answer: They are not the same, but Lorentz transformation transforms between the coordinates of different inertial frames. At most one can say: All inertial frames are equivalent concerning the description of nature. But note that GR extends the concept of frame transformation and allows also non-inertial frames.

  • I'm not sure I fully agree with your assessment on 1: global simultaneity is abolished - I agree there - but local simultaneity remains; absolute time as it's usually modelled via Euclidean space is thus abolished; but this is not, I think how Newton defines it above; or rather asserts it: it's an intrinsic, local definition; he doesn't use coordinates. – Mozibur Ullah Aug 28 '15 at 10:01
  • The concept, I would suggest, is better considered as being modified: thus in two widely separated inertial (or tie them to the previous concept - absolute) frame, we have time flowing at the same rate: or as your third statement puts it, all inertial or absolute frames are equivalent. – Mozibur Ullah Aug 28 '15 at 10:13
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    I think 2 is wrong. Newton's relative time corresponds to the measure of duration by agents, and its best equivalent in SR is: the measure of time in an arbitrary referential, not proper time. 1 is true insofar as there is no absolute time in SR but perhaps proper time is not too far from playing the same role in SR: that caracterising of the fundamental and absolute metric of space-time. – Quentin Ruyant Aug 28 '15 at 18:29
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    @quen_tin If you place clocks at rest everywhere in the same inertial frame they will show the same proper time and stay synchronized. This synchronous proper times can serve as the time within the referential frame. Are these clocks the agents you mention? – Jo Wehler Aug 28 '15 at 18:37
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    @quen_tin: ok, it's the notion of proper time that's puzzling me; it looks like I need to think further on it; thanks for your help. – Mozibur Ullah Aug 29 '15 at 10:15

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