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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?

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Mozibur Ullah
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  • 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. –  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. –  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
  • This is classical mechanics, are you suggesting this neutral frame is not there? Personally, I'd just draw a line between these two bikes and take the mid-point... – Mozibur Ullah Aug 28 '15 at 16:50
  • I am suggesting that it resolves none of the issues of SR and definitely IS NOT absolute time. Each newcomer to the system moves it. And if you are suggesting the center of motion of the universe exists, you have to contend with relative space first. –  Aug 28 '15 at 16:53
  • I'd suggest you're missing the point of the argument if you think I suppose there is a midpoint to the universe - there's nothing in the argument above that indicates this; lets stop here - it's clogging up the comments - unless you want to take into chat ... – Mozibur Ullah Aug 28 '15 at 17:12
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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. –  Aug 28 '15 at 17:25
  • Ok, I've thought about it more; and I think we're arguing from different situations; inertial frames are equivalent by definition, so the time-flow are equivalent by definition; the arguments not neccessary to establish this. – Mozibur Ullah Aug 28 '15 at 22:50
  • Thus no need for a third parties or centres of universes :). – Mozibur Ullah Aug 28 '15 at 22:53

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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.

Jo Wehler
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  • 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
  • And this concept of global/local absolute time/space/frame connects it with the distinction between global/local simultaneity; all this though isn't standard terminology - I know. – Mozibur Ullah Aug 28 '15 at 10:40
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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
  • What Newton had in mind is similar to the difference between relative positions (from a referential) and absolute position. Then clearly the equivalent is time as measured from a referential, not proper time. – Quentin Ruyant Aug 28 '15 at 18:31
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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
  • @JoWehler not really. An agent can place different synchronised clocks to measure durations in various places but I wouldn't say each clock is an agent (the agent doesn't have to be in the same frame of reference: s/he can be anywhere). The clocks are measuring apparatus, not epistemic agents. – Quentin Ruyant Aug 28 '15 at 18:59
  • @quen_tin OK, I understand your use of the term "agent", which is also common use. But what do you need the agents for? Why are the clocks not sufficient? – Jo Wehler Aug 28 '15 at 19:03
  • @JoWehler a single clock cannot know the time interval between two distant events in a frame of reference. You need two synchronised clocks for that. Anyway I'm not saying agents are part of physics it's just a remark on Newton's insight. – Quentin Ruyant Aug 28 '15 at 19:13
  • @JoWehler I think Newton's remark is epistemological: we, human, can only measure relative distances and durations but there is a real space and a real time out there (a real topology+metric). – Quentin Ruyant Aug 28 '15 at 19:15
  • @quen_tin: I was looking for a physical argument that showed that proper time flowed at the same rate in inertial frames that are separated; but it maybe that my argument is circular - as I'm already establishing inertial frames there - and by definition time will flow at the same rate for inertial frames; still, I feel something is not quite clear there. – Mozibur Ullah Aug 28 '15 at 20:18
  • I mean locally in an inertial frame we can see that the clocks are flowing at the same rate; but for two separated frames - would we not need some kind of operational definition? I mean to compare them? – Mozibur Ullah Aug 28 '15 at 20:26
  • @Mozibur I'm not sure you can find such an argument. Take two inertial trajectories with the same origin and the same length (same proper time) but different directions. You want to show that the end points of these two lines are simultaneous? The problem is that simultaneity is not absolute. You can choose a coordinate system so that it'll be true, but coordinate choice is arbitrary, and if you add a third trajectory you won't be able to find a coordinate system where the three end-points are simultaneous. – Quentin Ruyant Aug 28 '15 at 21:18
  • @quen_tin: given that setup I agree with you; it seems to be also how jobermark has understood my argument, so most likely I did a bad job of explaining it; but this isn't how I set up my argument: I'm supposing two inertial trajectories, starting from the same origin, and moving in opposite directions from that origin; because the setup is *symmetric* around the origin - it seems to me I can conclude that the proper times associated with these two frames ought to be the same; if this is wrong, then the rest of the argument fails - but I don't see where the mistake in the reasoning is here. – Mozibur Ullah Aug 28 '15 at 22:13
  • The more I think about it though; the more it seems I'm trying to demonstrate something that is true by definition: all inertial frames are equivalent - so time in any inertial frame must flow at the same rate as any other; but I don't mean here by comparison ie frame A relative to frame B. – Mozibur Ullah Aug 28 '15 at 22:42
  • @MoziburUllah the setup is symetric only in a specific coordinate system (you need one to say that the directions are opposite), so I don't see the difference between your setup and mine, except that you introduce the coordinate system first. Also I'm not sure what you mean by proper times being "the same": proper time is the absolute length of a trajectory. You must stipulate where in space-time both trajectories end before asking if their proper time is the same. I assume you mean that they end at the same time in the coordinate system you choosed? – Quentin Ruyant Aug 28 '15 at 23:39
  • @MoziburUllah also note that you have to explain the twin paradox, and I think in general relativity you can have a twin paradox with inertial trajectories (geodesics) which seems to show that proper times are not "the same". – Quentin Ruyant Aug 28 '15 at 23:43
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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