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I know the following question is sure to cause howls of anguish. I can only apologize for the length at which I have had to write in order to be precise, and I do hope people will bear with me for a question asked in good faith.

I have just been reviewing the Wikipedia entries on Time Dilation and the Twin Paradox.

The following statements are made on the entry for Time Dilation:

The dilemma posed by the paradox, however, can be explained by the fact that one of twins must accelerate while the other remains inertial.

and

the rate at which a clock is affected by time dilation does not depend on its acceleration but only on its instantaneous velocity

And, on the Twin Paradox page, the following is asserted:

one must understand that in special relativity there is no concept of absolute present

and also the following scenario is described:

If, instead of incorporating Einstein's clock synchronization (lattice of clocks), the astronaut (outgoing and incoming) and the Earth-based party regularly update each other on the status of their clocks by way of sending radio signals (which travel at light speed), then all parties will note an incremental buildup of asymmetry in time-keeping, beginning at the "turn around" point. Prior to the "turn around", each party regards the other party's clock to be recording time differently from his own, but the noted difference is symmetrical between the two parties. After the "turn around", the noted differences are not symmetrical, and the asymmetry grows incrementally until the two parties are reunited. Upon finally reuniting, this asymmetry can be seen in the actual difference showing on the two reunited clocks.

Firstly, I believe I'm right in saying that, as far as time dilation is concerned, the quantity of difference between the clocks when the twins reunite is purely a function of the speed reached during the travelling twin's journey, and the distance of the journey undertaken at that speed.

Acceleration forces play no fundamental part in accounting for the difference. I would only note that, collaterally, one must accelerate in order to change speed in the first place. But it is not the force of acceleration that causes the difference to be incurred, and the differences are not incurred purely during the periods of acceleration.

That is, the difference accrues more or less steadily over the entire round-trip journey (as proven by back-and-forth signals in the scenario in which each twin examines the state of the other's clock, in which differences accrue steadily), and it is accruing even when the travelling twin in steady motion and no acceleration is occurring at that time.

Were it otherwise, a very short journey incurring given acceleration forces and reaching a given top speed, would have a dilation equivalent to a very long journey involving the same acceleration and same top speed - but this (I think it will be agreed) is not the case.

But again, collaterally, acceleration is relevant in that it provides an objective reason for treating one twin as non-inertial, and it would act as an observable cue to the travelling twin that he has "changed frames" during the course of the journey. But that change, at the moment of happening, is not what accounts for the difference. The difference is on account of motion.

Secondly, I find the assertion that there is "no absolute present" problematic. I differentiate this from the notion of a "relative passage of time", or a "relative clock rate" against which the passage of time is measured, with which I do not take issue.

It must surely be the case that, when the twins are reunited, they are both in a shared moment of "the present" or "now". So too, they were in the shared "present" before the journey began. It also seems reasonable to say that, from the perspective of either twin, the other always remained in the present moment - there was never a moment during which the one twin somehow disappeared from or ceased to exist in the present of the other twin.

The present moment is not itself a quantum of time that is (or can be) measured on any scale - not being a quantity of anything, it is universal in it's meaning and free of measurement. To talk of the present instant is to talk of a static snapshot of the state of the universe, free from consideration of its dynamics or what will be its future states, or any notion of the "passage of time". I think that captures what people would mean by reference to "the present".

It would not seem like a credible composition of the concepts involved to say that, in some sense or another, the travelling twin remains somewhat more "in the past" than the home-twin (though undoubtedly the travelling twin is looking younger), or that the present of the travelling twin is somehow behind the present of the home-twin. He looks younger but he's not in the past. This is because both are clearly together in the same present. So it does not seem to me that a "relativity of the present" accounts for the difference. Certainly, taken as a bald statement without more reasoning, it has no power to communicate an explanation for the phenomena observed in relativity.

Thirdly and finally, assuming the scenario described at the outset to be correct, I'm not clear why the "asymmetry" in the clock rates accrues only on the inbound stretch of the journey. It is said that, on the outbound stretch, that each twin measures the other clock to be running slow, but both measure the other to be slow by equal amounts, whereas on the inbound trip after the "turn-around" this ceases to be the case.

Now to conclude, I don't think I'd be unreasonable in saying that the explanations given on those Wikipedia pages present and communicate a confusing picture for anyone trying, in good faith, to get properly to grips with relativity and gain an understanding. It presents a confusing account of what role acceleration plays in the explanation, it invokes a "relativity of the present" which is a confusing concept when stated baldly, and it describes a scenario with confusing asymmetries that arise on only the return leg of the journey and don't seem to be accounted for by the process being described.

I'd be tempted to cast my question quite widely in terms of "have I missed something?", but to be more specific, what is the explanation for the asymmetry that arises on the return leg? Does it occur specifically on the second leg of the journey, or does it occur specifically on the inbound leg** of the journey? And in either case, what is the explanation for why the difference arises only during one leg and not during both?

**I say "inbound leg", because it would be easy to adapt the scenario where two twins start off on different planets with synchronised clocks, then one flies in to meet the other, and then returns back to the planet where he started (at which point, they compare the current state of their clocks by signalling to each other between the planets). In such a case, would the asymmetry occur up-front on the inbound leg, or would it occur on the second, out-bound leg?

Steve
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    The acceleration matters. See this answer. Also relevant. – Chris Mar 03 '18 at 04:50
  • @Chris, thanks, but if acceleration is the explanation, then why, in the scenario I quote, do the clocks continue to slow under steady motion? The answers you link only seem to confirm that motion is the key factor in SR. – Steve Mar 03 '18 at 05:04
  • I didn't say velocity doesn't matter. You can have multiple things that matter ;) – Chris Mar 03 '18 at 05:10
  • See also What is time dilation really? for background info. – John Rennie Mar 03 '18 at 06:05
  • @JohnRennie, I'm unable to see how that relates to my specific question, about why the asymmetry occurs on the inbound leg. – Steve Mar 03 '18 at 06:07
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    The asymmetry in the time dilation doesn't occur on the inbound leg so your question is ill founded. The asymmetry of the radio signals is real, but that's to do with the propagation time of the radio waves rather than the underlying physics of time dilation. – John Rennie Mar 03 '18 at 06:12
  • Hi Steve, can't add an answer, as the question is marked a duplicate. I think I can help you put your confusion in a larger perspective, allowing you to rethink. Since I can't add an answer: on my stackexchange profile page there is a link to the contact page on my own website. Feel free to mail me. I wrote an answer (moving to mentioned larger perspective); perhaps we can work out a non-duplicate question that my answer can be used for. – Cleonis Mar 04 '18 at 18:20
  • No acceleration, forces, or even changes in frame of reference are needed at all. You are right that the time dilation is due solely to their relative velocity. Adopt the stationary twin's frame. Synchronize the clocks between relatively stationary points A and B that are 4LY apart using the speed of light. The traveling twin passes point A towards B at 0.8c at T = 0. In our frame, his trip will take 5Y. In his frame, the trip will be reduced by the Lorentz factor 5/3, so 3 years. When he gets to B his clock will read 3 years while the synchronized clock at B will read 5 years. All done. – jschultz410 Jan 07 '22 at 03:12
  • @jschultz410, thanks for this. I eventually found a satisfactory solution to my overall questions, which is basically the Lorentzian interpretation of relativity. I think a crucial realisation along the way was that clocks are often treated by physicists as measuring the progression of time, when the objective reality is that they measure the progression of a physical process, which itself has a rate. That rate is asserted to be constant, but there is no objective basis for that assumption - it's a philosophical axiom, rather than a scientific fact, and which Lorentz rejected. – Steve Jan 07 '22 at 07:55
  • @Steve Time dilation and length shortening in different frames with constant relative motion (i.e. - SR) is due to the axiom that the speed of light in a vacuum is constant in every frame and in every direction. That axiom has been experimentally tested and proven repeatedly to a very high degree of accuracy and precision. You are right that the measurement of time is the measurement of the progression of a physical process which has a fixed rate. For example, the SI definition of a second is based on the quantum frequency of cesium-133 (i.e. - counting how many transitions defines a second). – jschultz410 Jan 07 '22 at 15:30
  • @jschultz410, the lightspeed rate is constant relative to a local clock rate. That is not the axiom. The axiom - which has no experimental justification - is that the quantum frequency of Cesium-133 is not subject to environmental influence. In the Lorentz interpretation, that frequency does vary, which is how the consistency is maintained between the two-way lightspeed rate and the local clock rate. (1/2) – Steve Jan 08 '22 at 10:01
  • What physics doesn't yet explain - probably because of their collective preference for the axiom that the Cesium frequency isn't varying, and therefore there is no variance to investigate - is why the Cesium frequency varies under translation. We already know experimentally that it does vary under environmental conditions: under rotation and under gravitation. The axiom that the frequency doesn't vary under translation is an unjustified one, because the Lorentz interpretation makes the same relativistic predictions with the opposite assumption, that it does vary. (2/2) – Steve Jan 08 '22 at 10:06
  • @Steve That sounds like the two interpretations might just be two different but ultimately equivalent ways of saying the same thing? – jschultz410 Jan 08 '22 at 14:31
  • @jschultz410, they clearly don't say the same things, because the Einsteinian interpretation says the Cesium frequency is fixed, the Lorentzian interpretation says it varies. The Einsteinian interpretation also postulates a one-way flow or progression of time that is local to each co-moving set of matter. The Lorentzian view postulates absolute time, an aether, and explains relativistic effects in terms of the influence of the aether, and movement through it, upon the fundamental processes used to devise clocks. (1/3) – Steve Jan 08 '22 at 17:34
  • They both basically fall back on some sort of all-permeating physical thing to explain the same actual variation. In the Einsteinian view, that all-permeating thing is the progression of time, although its exact nature as a physical thing, and why that progression varies, is left unspecified. In the Lorentzian view, that all-permeating thing is the aether, whose workings are analogous to other wave mediums and explain most ​relativistic effects directly. (2/3) – Steve Jan 08 '22 at 17:34
  • What neither theory explains exactly is what causes fundamental atomic processes like radioactive decay. The view of those holding the Einsteinian view today seems to be that they are acausal, but that variation in the progression of time would naturally slow down their intrinsic rate, case closed. The Lorentzian view would suggest they are caused by something mediated through the aether, although it is beyond today's physics to say what exactly. (3/3) – Steve Jan 08 '22 at 17:35

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The asymmetry is all created at the moment of acceleration, when the traveling twin changes frames. They just gradually notice the asymmetry over time as they are coming back together. The only reason the return path looks any different than the path out is because it is after the acceleration which caused the asymmetry.

Basically, what happens is that before and after the acceleration, the traveling twin is in a different frame, and so has a different concept of simultaneity. If they he could magically see what Earth was like at the current time (based on his concept of simultaneity), his twin would appear to rapidly age during the period of acceleration. And then the time dilation would go back to being symmetrical as soon as the acceleration is over.

He can't magically see Earth at that moment, because of the light speed delay. So the discrepancy from symmetry appears to add up over time as he travels back to Earth.

Chris
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  • But if the "discrepancy" (i.e. the full quantity of difference) is created at the moment of acceleration, then you're unable to explain why shorter journeys have less discrepancy than longer ones. It must be the case that the discrepancy accrues over the whole journey, not at moments of acceleration (or in proportion to any force experienced whilst under acceleration). – Steve Mar 03 '18 at 05:20
  • @Steve The acceleration matters, but so does the exactly how far away the acceleration occurs. You'll notice that the position appears in the Rindler metric mentioned in the answer I linked to, multiplied by the acceleration. The Rindler metric isn't the right one to use here, since the acceleration is not constant, but it demonstrates that it's not just acceleration that matters, any more than it's just speed. – Chris Mar 03 '18 at 05:24
  • But I've acknowledged that acceleration is relevant in a collateral sense, that no motion (or change of speed) can occur without it. The point is the difference is not on account of any experience of the forces of acceleration. – Steve Mar 03 '18 at 05:28
  • If you consider the symmetric case, where both twins accelerate outwards and come back, keeping their relative velocities the same as they would be in the asymmetric case, then there is no time dilation. The relative speeds of the twins were identical for the whole experiment. So clearly acceleration matters. You can't figure out the accumulated time difference with just the relative speed. Particularly in cases where both twins are accelerating. – Chris Mar 03 '18 at 05:35
  • Agreed, but I acknowledged that in my question when I said "acceleration is relevant in that it provides an objective reason for treating one twin as non-inertial". – Steve Mar 03 '18 at 05:45
  • And sometimes both twins are non-inertial. And in that case, you can't do it without knowing the exact details of the acceleration of each twin. – Chris Mar 03 '18 at 05:51
  • Agreed again. But it doesn't seem to address anything in my question, or clearly establish that acceleration is relevant to it (other than in the ways which I already acknowledged that it was relevant, in my very question)! – Steve Mar 03 '18 at 05:54
  • @Steve If you have asymmetrical acceleration, you get time dilation (or maybe not, depending on the exact details of the acceleration). If you don't, you don't get time dilation. If you read that and your interpretation is "acceleration isn't relevant," I'm not going to try to convince you. I've answered your question (acceleration is the source of the asymmetry), if you don't like my answer downvote it and move on. – Chris Mar 03 '18 at 06:03
  • But I haven't said acceleration isn't relevant. I've said I've described how it is relevant in my question, and your just reiterating the acknowledgements I made ahead of time in my question. – Steve Mar 03 '18 at 06:10
  • @Chris Acceleration, forces, and changing frames of reference aren't needed at all. You will get time dilation due to relative velocities alone. Adopt the stationary twin's frame of reference. The distance between S and D is 4 LY. At T=0 S emits a radio signal and the traveling twin passes by S at 0.8c towards D. 4 years later D will receive S's signal, initialize its clock to be 4 years, and start its clock running. The traveling twin will arrive at D when D's clock reads 5 years. However, the trip will have taken less time for him by the Lorentz factor of 5/3: 3 years, his clock's reading. – jschultz410 Jan 07 '22 at 23:00
  • @Chris I don't quite understand your comment. When you say "you get the same numbers if you look in the non-stationary twin's frame of reference" what exactly do you mean? If you mean in the traveler's frame 3 years pass before D reaches him and D's clock when he gets there reads 5 years, then I agree. That alone establishes that time passes slower for the traveler relative to his stationary twin. The exact same thing will happen again if he "reflects" back to S at that point. Or you can use triplets, "unfold" the asymmetry, and have him travel on to S' in a straight line another 4LY. Same. – jschultz410 Jan 08 '22 at 03:17
  • The asymmetry is that as you move away from a clock while observing it, then the distant clock looks to run slower than yours whereas if you move towards a clock while observing it, then the distant clock looks to run faster than yours. Synchronize the clocks at S and D in their frame beforehand. Have them continually transmit their times. At T=0 at S, D's distant clock will read -4 years. When the traveler gets to D, D's clock will read +5 years. During his 3 year journey, the traveler will observe D's clock progress through 9 years, while observing S's clock only progress through 1 year. – jschultz410 Jan 08 '22 at 05:59
  • If the traveler magically and instantaneously "reflects" when he gets to D, then he will observe that S's clock now seems to be running 3x faster than his while D's is now running 3x slower than his. During his 3 year journey back to S, the traveler observes S's distant clock progress through 9 years while D's distant clock only progresses through 1 year. When he gets back to S, S's clock will read 0 + 1 + 9 = 10 years, the traveler's clock will read 6 years, and D's distant clock will read -4 + 9 + 1 = 6 years. – jschultz410 Jan 08 '22 at 06:16
  • @jschultz410 I would have left a comment suggesting that you ask a question to resolve your confusion rather than trying to resolve it through comments on an old answer, but I see you've already done so. ;) – Chris Jan 08 '22 at 22:35