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So I've been doing a lot of reading about the twin paradox and have encountered several different explanations that strive to resolve it. First off let me start by saying general relativity is not an adequate explanation and in fact has nothing to do with resolving the paradox. (That much has been made clear to me from what I have read, as it has been pointed out that believing general resolves the paradox is a common misconception) To drive that point home let me propose a slight variation on the twin paradox that removes acceleration all together.

Some ancient race of aliens long ago set up an experiment for us without our knowledge to help us understand space time. The experiment contains two space craft with clocks on board separated by a very large distance. The first clock, clock A, was accelerated to .866 speed of light millions of years ago (Thus time runs at half speed) and is set on a trajectory to fly past earth. As it flies past earth it resets its clock to 0 and continues on its way. (The aliens also left behind a clock on Earth, clock C, that starts ticking the moment Clock A passes earth and resets itself to 0) The other clock, clock B, was also accelerated to .866 the speed of light long ago and is on the same trajectory as clock A but in the opposite direction so that it heads towards Earth. The two ships and their respective clocks pass each other at a distance of four light years away from earth at which point clock A transfers its time reading to Clock B. Clock B flies past earth and relays its time measurement so as to be compared to Clock C. The time reads half the time elapsed by Clock C, but how could this be possible if time dilation is always symmetrical?

John Rennie
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Krel
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    The total elapsed time you're measuring doesn't belong to one inertial frame anymore, but to two. In tracking the signal you switched reference frames halfway through. This is the same situation as the accelerated twin; you stitched results from different reference frames together. What caused the turn around is irrelevant, the point is that the one signal traveled over a path through spacetime that geometrically takes less time than the one stuck at Earth. The time measurement accelerated, functionally speaking, whether or not it was tracking the acceleration of a single physical object. – Robert Mastragostino Jul 04 '14 at 15:07
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    For any path $\gamma$ in space, the time a traveller along $\gamma$ experiences (and the time a clock moving along $\gamma$ measures) is the proper time

    $ \tau = \int_\gamma\sqrt{\mathrm{d}x^\mu\mathrm{d}x_\mu}$ The clocks travelled different paths through spacetime, so they read differently. I fail to see the paradox.

     – ACuriousMind Jul 04 '14 at 15:10
  • Both comments would qualify as answers, in my opinion. – pfnuesel Jul 04 '14 at 15:16
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    I suspect the reason for comments instead of answers is that physicists find this questions to be boring. The twin paradox has been fully explained for around 100 years at this point. It is still difficult to communicate why the explanation is true to the layman simply because Minkowski space is so very different from how people think the world works: "acceleration" is a cop-out to avoid the hard work, but the hard work can't be done in a page or two if the audience doesn't have the preparation (because first you must explain how the world actually works and they won't believe it). – dmckee --- ex-moderator kitten Jul 04 '14 at 15:29
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    I understand this is a failure of understanding on my part but I see significant flaws in both your answers that I assume arise from simplifying the answer. In order for what you are saying to be true Robert, there would have to be a portion of the journey in which clock A or B perceived clock C to be running at a faster rate. This makes very little sense to me as I have been led to understand velocity is irrelevant and only speed matters, and that at any speed it appears that everything else is moving while you are stationary and thus everything else moves at a slower rate of time. – Krel Jul 04 '14 at 15:47
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    Yet in this instance you are saying that changing velocity despite maintaing identical speed actually has an effect on how the rate of time is to be perceived. – Krel Jul 04 '14 at 15:49
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    World lines. You must track the world lines because that is the only way to compute the proper time. I know every discussion of relativity starts by talking about relative speed but those methods are the hardest way to work these problems. The invariance of proper time is the easy way to work them. – dmckee --- ex-moderator kitten Jul 04 '14 at 16:40
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    General relativity does resolve the twin paradox. This question is based on a misconception. – Brandon Enright Jul 04 '14 at 16:49
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    @Krel A decisive answer is what ACuriousMind writes about arc length along a curve being he same as the time measured by an observer traveling along that curve, regardless of acceleration. You might find this illuminating in that regard; http://physics.stackexchange.com/questions/53334/why-do-clocks-measure-arc-length – joshphysics Jul 04 '14 at 18:18
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    Just a little Idea, why your proposal is not different from the twin-paradox. How do you send the Signal from Clock A to Clock C? If you watch for it to fly by, there is a photon travelling with Rocket A hitting you receptor on Rocket C and whilte hitting being accelerated to the speed of Rocket C. To transfer the information you will have acceleration in a sense ;-) – Falco Jul 21 '15 at 15:49

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The idea of "proper time", is a fudge-factor appended to the Special Theory in an attempt to get it to seem to work. In Einstein's original presentation, the phenomenon of time-dilatation is derived purely as a function of (relative) speed, and owes nothing to a geometrical account, such as that offered a few years later by his former tutor, Herman Minkowski; but this leads to the obvious contradictions discussed above.

Initially sceptical of Minkowski's spacetime, Einstein later felt obliged to accept his argument as a matter of expediency. However, it is not possible to derive or postulate such a model without undermining supposedly fundamental objections to simultaneity as an a priori concept. That is because "spacetime" presupposes a uniquely fixed standard of simultaneity with respect to a nominally "stationary" frame, (see David Malament, 1977, "Causal Theories of Time and the Conventionality of Simultaneity"). On the other hand, and in any case, it is impossible to think of a physical criterion to justify one's use of the epithet "stationary" as though this referred to a property of some sort, of a reference frame, such as the privilege of using synchronized clocks. Thus the supposed standard required by Minkowski spacetime becomes "unfixed".

Stuart G
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  • Proper time is the time read on a local clock. That is probably the most pure measure of time that you can get. So no, it is not a "fudge-factor". – fishinear Jan 31 '24 at 12:47