The Twins Paradox and the speed of light

The best I can do is a reference to Journal Article called "Einstein and the twin paradox" which describes an attempt in 1918 to explain the twin paradox using GR and the equivalence principle and focusing on the region of acceleration as the cause of the time dilation. I believe it is easy to show that for the linear ingoing/outgoing case this won't work because we can use the same acceleration region for various voyage lengths.Below is a google docs link to the article. See pp 587-588https://docs.google.com/viewer?a=v&q=cache:56ZgKAyYYE4J:f...Of course the article makes clear that Einstein did understand the paradox despite making errors at times.

Ah, if you'd said 1918, I would have guessed what you were talking about. I erroneously read 1910s as 1910. Sorry, but there's nothing wrong with Einstein's explanation. And your linked paper is demonstrating too little knowledge of relativity to appreciate that. Hmmm, I'm intrigued - though I certainly think you are wrong, because Einstein's explanation is a wonderful example of the equivalence principle in full flight. But by all means present your thoughts and we can have a look.My own thought on why Einstein presented it in this way is that by then he had a full theory of relativity that actually corresponded to the real world.Your paper seems to think that there are three explanation being bandied around: lack of simultaneity, acceleration, and gravitation. There's actually only one, and these three approaches deal with different aspects of the same thing.

If the story in the article is correct, Einstein appears to have acknowledged the error. In reading up on this, I've seen others indicate that Einstein's formulation was in error as well. But at least one of those others was hawking his own Mach principle explanation, so perhaps there is some doubt.This link below includes a critique of Einstein's 1918 position
LKB | Laboratoire Kastler Brossel - ENS - Sorbonne Universit - Collge de France

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His resolution involving pseudo-gravitational time dilation, inspired by the equivalence principle and general relativity crucially relies on uninterrupted running of the clocks during accelerations, and this requirement makes the Einstein resolution is 1918 ineffective, because clocks can be stopped and restarted, and the result on time dilation is not significantly changed

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In any event, I have no doubt that there is a GR method of resolving the paradox. But Einstein has been quoted as saying at one point that there was no resolution of the twin paradox within Special Relativity. That at least indicates muddled thinking on the subject.

Where? I can't see it in the paper. Ah yes, but I have seen many times the bollocks that "others" can bring to the table Thanks for that - that's 5 minutes I will never get back Should I perhaps stress the "bollocks" and "others" again? And in terms of the twin paradox within our Universe, this is certainly true. I would need to see much more than this to even begin to entertain this possibility: Einstein's actual quote on this matter, in context, would be a great start.I'm not wedded to the idea that Einstein was always right. I know damn well that he was wrong about multiple things. But the twin's parardox is a ridiculously simple property of the SR/GR that tends to separate those who dabble in relativity and those that actually understand its foundations.

Would the Hafele-Keating experiment be of any help?Hafele—Keating experiment - WikipediaIt involves acceleration by Earth's gravity and airplanes moving at constant speed (after accelerating of course).

Well, it's a perfect example of the Twin's Paradox at work. It shows us that we do actually know what we're talking about

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There is no resolution of the twin paradox within Special Relativity

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I don't understand what you mean here. Haven't you and I both been discussing resolutions of the twin paradox using strictly Special Relativity?

Sure, within the constrained context of a Special Relativity universe. But we live in a GR universe. If you make an accelerated trip out towards alpha C, you will experience the "gravitational field" of the acceleration. By the equivalence principle, you may well account for the expected gravitational time-dilation, and the calculations had better come out right!

I understand that, but I think we are talking past each other.My understanding of Einstein's 1918 GR position (which admittedly is based on a description by a detractor) is that Einstein's analysis was conducted by using the equivalence principle during the small portion of the trip in which the ship was accelerating. I just don't see how that can be a correct resolution of the paradox, because the acceleration period would be the same regardless of the length of the voyage. Yet, any time dilation due to the acceleration must end once the acceleraton ends.I understand that there is a completely GR based resolution of the twin paradox. After all GR subsumes SR and can also account for the acceleration period which we basically ignore when doing a back of the envelope calculation. But the twin paradox itself is a pure SR postulation in which the acceleration period is set up to be a vanishingly small portion of the trip. I know, but what if the acceleration is only at the start, middle and end of the trip. Can the twin paradox be resolved by simply using the equivalence principle during those portions? I think that is what is being alleged in the criticism in that time-wasting article I pointed you to.-----------------------------------
But I'd really rather talk about the implications of this article if it is on topic. Particle physicists confirm arrow of time for B mesons

Yes, of course. If only minimal periods of acceleration are used, then the accelerations must be very large (if we are talking about relativistic speeds) and thus the equivalent gravitational field is large, and the time dilation significant.What is funny about this is that to me it is all so obvious and clear. I can see the dilation occuring on a round trip, and I can see how to project out all the possible explanations from the big picture: no explanation ever quite capturing the whole story. All I can say is that give it another few years or so, and you'll be in the same place

Perhaps I am doing a poor job of posing what I perceive to be the issue.I don't question that the time dilation can be significant during those periods.But the amount of time dilation during those periods is independent of the length of the moving twin's trip (Provided of course that the moving twin does not accelerate during the other portions of the trip). Yet we expect that the aging differential between the twins will be function of the length of the trip.I don't see how focusing on the accelerated portions explains this relationship between trip length and aging differential.

Nope, we don't. And what's more, it can't be. The length of the trip (if you mean the time duration, or the distance of the trip) is an observer-dependent quantity. The aging differential is a scalar quantity - i.e. observer independent. The scalar cannot simply be a function of an observer dependent quantity.

So if the spacecraft accelerated at 1 G both there and back while the other twin was on Earth also experiencing 1 G then they should be the same age? Their clocks should tick at the same speed relative to each other?Edited by Taq, : No reason given.

Yes. The length of the trip is an observer-dependent quantity. But the length and duration of the trip as measured from the stay at home twin's perspective is a fixed value.And I am suggesting that if we use the length as measured from the frame of the at rest twin, that the difference in ages (measured in years) between the twin that leaves and the twin that stays home varies with the length of the trip (in time or distance) and the speed of the rocket ship measured in the stat at home twin's frame. The ratio of the measured time difference for the stay at home twin is a measure of the velocity only (in the SR only version of the problem).I've never seen a calculation of the twin problem that suggested otherwise. For example I refer here to the Specific Example in the wikipedia articleTwin paradox - Wikipedia.In the example, the time difference accumulates at a rate dependent on the velocity of the space craft (in the stay at home twin's frame) however the accumulate number of years is proportional to the time experienced by the stay at home twin during the traveling twins trip. Is that incorrect, or am I missing your point completely?Edited by NoNukes, : No reason given.Edited by NoNukes, : No reason given.

No. Gravitational time dilation is related to differences in potential of the gravitational field and not to the magnitude of the acceleration. For example, in a uniform gravitational field there would be no time dilation experienced based on changing position in the gravitational field.