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Author | Topic: The Twins Paradox and the speed of light | |||||||||||||||||||||||||||||||||||||||
cavediver Member (Idle past 3671 days) Posts: 4129 From: UK Joined:
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You don't mention anything about acceleration, do you? No, because it's not really an important point other than when you approach Special Relativity from its limited historical persepctive. To create two different 4d paths through space-time between the same two space-time points, acceleration must be involved with one or both paths. This is a trvial consequence. The important point is the differing path-lengths, not the acceleration.
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cavediver Member (Idle past 3671 days) Posts: 4129 From: UK Joined: |
Einstein did publish a paper in the late 1910s in which he made remarks about the twins paradox that are now known to be incorrect. Can you point me to this, as I haven't come across this before. Admittedly, there was a whole host of arguments and counter-arguments in the SR early days and I have this picture of Minkowski simply banging his head against his desk, saying "please, just look at it my way". Of course, by 1910, he had sadly already died.
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cavediver Member (Idle past 3671 days) Posts: 4129 From: UK Joined: |
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. 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.
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. 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.
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cavediver Member (Idle past 3671 days) Posts: 4129 From: UK Joined: |
If the story in the article is correct, Einstein appears to have acknowledged the error. Where? I can't see it in the paper.
In reading up on this, I've seen others indicate that Einstein's formulation was in error as well. Ah yes, but I have seen many times the bollocks that "others" can bring to the table
This link below includes a critique of Einstein's 1918 position Thanks for that - that's 5 minutes I will never get back Should I perhaps stress the "bollocks" and "others" again?
But Einstein has been quoted as saying at one point that there was no resolution of the twin paradox within Special Relativity. And in terms of the twin paradox within our Universe, this is certainly true.
That at least indicates muddled thinking on the subject. 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.
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cavediver Member (Idle past 3671 days) Posts: 4129 From: UK Joined: |
Would the Hafele-Keating experiment be of any help? 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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cavediver Member (Idle past 3671 days) Posts: 4129 From: UK Joined: |
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!
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cavediver Member (Idle past 3671 days) Posts: 4129 From: UK Joined: |
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? 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
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cavediver Member (Idle past 3671 days) Posts: 4129 From: UK Joined: |
Yet we expect that the aging differential between the twins will be function of the length of the trip. 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.
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cavediver Member (Idle past 3671 days) Posts: 4129 From: UK Joined:
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Is that incorrect, or am I missing your point completely? Sort of, but it's damn difficult explaining this stuff back and forth in text like this. I should set up an EvC Skype account What we are doing is trying to construct a 4d path through space-time for each of our two twins, and then measuring the length of these paths. Artificially arranging a constant velocity trip to some star system, using infinite accelerations to generate that velocity, to reverse the direction at the star system, and then bring the twin to rest back at earth is one way to make life easy in working out the length of the total 4d path. But to say that the length of the path "depends" on the velocity at an particular point, is like... well, like the following: start at a point. Move distance . Turn through an angle and reverse for a distance . How far are you from the origin? Answer So does your distance from the origin depend on ? Well, sort of, but only if that is how you arrange your path. You could have spiralled out from your starting point for a distance , with say a widening of per revolution. Now the relation between and your distance back to the origin is totally different. What I'm trying to say, is that you are getting hung up on the precise way you are arranging your particular path through space-time that you are attributing to it importance that just isn't there. If you assume the infinite accelerations, then you are in the nice position of being able to work out the time difference from the velocities. But that is because you have given yourself these infinite accelerations to make the situation easy. The time dilation itself is not arising from the velocities even though we are using the values of the velocities to work out the total time difference. Am I making any sense?
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cavediver Member (Idle past 3671 days) Posts: 4129 From: UK Joined: |
The SR result is completely understandable using GR and the equivalence principle. I'm glad to hear it The point to take away is the fundemental difference between the observer dependent "explanations" and the actual 4d geometry of the situation, which is the true "physics" so to speak.
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