Can the Twin Paradox be simplified?

How do you get them to resynch? Do you do the calculations by using the geodesic deviation in order to account for the acceleration at liftoff? What metric do you use for calculating the connection coefficients: Schwarzschild, Kerr? Something else?

What you "maintain" is irrelevant, what you can "prove" is what is relevant. Turns out that having identical acceleration profiles is irrelevant, the twins aging differential is not a function of acceleration EVEN if they have DIFFERENT acceleration profiles. You, too can prove that but it requires that you write down a fairly involved formalism. Which one are you using, geodesic deviation, hyperbolic motion , Rindler coordinates?

No, you don't need to refine the setup anymore, I just gave you a generalization to arbitrary acceleration profiles, all you have to do is put the above in a mathematical formalism. Which one are you using?

 

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I phrased this in terms of both proper time and time dilation, to be certain that my meaning was intact and I do recognize that it is at least a bit awkward. But at least here we are in agreement.

Again the phrasing is not as clean as it could have been.

My intent was to ask.., if the conclusions within the standard construction of the twin paradox hypothetical, once established, can be applied to a traveling twin who does not return home, as we agreed above.., can those conclusions then be applied in practice, to a twin or an observer who sets off from the Earth and never returns?

Granted the calculations would not be even practical, too many variables... And the result would not be totally consistent with the hypothetical... But would a real observer age slower, than the stay at home observer, if they never return home?

And Tach, this is an honest question. I can say that I am not sure myself that it would apply in the same global way, as it does within the hypothetical.., in practice.

 

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I think that you have been consistent on the issue, that even in the ideal case I suggested, involving only acceleration for the traveling twin, the age difference when reunited, is explained only by the difference in relative velocity and not the acceleration. I believe that you were at least implying that this proves that acceleration plays no part in any difference in their age when reunited.

That at least has been my impression. Things do get confused or confusing on occasion.

 

So, how do you do your calculations? what method are you using? I asked several times, no answer.

 

I don't believe that we have any evidence that the two situations are equivalent, except under the conditions defined within hypothetical thought experiments. In practice there are conditions and interactions which are by design excluded from the environment of the hypothetical.

While you are correct in your description of what is observed to occur in the lab, those observations are not confined to the construction of a hypothetical. How a shift in the lab's frame of reference, involving similar velocities exceeds any evidence we can draw from either experience or experiment, with the technologies and practical limitations, we are constrained to at classical scales.

In other words, I don't know. But I am still thinking about it....

 

I find these mental exercises interesting, but I still consider there to be an elephant in the room. Namely, the unambiguous time dilation differential between the body residing on a mass and one residing outside the gravitational influence of said mass. Alternatively, the constantly-accelerating rocket with a clock in the nose and tail. In either case I find it difficult to attribute time dilation to relative velocity, even if we try to make the claim that these are special scenarios in which relative velocity is not well defined...

Analogy: I say it takes bread to make a sandwich, you say it takes jam. You guys are busy trying to make 5 sandwiches from jam, bologna, and 2 slices of bread so we can conclude it was the jam; in the meantime...I hand you a bread sandwich.

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"Very deeply flawed" is quite harsh. The analogy is decent. We're descending into semantics, now, and you're resting your definition of relative velocity on top of the EEP; it's an additional degree of separation, when every definition I've ever seen involves a change in distance over time, having nothing to do with acceleration.

I'm not sure it gets you much anyway, because if you're defining relative velocity as that which is caused by acceleration, then acceleration CAUSES time dilation via that same additional degree of separation.

 

That's incorrect, if the twins are subjected to different acceleration profiles and the difference in the total elapsed time is function of their relative speed only, this is proof sufficient that their aging does not depend on acceleration.

 

Tach, I do not see the difference in what Trippy is saying and what you are saying???

Both of these statements reduce to the samething, any difference in aging is due to velocity not acceleration!

They are just said in different ways.

 

You think so? Too bad.

 

That's really too bad since countless of mainstream scientists don't find this difficult at all. Is this one of those cases "it must be wrong because it offends my intuition"?

 

You must have put a great deal of thought into such a profound out of context comment!

 

If the acceleration profiles are the same, as you mistakenly consider, then they cancel out, so only someone totally incompetent in experimental physics would conclude that this is equivalent to the acceleration playing no role in the differential aging of the twins. While the correct conclusion is all along that applying identical acceleration profiles results in the acceleration effects canceling each other or , more probably, the experiment being totally brain dead.

On the other hand, using different acceleration profiles and observing no effect on the differential aging of the twins , mainstream scientists would correctly conclude that acceleration indeed doesn't play any role. This is very simple, basic experimental physics, I wonder how you could miss. On the other hand, I am not wondering anymore.

The solutions are of course, not equivalent. Only someone ignorant in experimental physics would claim such a thing. If you really and truly want to prove that acceleration has no role, you really need to impart non-equal accelerations to the twins. Get it yet? If you do what you did, any fool will point out that the equal accelerations cancel out, so you've proven nothing.