Can the Twin Paradox be simplified?

Discussion in 'Physics & Math' started by timewarp, Nov 20, 2011.

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  1. Trippy ALEA IACTA EST Staff Member

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    :Shrugs:
    Your opinion, you're entitled to it. Personally I got the impression he was wanting to make sure we all agreed to the experimental setup before we started discussing the consequences of the experiment. This is something that you have demonstrated yourself incapable of doing in several threads now.

    The reason I presumed error over ignorance, was because he seemed to understand that both in what I proposed and in the case of GPS satelites that a stationary clock runs fast, not slow.
     
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  3. OnlyMe Valued Senior Member

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    You are right. I should have gone back myself. I guess that this is a case where I let a knee jerk reaction to Tach's style get ahead of actually re-reading my own post. It is often the case that when trying to proof for yourself you always read what you meant instead of what you wrote.

    So, thanks.

    Tach, if you were a little less Tachy about the way you address issues like this many discussions would proceed better.

    I will go back and correct the misstatement.
     
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  5. Tach Banned Banned

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    Well, stop trolling my posts while attacking me and I promise I will be more polite when I correct you. How's that?
     
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  7. Tach Banned Banned

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    Good , you corrected your errors. Now trouble is , the above problem statement doesn't help any with a twin paradox problem. Turns out that the traveling twin always returns younger, regardless of his acceleration. Which tells you what? That acceleration doesn't matter, only speed does. This also happens to be the standard view of mainstream physicists....
    Correct application of the equations of accelerated motion in SR also teach you another fascinating thing, that the age differential between the two twins is:

    \(\Delta \tau=\tau_h-\tau_r=\tau_h(1-\frac{arcsinh(\beta \gamma)}{\beta \gamma})\)

    where

    \(\tau_h\) is the age of the "stay at home twin"
    \(\tau_r\) is the age of the "rocket twin"
    \(\beta=\frac{v_1}{c}\)
    \(v_1\) is the cruising speed of the "rocket twin"
    \(\gamma=\frac{1}{\sqrt{1-(v_1/c)^2}}\)
     
    Last edited: Dec 16, 2011
  8. OnlyMe Valued Senior Member

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    Tach, do you recall what that particular post was a reply to?

    RJBerry had asked for, in essense a construction that did not involve an inertial frame of reference for the traveling twin. That was what I was setting up.

    If you include my earlier post and further discussion with Trippy, while I can say that it would involve acceleration and the equivalence principle, I am not as certain about the impact and intermingling of the SR effects.

    Not that they don't exist, just that the issue is not put to rest in my own mind.

    And the post we were referring to offered no real conclusion. Just the two ways that the acceleration could be treated within the context of the equivalence principle.
     
  9. OnlyMe Valued Senior Member

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    Trippy, I got all this and understand the logic. It does not fully resolve the issue for me, but at present I am at a loss for a, shall I say coherent description of the issues I still have...
     
  10. Tach Banned Banned

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    There is no "intermingling of SR effects", as you described it, in the absence of gravitational fields, this IS a SR problem. I just gave you the answer, how I arrived to it is another story, requires knowledge of the equations of accelerated motion.

    The solution has nothing to do with EP, this is an SR problem, not a GR one.
    Now, if you want to consider the effect of the Earth (or , more generally the gravitational body where the rocket launches off), this becomes a hideous problem of accelerated motion in GR, I have solved it long ago, you don't want to go there. BTW , the solution that involves gravitational fields does not use EP either. So, it is time you dropped EP from the problem statement.
     
    Last edited: Dec 16, 2011
  11. OnlyMe Valued Senior Member

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    The way I constructed the example, was defined as one involving the equivalence principle. And yes the gravitational effects associated with the equivalence principle can be addressed using SR, that in itself does not confine the problem to SR. It only demonstrates that it can be solved with those fundamental assumptions.

    This is one of those picky technical points, but even the original twin paradox did not completely eliminate the influence of gravity. It only excludes effects of gravity for the traveling twin. The stay at home twin and his clock are in a gravitational field and the clock rate is defined by its position in that field.

    But none of that represents any issue of import.

    Let me ask this. If we arrive at a solution to the proper time or time dilation paradox, within the twin paradox, and here I am referring to the standard construction, can we then apply that solution to a twin, who never returns home and know with any certainty that the traveling twin, in that case does age slower than the stay at home twin?

    I believe the answer is yes. So, if that is the case, can anything we conclude here be applied where we don't exclude the rest of the universe, given of course that we would have to take the rest of the universe into account to reach a credible conclusion. (acknowledging that in practice this is not "practical")
     
  12. Trippy ALEA IACTA EST Staff Member

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    I don't think you've quite grasped the reason for discussing the EP in relation to this problem in the first place.
     
  13. Neddy Bate Valued Senior Member

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    Back on page 26, I showed that the accelerated case and the non-accelerate case produce the same magnitude of time dilation:


    Can you see why I interpret the above to mean the magnitude of the unambiguous time dilation does not appear to be related to acceleration?
     
  14. Tach Banned Banned

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    I grasped it ok, testimony is that I pointed out your misapplication. Now, you can continue to argue about it or we can solve the exercises together. Which one is going to be?
     
  15. Trippy ALEA IACTA EST Staff Member

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    The only thing you pointed out successfully was your misunderstanding of its application in this instance.
     
  16. Tach Banned Banned

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    This is not true, there is no "influence of gravity" in the original twin paradox. You bring gravity in, the problem becomes very, very complicated.


    You can't select which twin is affected by gravitation, they are either both affected or none is affected. Having solved the problem both ways I suggest you keep it on to none affected (but acceleration is present).


    Unfortunately, it complicates the problem significantly for the traveling twin as well (see above). And no, you can't do any tricks with EP in order to make it simpler. The best thing is to forget about the presence of any gravitating bodies.


    You need to drop the time dilation bit. The answer to other part of the question is yes and yes.

    What do you mean by "Universe"? Other gravitating bodies? I just explained that the solution including gravitating bodies is hideous even in the case of considering only one gravitating body (the launch base for the traveling twin).
     
    Last edited: Dec 16, 2011
  17. Tach Banned Banned

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    So, you don't want to work together. Ok.
     
  18. OnlyMe Valued Senior Member

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    Tach, it sometimes seems that your idea of working together comes up lacking.

    It is like saying if you agree we me on every point we can work together.

    You are not the smartest person I have ever met, nor the most knowledgeable, so slow down!

    If you are interested in discussions or working "together" you need to lighten up on the "I know everything, attitude."
     
  19. Tach Banned Banned

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    see, there you go again, and you wonder why I arse you


    Was short lived, I have no interest in working with you since you can't behave.
     
  20. Trippy ALEA IACTA EST Staff Member

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    You're the one that can't handle it when people have the audacity to question your authority or take a different approach from you.

    You're the one that argued that spaceships don't fly backwards.

    You're the one that consistently refuses to take the time to understand what other people have to say.

    I'm interested in people that are actually willing to talk things through, rather then simply stating and proclaiming they're right.
     
  21. OnlyMe Valued Senior Member

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    You know you sometimes remind me of this young man who once worked under my direction. He would shout out something he believed and when confronted with an opposing view, he literally covered his ears and began to blabber out loud so he could not hear anyone. In his late twentys even. He never did realize that EVERYONE was laughing at his antics.

    Unless you believe you are the smartest person around, there was nothing in my post that could not have been taken as constructive criticism.
     
  22. Tach Banned Banned

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    That is not true, I am not the one that throws his toys from the pram when contradicted. I might disagree with you but you are the one throwing hissy fits, not me.

    I argued that the turnaround flip is detectable from inside the ship. I also argued that changing direction plus the presence of the gravitational field at launch invalidates your ill-conceived attempt at using EEP. You threw your toys out the pram,not me.


    Actually I do. Problem is, every time I point out one of your errors, your answer is invariably "it is not my error, you don't understand what I am saying. I am not misapplying EEP, I am just tweaking it a bit".
    Here is the deal, you just created a new scenario, I can promise you that you will never be able to put it in a solvable form, let alone solve it. The mathematical formalism requires profound GR knowledge.
     
    Last edited: Dec 16, 2011
  23. Tach Banned Banned

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    You mean the way we laugh at your pretentious goofs, like the one with the simple exercise with gravitational time dilation that you fought until you realized that you had to edit?
     
    Last edited: Dec 16, 2011
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