The Twin (Earth) Paradox

Discussion in 'Physics & Math' started by conscienta, Mar 23, 2012.

  1. origin Trump is the best argument against a democracy. Valued Senior Member

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    Ahh.

    edited to add: I meant Ahh as a slightly sarcastic and somewhat aloof, Ohh.
     
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  3. conscienta Registered Member

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    This is not directed to anyone in particular but it is in response to the preceding general discussion regarding distance contraction.

    I think it is quite clear from the experiment with muon’s that in the muon’s frame of reference the theory predicts that the distance is measured to be foreshortened. Reality is based on measurement and that is what is real. From the observer/scientist’s perspective the muon’s time is dilated and as a result its lifetime is extended.

    The only point I would make is that from an experimental standpoint the only proof we have is that the muon’s life is in fact extended so it is possible to experimentally confirm time dilation. Whether or not the distance actually contracted for the muon is based on the special theory of relativity which is a mathematical model that seems to imply that, but I have not seen any experimental proof to confirm that the distance actually contracts.

    This returns me to the point made at the beginning of the thread. In most treatments of the original Twin Paradox it is suggested that acceleration is the cause of the asymmetry in this thought experiment. It is, however, usually pointed out that it is not the acceleration per se that causes the time dilation but rather it is only dependent on the relative velocity.

    However, when one changes inertial frames something happens. There is a difference between an accelerated frame and inertial frame. Now it may be adequate to say that what happens are changes in the geometry of space and time. If that is the end of the story then that is OK. But I believe that there is something fundamental about how motion affects time that we do not yet understand.

    I think that it is a subject worth exploring.
     
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  5. AlexG Like nailing Jello to a tree Valued Senior Member

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    Direct confirmation is difficult, because we simply can't get macrosopic objects moving at relativistic speeds, however, there is more indirect confirmation than just the muon.

    http://en.wikipedia.org/wiki/Length_contraction#Experimental_verifications

     
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  7. conscienta Registered Member

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    I agree with the article you cited that from an outside observer’s frame of reference the shape of the muon will be/is length contracted. Your other references address similar aspects of the length contraction phenomena. The question is whether the distance the muon traverses between its creation in the upper atmosphere and its detection on Earth is similarly contracted.

    In the Twin (Earth) Paradox I proposed it is implied that the distance Twin B (in Twin B’s frame of reference) travels from Earth to Twin Earth is measured to be 4.8 light years. I guess one could say that the reason Twin B only ages 6 years over the course of this journey is because the 8 light years as measured in Twin A’s frame of reference has been contracted to 4.8 light years. However, that leaves unexplained why in this instance Twin A and Twin Earth experience 10 years during that same interval. There is no correlation between what happens in Twin B’s frame of reference and Twin A/Twin Earth’s frame of reference. The only thing one can conclude then since this is in fact what happens (6 years for Twin B and 10 years for Twin A/Earth) that something “really” happens to time when traveling at relativistic speeds from Earth to Twin Earth.

    This is problematic because according to SR time in Twin B’s frame of reference – during the inertial part of the journey - te is unaffected. So something must be happening during the phases where Twin B changes inertial frames. It is like Twin B’s temporal relationship with the universe and with Twin A is changing – at least that is what I think.
     

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