The No-Acceleration Scenario Does NOT Resolve the Twin "Paradox"

Discussion in 'Physics & Math' started by Mike_Fontenot, Dec 31, 2017.

  1. Confused2 Registered Senior Member

    Messages:
    482
    Sorry, missed your post post. Some new mystery here. By symmetry left and right twin clocks must agree when they meet yet by... ? they don't. Help!
     
  2. Google AdSense Guest Advertisement



    to hide all adverts.
  3. Neddy Bate Valued Senior Member

    Messages:
    1,512
    Your distributing the travelers around the origin is not necessary. Go back to my train example, and remember that the eastbound and westbound trains have the same speed, just in opposite directions. Of course the traveling twin will travel just as far on the eastbound train as he travels on the westbound train, because he returns to the station where his twin sibling has been sitting the whole time. You can easily work out where on the westbound train he will land, and where that spot on that train was at the moment he jumped on the first train. Of course it is twice the distance away as the turnaround point. And of course if the home twin has Einstein synched clocks spread out along the railroad tracks, the traveling twin can see that the nearest one says t=40 in the instant before and after he jumps from one train to the other. But when he is riding either train, he does not agree those clocks by the side of the tracks are all displaying the same time as one another. He does not even agree that the Einstein synched clocks on the "other" train are all displaying the same time as one another. He always insists that the only Einstein synched clocks which are all displaying the same time as one another are the ones at rest in his own train, whichever train he is in.
     
  4. Google AdSense Guest Advertisement



    to hide all adverts.
  5. Neddy Bate Valued Senior Member

    Messages:
    1,512
    For simplicity, we want all the Einstein-synched clocks on the Eastbound train to say t'=0 in the moment the traveling twin lands on the train with his own wristwatch saying t'=0. Naturally it follows that all the Einstein-synched clocks on the Eastbound train will say t'=20 just like the traveling twin's wristwatch in the moment the traveling twin jumps off to get to the other train.

    Likewise, for simplicity, we want all the Einstein-synched clocks on the Westbound train to say t'=20 in the moment the traveling twin lands on the train. Naturally it follows that all the Einstein-synched clocks on the Westbound train will say t'=40 just like the traveling twin's wristwatch in the moment the traveling twin jumps off to get back to his twin sibling in the station.

    But a set of Einstein synched clocks only display the same time as one another in their own reference frame. Other frames will say those clock times are all different, and so they will always prefer to use their own clocks instead.
     
    Last edited: Jan 2, 2018
  6. Google AdSense Guest Advertisement



    to hide all adverts.
  7. Confused2 Registered Senior Member

    Messages:
    482
    Alternative to the long train... length contraction.
    So the traveling twins start 2x apart in the home twin frame, x apart in each traveling twin frame and (2/7)x apart in the twintwin frame. Divide each by two for the distance to the x=0 line. At velocity v each twin expects to reach the centre at, (I'm writing s=ut - I've fouled up like that before) x/v with a time dilation factor relative to home frame of 2 so t=x/(2v) and looking at both twins ... they expect to meet (half way) at (1/7)x/v at a time dilation factor of 7 so (home frame again) t=x/v . I fouled up anyway (factor of 2 - I can't see it right now) but I suspect that's where to look. Could be wrong of course.
     
  8. Neddy Bate Valued Senior Member

    Messages:
    1,512
    So, to summarise the train example:

    1. In the moment the traveling twin jumps on the eastbound train, his own watch and a local clock on the eastbound train both say t'=0 in the same spacial location as the home twin whose watch says t=0. We can say the time coordinates of the home twin in this instant are t=0 & t'=0, and likewise the time coordinates of the traveling twin in this instant are t'=0 & t=0.

    2A. In the moment before the traveling twin jumps from the eastbound train to the westbound train, his own watch says t'=20 and there is also a distant clock on the eastbound train which is in the same spacial location as the home twin, and that clock on the eastbound train says t'=20 in the same spacial location as the home twin's watch which says t=10. We can say the time coordinates of the home twin in this instant are t=10 & t'=20. Note that at this point the home twin would say that the traveling twin's watch says t'=5 but it is not near him, it is far away, yet very close to him is a clock on the train which says t'=20 and so that is part of his own coordinates. This shows that the home twin does not find the set of E-synched clocks on the eastbound train to all be displaying the same time, he says they are all saying different times.

    2B. In the moment before the traveling twin jumps from the eastbound train to the westbound train, his own watch says t'=20 and there is also a nearby clock on the side of the tracks (E-synched to the home twin) which says t=40, so we can say the time coordinates of the traveling twin in this instant are t'=20 & t=40. Note that at this point the traveling twin would say that the home twin's watch says t=10 but it is not near him, it is far away, yet very close to him is a clock on the side of the tracks which says t=40 and so that is part of his own coordinates. This shows that the traveling twin does not find the set of E-synched clocks on the side of the tracks to all be displaying the same time, he says they are all saying different times.

    3A. In the moment after the traveling twin jumps from the eastbound train to the westbound train, his own watch says t''=20 and there is also a distant clock on the westbound train which is in the same spacial location as the home twin, and the clock on the train says t''=20 in the same place as the home twin's watch which says t=70. I am using double primes now ('') so that we can say that the time coordinates of the home twin in this instant are t=70 & t''=20. Note that at this point the home twin would say that the traveling twin's watch says t''=35 but it is not near him, it is far away, yet very close to him is a clock on the train which says t''=20 and so that is part of his own coordinates. This shows that the home twin does not find the set of E-synched clocks on the westbound train to all be displaying the same time, he says they are all saying different times.

    3B. In the moment after the traveling twin jumps from the eastbound train to the westbound train, his own watch says t''=20 and there is also a nearby clock on the side of the tracks (E-synched to the home twin) which says t=40, so we can say the time coordinates of the traveling twin in this instant are t''=20 & t=40. Note that at this point the traveling twin would say that the home twin's watch says t=70 but it is not near him, it is far away, yet very close to him is a clock on the side of the tracks which says t=40 and so that is part of his own coordinates. This shows that the traveling twin does not find the set of E-synched clocks on the side of the tracks to all be displaying the same time, he says they are all saying different times.

    4. In the moment the traveling twin jumps off the westbound train and lands in the station, his own watch says t''=40 and he is in the same spacial location as the home twin twin's watch which says t=80. We can say that the time coordinates of the home twin in this instant are t=80 & t''=40 and the time coordinates of the traveling twin in this instant are t''=40 & t=80.
     
  9. Neddy Bate Valued Senior Member

    Messages:
    1,512
    I don't see any reason for one train to consider the length of the other train, although yes it would be length contracted by 1/7 in this case.

    Although the idea of length contraction is useful to see that two frames do not agree on the simultaneity of events. In the train station frame, there will be a time when the two trains (of equal proper length) share front and rear endpoints simultaneously because they are both length contracted by 1/2 in that frame. But in each train frame the front and rear endpoints can never be aligned at the same time, because one train is not length contracted at all, and the other is by 1/7.
     
  10. Confused2 Registered Senior Member

    Messages:
    482
    Sorry, owing to some sort of UK cache problem (possibly internal) I missed your first train post - I have it now. I have to restart from there. Time passes.
     
  11. Neddy Bate Valued Senior Member

    Messages:
    1,512
    Do you mean you hadn't seen post #38? I think that one combined with #45 is all you need, but other posts in between are good to review as well.
     
  12. Xelasnave.1947 Valued Senior Member

    Messages:
    4,314
    Yes.
    I spent all yesterday reading about the history, the flying of clocks, particle observation and finally drifted to reading about the various approaches to atomic clocks.
    Alex
     
  13. Neddy Bate Valued Senior Member

    Messages:
    1,512
    To Alex (Xelasnave) and post #27,

    Perhaps I am wrong to interpret your posts the way I do, and perhaps you mean something other than what I am gleaning from reading your posts in this thread. But the way I interpret them (even now, because frankly you have given me no reason to think otherwise) is as follows:

    1. You think time dilation (in general) is not and can never be the same thing as as time dilation of the age of human twins, and therefore no test of time dilation will ever tell us anything about time dilation of human twins, and therefore you question what is the use of even discussing it.

    2. You are not impressed with Einstein's theory of relativity on the grounds that you think that an observation should come before a theory, even though I explained that relativity was derived from the prior observation that the speed of light is a physical constant, which you say you understood to begin with.

    3. You would be more impressed if time dilation had been discovered first, and then some theory was proposed to explain it, rather than first having a theory (derived from the prior observation that the speed of light is a physical constant) which already predicted time dilation before it was even observed, because you suspect that having a theory predict something, and then having that thing become discovered, is a bad idea because there could be a rush to conclude that the observation was indeed the thing which was predicted by the theory, (or something along those lines), and you imply that you do not trust that anyone in science would be paying attention enough to be able to look for such a thing to try to expose it and correct it in all the years following.

    As for #1, I tried patiently to help you overcome the fallacy of #1, but at no point did you ever abandon your stance that testing time dilation of 'something' would never be the same as testing time dilation of 'something else' as if human twins are a special case. You never said, oh I see, yes I was wrong.

    As for #2, I tried (perhaps not as patiently) to show you the blatant internal contradiction within #2 which should be obvious, (just read it again). But at no point did you ever say, oh I was wrong, yes relativity does meet the preference that an observation come before a theory.

    As for #3, I admit that I finally lost patience, and I apologise for that. But the implication there was that you do not like when a theory predicts something, because if the predicted thing is discovered, then you have to suspect a conspiracy of some sort. Yet you do not voice any concern that the opposite case, which you prefer, where a theory is fitted around an existing observation, could have that same problem. And in neither case do you seem contented that the scientific method would have years and decades to expose or correct it by refining the experiments and ruling out bias and other errors. Not to mention that the only way to make you happy would be if all theories had no predictive power at all.

    I am happy to hear that you insist that you value the scientific method, but I just did not see it in your posts here. I humbly apologise if I am wrong.
     
    Last edited: Jan 3, 2018
  14. Xelasnave.1947 Valued Senior Member

    Messages:
    4,314
    Neddy you are a good man.

    I assure you that whatever message you are receiving is not the one I am sending.
    I think my ignorance on the subject is misinterpreted somehow and what are questions of curiosity you presumably see otherwise.

    I wont try and explain myself as there is no need and as it seems I rub you up the wrong way I would rather just move on.
    Well so long as you know I am very happy.
    And Neddy you have my total respect.

    I think things somehow did not go right for which I accept the blame.

    Thank you sincerely for your time.

    Alex
     
  15. phyti Registered Senior Member

    Messages:
    271
  16. Confused2 Registered Senior Member

    Messages:
    482
    Let us imagine that there is a train that travels at high speed from station A to station B. Alice is standing on the first station, Beatrice is standing on the second station (I am assuming Alice and Beatrice and the clocks on the stations are all Einstein synced) . 'Physics' (SR) has no memory of whether a train started at A and travelled to B or started at B and travelled to A. So the B->A result can be considered to be independent of the A->B result as though the two experiments were carried out on different days. All we need to know is the speed between stations (assumed constant for convenience).
     

Share This Page