New Arguments In A Possible Proof That Negative Ageing Doesn't Occur In Special Relativity

Discussion in 'Physics & Math' started by Mike_Fontenot, Aug 7, 2021.

  1. Ssssssss Registered Senior Member

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    The signal from the female observer and helper friend cannot reach the male observer unless he reduces acceleration enough that he enters the future light cone of their transmission event at which point his "now" on their worldlines is necessarily after the transmission.
     
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  3. Mike_Fontenot Registered Senior Member

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    Regardless or whether or not "d" changes (according to either frame), that doesn't affect the proof that she doesn't get younger.

    As soon as I found a way to effectively provide an array of clocks attached to the distant accelerating observer, and stretching back to the "home twin", negative ageing becomes impossible. It doesn't matter that the clocks aren't synchronized, because we know how their rates are related, and that they started out synchronized, so they still provide a "now" instant across space for the accelerating observer. That array of clocks is as important to the accelerating observer as the array of clocks is to a perpetually-inertial observer. The accelerating observer has been emancipated!
     
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  5. Mike_Fontenot Registered Senior Member

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    Correct.
     
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  7. Neddy Bate Valued Senior Member

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    Thank you. So let us call it an "established fact" that when she is 40 years old, her entire array of clocks displays 40, simultaneously in that reference frame.

    Surely that must still hold true then, if the traveler does exist, because his mere existence cannot change that fact. So what are the implications of the following:

    It looks to me like you are trying to prove that the traveler "can't agree" with an established fact. Surely no valid proof can ever do that.
     
  8. Mike_Fontenot Registered Senior Member

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    ACCORDING TO HER, the entire array is synchronized.

    True, whether he exists or not, she concludes that her array of clocks are synchronized.

    The established fact is that she concludes that her array of clocks are synchronized. That doesn't require that anyone but her (and her perpetually-inertial helpers permanently co-located with those clocks) has to agree that her clocks are synchronized. Other perpetually-inertial observers who are moving with respect to her don't agree that her clocks are synchronized. And the accelerating observer, or an observer who has accelerated recently, doesn't necessarily agree with her either, even if he is stationary with respect to her for some period of time.
     
  9. Neddy Bate Valued Senior Member

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    I said, "When she is 40 years old, her entire array of clocks displays 40, simultaneously in that reference frame," and you were correct to agree. In SR simultaneity depends on the reference frame, not on individual people. That way, we can unambiguously say that the event of the traveler jumping off the train has these coordinates in the reference frame of the train tracks: (x, t) = (34.64, 40.00) and these coordinates in the reference frame of the train: (x', t') = (0.00, 20.00) and that one can use the Lorentz Transforms to get either one from the other.

    If you were correct in your assertion above, (which you are not), then the event of the traveler jumping off the train would also have these coordinates in the reference frame of the train tracks: (x, t) = (34.64, 10.00) but only according to one guy in that frame, only for the traveling twin! Notice that you cannot even use the Lorentz Transforms to get those coordinates, because it is not SR, you made it up.

    Also, how could the traveler have gone from x=0.00 to x=34.64 in only 10.00 years time? He would have to travel over 3 times the speed of light. It's not physics anymore, its nonsense. There's a reason we call the time t=40.00 in that frame, because that is how long it takes for the traveling twin to reach x=34.64 when traveling at v=0.866c there is no disputing it. The jump-off-the train event has nothing to do with the time t=10.00, and to claim it does is simply WRONG.*

    *But it is true that the traveler was correct in assessing that her age was 10 at the time he jumped off the train, but only because he was on the train then, so her clock array was not synchronised then. Once he is stationary on the ground he can no longer say that her clock array is not synched.
     
    Last edited: Aug 10, 2021
  10. Neddy Bate Valued Senior Member

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    2,316
    Here is a list of events:

    1. Both twins are born, the origin of the train is passing them, and the boy jumps on the train which moves at v=0.866c:
    (x, t) = 0.00, 0.00 ---> (x', t') = 0.00, 0.00

    2. The girl is celebrating her 10th birthday, and someone takes a photo of her as a train clock is passing her which displays 20, but of course this is not the train car that her brother is in because he is at the origin of the train x'=0.00, and this one is at x'=-17.32:
    (x, t) = 0.00, 10.00 --> (x', t') = -17.32, 20.00

    3. The boy is celebrating his 20th birthday, and getting ready to jump off the train, but he wants to calculate his sister's age first. He does not use the location x'=0.00 of his own train car, but rather uses the location of the train car which should be passing her now:
    (x', t') = -17.32, 20.00 ---> (x, t) = 0.00, 10.00

    4. The boy jumps off the train on his 20th birthday:
    (x', t') = 0.00, 20.00 ---> (x, t) = 34.64, 40.00

    From #2 we know that if the train clocks are simultaneously displaying the same time (which they are, but only in the train frame) then she is 10 when he is 20. We know this because there is a photo of her turning 10 and there is a train clock displaying 20 in the photo.

    From #3 we see that he had calculated that she was 10 just before he jumped, which was when he was 20. The photo in #2 confirms that this was a correct calculation (but only if the train clocks are simultaneously displaying the same time).

    From #4 we see that when he jumps off the train, he lands next to one of her array clocks which displays 40. That by itself does not mean she is 40 years old, she could still be 10 if her clocks are out of synch, as they are in #3. But once he lands on the ground, he notices a sign saying that the distance to her is x=34.64 light years, and he calculates that he could only have gotten that far at v=0.866c if she was 40 years old. He concludes that her array clocks are now synched, as the array-clock next to him displays 40, and he knows she is 40 as well. He realises that him being 20 and her being 10 simultaeously was only true when he was on the train a moment earlier, because now he is 20 and she is 40. He concludes the train clocks are not synched now that he is stationary on the ground.

    Case closed.
     
    Last edited: Aug 11, 2021
  11. Q-reeus Banned Valued Senior Member

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    Yes Rindler horizon is the standard result based on Einstein's formulation, which however has long been shown to be only a first order approximation to a more rigorous application of Equivalence Principle. Excerpted from a posting in a different thread:

    "And elsewhere here at SF I have pointed to astronomer/astrophysicist Stanley Robertson's rigorous derivation of the horizonless exponential metric in appendix A here:
    https://arxiv.org/abs/1606.01417
    Some time back I started having doubts that metric is more than the asymptotic limiting form at very large r from some gravitating mass. I haven't got round to try and work out the fully self-consistent form correctly incorporating positive energy density contribution from the field itself, but it doesn't seem to me it will be a simple exponential. But nevertheless still horizonless by way of the spatial isotropy requirement..."
     
  12. Ssssssss Registered Senior Member

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    That can be done and is no problem as long as you are happy to use non-inertial frames but can't be done by slicing and dicing inertial frames. What you are doing is using the global inertial frame that is currently most convenient and transforming everything backwards and forwards which is fine because you don't have positive or negative age jumps you just have a changing definition of now which is completely ok but is not what Mike_Fontenot is arguing against. What Mike_Fontenot is doing is finding the inertial frame where his male observer is instantaneously at rest and cutting out the bit of its Minkowski diagram that's simultaneous with the time he's at rest then drawing a new Minkowski diagram in the next rest frame and cutting out the bit while he's at rest and so on and so on then gluing all his snippets side by side then trying to prove why doing that's a bad idea. I can't work out why he thinks he needs to prove that an obviously bad idea is a bad idea and his proof involves two people who can't communicate communicating anyway and his redshift formula is obviously wrong so it all seems like a waste of time to me.
     
  13. Ssssssss Registered Senior Member

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    At a glance Robertson's elevator isn't Born rigid since both ends look to have the same proper acceleration so it will be changing length in its rest frame as it accelerates so I think he's just transformed coordinates so that the Rindler horizon is at an infinite coordinate distance instead of a finite one but I'd have to check properly to be sure. The reference to Einstein is 1907 which is early enough in the development of SR that I'd guess he hadn't completely grasped what was going on. Spacetime wasn't even a thing back then (1908) and nor was Born rigidity (1909). The Rindler horizon is just the asymptotes of the hyperbolic trajectory of an eternally accelerating observer and are obviously null so there are events that can't communicate with an accelerating observer unless he stops accelerating.
     
    Last edited: Aug 11, 2021
  14. Ssssssss Registered Senior Member

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    And all this stuff about horizons is irrelevant to the point really which is that the male observer can't receive the female's "I'm older" signal until he's in the future lightcone of the transmission event when his definition of her age has to be older than when she transmitted.
     
  15. Q-reeus Banned Valued Senior Member

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    4,695
    Born rigidity was introduced to account for the 'paradoxical' non-Euclidean situation for a rotating hoop. Where the Flatland formulation circumference C = 2πr breaks down. Something has to 'break' (not really - in practice there is just an imperceptibly minor adjustment of internal stresses/strains for any practically realizable physical scenario).
    The disparity is not evident within a given local proper frame - absent impulsive forces acting only at one end - but rather between frames having relative motion metween them. Robertson's derivation is correct, and has been preceded elsewhere e.g.
    https://www.powershow.com/view/1bbc8-ZjhlZ/P1246341516SeoJH_flash_ppt_presentation
    slides 7 to 19

    It's a priori assumed in Robertson/Alley/Yilmaz derivation of exponential metric that mechanical stresses/strains are ignored, and that the elevator/spaceship is accelerated via uniformly applied body forces. That eliminates any supposed alteration of elevator/spaceship proper spatial length. GR is broke on an internal self-consistency basis, but still sufficiently accurate observationally, that bandwagon momentum unfortunately prevails more than a century on.
     
  16. Ssssssss Registered Senior Member

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    I've thought about it a bit and Robertson's situation in flat spacetime describes two objects under acceleration that get closer then separate again so the parameter \(d\) is their closest approach and not a constant distance between them so this isn't a pure model of gravitational redshift since the measured distance between the two objects isn't constant which you can see from symmetry under Lorentz boost or by explicit calculation of radar pulses between the two.

    I don't know anything about Yilmaz gravity except that the Wikipedia page is a long list of criticisms and nothing else and I think we're discussing flat spacetime not alternative gravity theories anyway.
     
  17. Q-reeus Banned Valued Senior Member

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    4,695
    I think this confuses the transient case of an initial force applied to one end of the spaceship that must propagate via a mechanical stress/strain wave thus causing a compressive distortion, to the equilibrium acceleration case where initial transients have died out to negligible levels, and proper length is constant under uniform acceleration. The latter is what Robertson et. al. base the derivation of exponential metric on. It has no flaw, whereas the standard GR redshift derivation is a first-order approximation only. Further, if one doesn't like the Robertson et. al. derivation, where does that leave the Einstein usage of elevator experiment? This cuts both ways.
    See first explicitly approximate expression under '3.2 Early applications of the equivalence principle'
    https://en.wikipedia.org/wiki/Einst...rly_applications_of_the_equivalence_principle
    That the easily derived exact expression has been ignored in favor of an approximate one yielding 'BHs' with characteristic pathological unphysical 'event horizons' is scandalous imo.
    That Wikipedia article is practically owned by Chris Hillman who is a zealot for GR and makes incorrect assertions regarding Yilmaz gravity. For instance charting the original 1958 static version predictions not the later 1973 dynamic version. Akin to disproving GR by referring only to the 1911 version not the 1915 one.
     
  18. Ssssssss Registered Senior Member

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    If you think that then I suggest you write down the worldlines of two eternally accelerating particles with equal constant proper acceleration \(\alpha\) and some separation \(d\) when their relative velocity is zero and bounce light rays between them and write down the proper time between successive bounces and you'll find it grows over time whereas if you use a higher proper acceleration for the "lower" particle it doesn't or you can simply observe that this must be the case from the boost invariance of hyperbolas that share a focus. Notice that this is entirely a special relativistic calculation and there are no transients anywhere.
     
    Last edited: Aug 11, 2021
  19. Q-reeus Banned Valued Senior Member

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    4,695
    Umm...are you suggesting the Einstein elevator thought experiment is inherently flawed? For the elevator at rest on Earth's surface, there is obviously no steady 'growing apart' between the top and bottom of elevator. How is that fundamentally different to the case of uniform acceleration in 'gravity free' space? If it is fundamentally different, i.e. 'growing apart' happens, it implies a steadily increasing mechanical strain ie. intrinsic 'stretching' in the elevator/spaceship. Hence the Equivalence principle would be fundamentally wrong. I don't think so.
    There must be a level of nonsimultaneity regarding how the ends of the elevator are initially accelerated such that proper separation is constant. That factor correctly accounted for will you should find resolve the 'separation' paradox.
     
    Last edited: Aug 11, 2021
  20. Mike_Fontenot Registered Senior Member

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    I MEANT to say that the Age Correspondence Diagram (ACD) cannot have any discontinuities. The ACD is a plot of her current age, according to him, as a function of his age. THAT is the plot that has discontinuities in the CMIF simultaneity method. The Minkowski diagram doesn't ever have any discontinuities ... it is the same for all of the various simultaneity methods.
     
  21. Ssssssss Registered Senior Member

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    Ok. So do the maths I suggested and prove me wrong.
     
  22. Q-reeus Banned Valued Senior Member

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    Your worldlines scenario must be missing something - I suggest nonsimultaneity has been neglected - otherwise you have the conundrum I have described in #56.
    Do you agree with the obvious statement there the elevator at rest on Earth's surface has constant separation between top and bottom?
     
  23. Mike_Fontenot Registered Senior Member

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    The Bell's Spaceship scenario is different from my scenario. My scenario starts of as a GR scenario with no motion at all: it just says that for two clocks that are separated by a fixed (constant) distance, and subjected to a constant and uniform gravitational field oriented along the line between the two clocks, the clock that is closer to the source of the gravitational field will run slower that the other clock, by the factor exp(g d). So the equivalence principle then says that if the gravitational field "g" is replaced by an acceleration "A", the rear clock will run slower that the front clock, by the factor exp(A d). In both cases, the separation "d" is fixed and unchanging. Since the separation "d" in the gravitational scenario doesn't change, it can't change in the acceleration case either, according to the equivalence principle.
     

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