Time Dilation in Relativity

Discussion in 'Physics & Math' started by RJBeery, Feb 1, 2017.

  1. RJBeery Natural Philosopher Valued Senior Member

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    This paper is not yet complete but the heart of it is. I'm working with an experimentalist to actually test this, probably along the lines of atomic clocks at and below the Earth's surface (depending on sensitivity of tech available today, otherwise perhaps a Pound-Rebka derivative).

    All mature feedback is welcome!

    Causal Simplification of Time Dilation: https://goo.gl/pzMnGd
     
    ajanta likes this.
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  3. karenmansker HSIRI Banned

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    RJB: I have a problem following your premise, but I trust you'll clarify it. Looking forward to the experimental results!
     
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  5. RJBeery Natural Philosopher Valued Senior Member

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    No sweat, if there are areas I can clarify please let me know...
     
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  7. Q-reeus Valued Senior Member

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    A quick look and I stopped after reading:
    Wrong. It'a function of the potential, not it's gradient. 'The Schneib' made that same error some time back but was too stubborn to concede. Strangely, the following formula does not reflect that claim and is the standard one for gravitational time dilation. Except differentials dt0, dtf should have been used. Your passage there is only a slightly edited partial reproduction of that given here:
    https://en.wikipedia.org/wiki/Gravitational_time_dilation#Outside_a_non-rotating_sphere
    Credit should have been given in the References section. Similar situation in other places in your article?

    I'd suggest making a quick edit just on above. The rest I have not bothered to read through, as the standard picture is perfectly clear and has no contradictions. The Wikipedia article:
    https://en.wikipedia.org/wiki/Twin_paradox covers all the usual scenarios and approaches quite well imo.
     
  8. RJBeery Natural Philosopher Valued Senior Member

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    You're right, I'll make that change. I've actually tipped my hand here because this difference is exactly the heart of the paper. I contend that time dilation is determined by gravitational acceleration (i.e. the gradient) rather than the total potential. Above ground would produce the same results. The standard GR time dilation formula works because M is assumed to be a point mass.

    My original formulas had a very different look but I wanted to use standard notation so as to be familiar to readers. I don't particularly like t_0 and t_f but adding a reference is easy enough. I would really appreciate you reading through the rest of the paper. I make mathematical, logical and aesthetic appeals for the case to consider acceleration over potential, and I propose a test to decide which is correct.
     
  9. RJBeery Natural Philosopher Valued Senior Member

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    (Or rather I WILL propose a test but I think it's obvious what that test will generally consist of...)
     
  10. QuarkHead Remedial Math Student Valued Senior Member

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    Can you please explain why you use gravitational acceleration and the gradient as synonyms? (Gradient of what? Gravitational potential? What?)

    P.S. You know of course that the gradient operator acts on scalar fields to produce vector fields?
     
  11. RJBeery Natural Philosopher Valued Senior Member

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    Hi QuarkHead, if I did that it was unintentional. If you find other areas needing clarification I would appreciate the feedback. Note this isn't a paper currently being prepped for publication so, while I want it to be accurate and readable, I'm more interested in the premise.
     
  12. Confused2 Registered Senior Member

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    Hi RJB, can you give the time dilation of a point at potential U2 seen from a point at potential U1?
     
  13. RJBeery Natural Philosopher Valued Senior Member

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    Sure, but to what end? As a test of my knowledge or because you don't know? If you want to work with potentials check out the bottom of page 1 and top of page 2 here: https://arxiv.org/pdf/1604.05507v1.pdf

    Personally, I'd just calculate the dilation using the standard formula at each point and take the ratio.
     
  14. Confused2 Registered Senior Member

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  15. RJBeery Natural Philosopher Valued Senior Member

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    On first blush I like it. Check out equation 4 of the paper I linked to.
     
  16. Q-reeus Valued Senior Member

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    Well the article you linked to in #10 makes it perfectly obvious time dilation is indeed a function of the Newtonian potential, specifically sqrt(g_tt), not the spatial gradient i.e. 'gravitational acceleration g'. I do like what is covered in IV. DISCUSSION AND CONCLUSION. One or two here that are mindless devotees of famous scientists and science popularizers should learn from it. Should.

    See this thread: http://www.sciforums.com/threads/time-dilation-gravity-force-vs-gravitational-potential.156181/
    In particular my posts #2, #8, #9, #14 there. Also #15. There is no way you will ever get a consistent physics by trying to link time dilation to acceleration. In certain ad hoc special cases a numerical equivalence can be had, but will not and cannot apply in the general case.
     
  17. RJBeery Natural Philosopher Valued Senior Member

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    I don't agree with this. The paper is fine, of course, but you're taking an explanation of a theory as proof that the theory is valid. The fact is that I've presented an alternative theory which makes the same predictions as the ones we've tested (Pound-Rebka, et al) and I've identified a test that would allow us to determine which one is correct.
    Agreed 100%. "Proof by ethos" is a fantastic phrase.
    This may be true but I haven't found a case yet which cannot be attributed to acceleration and distance.
     
  18. RJBeery Natural Philosopher Valued Senior Member

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    Q-reeus you should read my paper, I think you may find it compelling. Compare what you wrote above to the following passage:
     
  19. Confused2 Registered Senior Member

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    Hi RJB, In a passing 10*1/sqrt(1-0.36) isn't 6

    We have a train travelling at constant velocity v. Alice is at a station and Bob is on the train. As the train whizzes through Alice's station at 0.00 am the twins synchronise watches. By the time the train reaches the next station the station clock shows T and Bob's watch shows t where
    t=T√(1-v²/c²)
    See muon experiment ( http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/muon.html ) for experimental confirmation of this.
    The point being that after travelling to the next station Bob is already younger than Alice and there has been no acceleration. For the sake of tradition we could arrange for Bob to travel back to Alice's station at constant velocity v in (again) time T in Alice's frame and t in Bobs frame
    giving a total for the round trip of
    2t=2T√(1-v²/c²) //edit ... factor of two added
    with no acceleration.
     
    Last edited: Feb 4, 2017
  20. Q-reeus Valued Senior Member

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    In #14 you wrote: "This may be true but I haven't found a case yet which cannot be attributed to acceleration and distance."
    If by 'acceleration and distance' one refers to a dot product of acceleration x distance (more accurately a dot product integral of acceleration over displacement), that amounts to a long-hand way of writing out the potential, or potential difference more generally. It works for e.g. static exterior Schwarzschild spacetime owing to a non-spinning spherically symmetric mass. Having there a rational physical basis - work equivalent owing to the non-zero dot product integral.

    In your first example pp 3-4 of circular accelerated turnaround, at all times the proper acceleration a is normal to v, hence an always zero dot product a.v. Thus the coincidence in calculated differential age is a formal one without physical justification. One expects it to be ad hoc and to fail in other situations. Which is the case.

    One well known but rarely mentioned counterexample is that of a 180 degree slingshot trajectory of the 'traveling twin' around a planet. In that scenario the traveling twin always moves on a geodesic thus always in free-fall thus never experiences proper acceleration the entire journey. (According to your stipulation; we ignore any initial and final accelerations that got the traveling twin up to speed at the point of initial coincident clock sync, and back down to zero relative speed after final coincident clock readings, respectively.) Yet traveling twin will return with reduced relative age in accordance with the standard spacetime path expressions (that incorporate GR metric), as per that linked to Wikipedia article given in #4.

    And how about this one: https://arxiv.org/abs/0905.2428
     
  21. Q-reeus Valued Senior Member

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    But that won't satisfy the twin paradox scenario that requires a full round trip comparison. It is a symmetrical case that allows Bob to equally conclude Alice is younger than Bob. Both of them neglect to allow for nonsimultaneity.
    How has the turnaround been achieved without any acceleration of Bob? Impossible. Barring gravitational slingshot scenario - which train stations are not equipped to provide! Maybe you are sort of thinking of a so-called triplets variant, where an acceleration-free round trip is indirectly achieved. An outbound triplet synchronizes clocks with an inbound triplet at point of coincidence. When the inbound triplet then compares coincident clock readings with the 'stationary' triplet, a time differential according to usual SR velocity formula is found. Such a scenario is considered a 'cheat' by many and not a genuine twin paradox variant.
     
  22. Confused2 Registered Senior Member

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    It is already asymmetrical by the time Bob gets to the first station because Bob is using a clock on his wrist and Alice is using clocks that are (say) 10km apart. In the muon experiment the muons self-time and the Earth observers use clocks that are 10km apart - the muons are time dilated seen from the Earth frame (s²=x²-c²t²) where for Bob/Muons x=0 and for Alice/Earth x=10km and s² is the same in both frames . I agree there must be some acceleration to turn Bob round but the trick is in the placing of the clocks not the acceleration. I'll follow up this but have to leave for work now.
     
  23. Q-reeus Valued Senior Member

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    They are not making equivalent measurements so there is no reason to expect their delta t's should be equal in that case. The symmetry shows when each records the tick rate of the other's clock. Each concludes the other's clock runs either slow or fast by the same factor. Notice - slow OR fast. Only when directly abreast will the other's clock appear slower by the inverse gamma factor. Otherwise, longitudinal Doppler shift enters the picture and not just relative speed but relative velocity needs to be taken into account.
    [I had made some blunders of my own earlier on by being too hasty to reply and not stopping to think carefully. Hence this is a drastic edit!]
     
    Last edited: Feb 4, 2017

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