Time Dilation in Relativity

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

  1. Q-reeus Valued Senior Member

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    So you're all set with contacts. Great. Getting back to basic concept. Take that case of thin static shell. Let it have a mass M, mean radius R, and shell thickness d << R. From shell theorem it's known Newtonian g acceleration drops essentially linearly from a maximum at the shell outer surface, r = R + 0.5d, to zero at the shell inner surface, r = R - 0.5d. Hence the tidal dg/dr is inversely proportional to shell thickness d. Whereas for a given mass M, g at the outer shell surface is only slightly dependent on d, and in fact completely independent if we slightly re-gauge to make outer surface at r = R rather than r = R + 0.5d.

    Write me out the equation according to Beery theory that yields time dilation as a function of g, distance (hence your 'gravity times distance'), AND dg/dr. Recalling your admission as per last line in #45 time dilation would be zero inside an offset spherical cavity with uniform Newtonian g field within.

    To make any sense of what you have previously claimed, time dilation must have an intensive dependence on dg/dr. I'm betting you cannot furnish such an expression that will be internally consistent. We already agree it will violate conservation of energy. But that is likely the least problematic issue to be faced.
     
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  3. RJBeery Natural Philosopher Valued Senior Member

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    I don't really see the problem here but I have to admit I just cursorily read it. Acceleration is maximized at the outer shell surface, as is time dilation. Acceleration linearly(ish) reduces to zero as we move from the outer to the inner shell surface. The equation

    \(t_0=t_f\sqrt{1-\frac{2*a*d}{c^2}}\)

    was already given and actually derived from the familiar

    \(t_0=t_f\sqrt{1-\frac{2*G*M_r}{d*c^2}}\)

    NOTE: I have replaced the traditional \(M\) with \(M_r\) where \(M_r\) refers to the mass contained in the sphere between the mass' center and radius r. The reason for this is that it now becomes a globally applicable equation (i.e. works above and below the surface) whereas the traditional GR equation has a different form below ground.

    I also hope that I don't need to point out that this is making presumptions about uniform density and spherical symmetry of distribution of mass, etc. This is a simplified scenario.
     
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  5. Q-reeus Valued Senior Member

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    The first formula is at least consistent with e.g. your sentence in #66: "ASSUME time dilation is a function of acceleration and distance."
    It's nothing more than another way of expressing potential differences (over short distances where constancy of g reasonably applies), though not implemented in a consistent way as you apply it.
    But as I expected neither incorporates tidal field dg/dr at all. So how do you justify your other claim? As per #45:
    Nowhere do you offer a mathematical expression connecting the two: 'acceleration x distance', and 'tidal acceleration' (whatever that could mean).
     
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  7. RJBeery Natural Philosopher Valued Senior Member

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    We're losing something in semantics here. \(\sqrt{1-\frac{2*a*d}{c^2}}\) is meaningless by itself, it's a way to relate time rate differentials (e.g. "here" to infinitely far away). When I say tidal forces I'm talking about a differential in experienced acceleration for a very specific reason: I actually consider gravity to be a consequence of a graded time dilation field (which is caused by mass), not the other way around, but I'm not prepared to go in to this just yet.

    I will say that you pointing out that a uniform gravity field is possible in theory has thrown me for a loop because I thought it wasn't possible. Long ago I imagined an infinite, massive wall (with zero thickness) and concluded that bodies would not be attracted to it for the same reason I do not think time dilation would occur in such a uniform gravity field...however it's difficult for me to understand the experience of being in such a field because I haven't given it much thought. Would a body experience acceleration even though they would apparently undergo coordinate acceleration? As I said I need more time on it but I'm busy with other things currently...
     
  8. Confused2 Registered Senior Member

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  9. RJBeery Natural Philosopher Valued Senior Member

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    Thanks Confused2, if you happen to come across a paper, ANY paper, which references time dilation experiments below the surface of the Earth it would save me a lot of time.

    I thought you guys might find this interesting. I pulled this quote from https://en.wikipedia.org/wiki/Gravi...rtant_features_of_gravitational_time_dilation
    Wikipedia is not the ultimate source of truth but this is evidence that "the general consensus" agrees with the statement in bold. This statement is in direct contradiction to the scenario laid out at the top of page 7 of https://goo.gl/pzMnGd
     
  10. Confused2 Registered Senior Member

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    I see this as evidence that the writer of that part of Wikipedia hadn't yet got as far as High School calculus not as any evidence of a general consensus. The article could be much better but this is an encyclopedia for laymen not physics students.
     
  11. RJBeery Natural Philosopher Valued Senior Member

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    That's fair and possibly true but the reality is I don't care why it's been written in such a way or even what the actual GR consensus is about the meaning of the equivalence principle(s). Aesthetically, I prefer the equivalence principle to actually mean what is written in bold and I'm taking steps to resolve the answer for myself.
     
  12. Q-reeus Valued Senior Member

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    Not an issue. Only the functional dependencies are important here. Radial component of tidal gravity i.e. dg/dr is not incorporated. Hence, basic conceptual conflict.
    You choose one component - temporal one g_tt, ignoring thus spatial components g_rr etc. which must also exist in any metric theory of gravity. And radial gradient of √g_tt for Schwartzschild metric yields just equivalent of Newtonian 'g' acceleration, not any tidal dg/dr (and transverse components which probably can be ignored). Which tidal fields requires a further differentiation.
    It's been analyzed many times. In Newtonian gravity, strictly analogous to the case of an infnite sheet of charge (except for the sign): http://www.mathpages.com/home/kmath530/kmath530.htm
    So that hypothetical case gives a strictly uniform Newtonian g field. As seen further down the extension to GR case is much more involved, but on one treatment suggests the same result will be had - in particular, zero tidal gravity dg/dr etc (strictly, metric 2nd derivatives).
    Not without violently disagreeing with the EP. Look up 'Einstein's elevator' again.
     
  13. Q-reeus Valued Senior Member

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    We have been over this numbers of times this thread and you have admitted your take leads to violation of conservation of energy. Something absent in the usual approach.
     
  14. RJBeery Natural Philosopher Valued Senior Member

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    Yes, it's possible, but not certain. There are a number of reasons why conservation of energy may not be violated, including some assumptions that we are currently making which turn out to be false. Regarding your previous post, I have no interest in convincing you of anything and if my attempted translation from an abstract concept in my mind to a mathematical model gives you offense then simply move on. I'm also not going to go too deep into the idea that time dilation causes gravity because, as I said, I'm busy with other things. I will make a thread on the subject eventually. Cheers!
     
  15. Q-reeus Valued Senior Member

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    Up to you. At the end of a lot of extra time effort and expense, a hard lesson will be faced. Which could have been avoided by exercising a critical self-reappraisal. You may recall how it went with this episode some time back: http://www.sciforums.com/threads/new-test-of-j-nordbergs-field-reversing-sphere-experiment.134191/
    You may say that was an entirely different situation. The details vary but the basic principle is the same. Any hypothesis lacking internal coherency and/or disagreeing fundamentally with established theory and observational evidence cannot be correct.
     
  16. RJBeery Natural Philosopher Valued Senior Member

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    That is an extraordinarily anti-science view, I'm not sure how any progress would ever be made without challenging current theory. Nordberg's supposed field-reversing sphere yielded positive results, which I verified! He wasn't a charlatan, and it wasn't a hoax. Only by doing the experiment myself was I able to identify the disconnect between theory and an unexpected lab result (i.e. that the magnets in the compasses were interfering with each other). I would do experiments like that 100 times over, I became smarter for it and my son learned something as well.

    Regarding my current model, I will obviously need to rethink things if GR's time dilation is verified. I'm OK with that. I don't tie my ego to theories (or at least I try not to) -- which is one of the reasons I don't really appreciate you calling it "Beery theory". It's just a model. One that I developed by visiting as many areas of physics that I could, viewed through my own lens of understanding.
     
  17. RJBeery Natural Philosopher Valued Senior Member

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    One more thing...if you asked me to announce which outcome is more likely I would say GR's prediction. That doesn't mean I think I'm wrong though - it's an open question. I acknowledge that an apparent violation of energy conservation could be a death knell.

    And regarding Nordberg's experiment I would remind you of this:
     
  18. Q-reeus Valued Senior Member

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    How is it anti-science? I nowhere suggest current theory should not be challenged. But certain criteria have to be met. Your postulate fails on several fronts to meet such.
    I was able, from the outset, to confidently predict the negative results finally confirmed. No such 'field reversal' was possible. It would have been an outright paradox and paradox's don't exist in nature.
    As for Nordberg being a charlatan or not, at the least self-deluded, and given the details of his setup, charlatan is the more likely verdict imo.
    OK but having learned the hard way there, why repeat it now?
    Sorry if that offended you but I was just reusing someone else's coining that term this thread. Check back and you will find it's first use somewhere here.
    I'm trying to save you effort. And using up considerable time and effort of my own in the process. Your postulate is not actually a theory as there is no coherent physical model having a mathematical basis for it. I tried to force a recognition of that by challenging you to incorporate tidal fields in a time dilation expression.
    As you could not, why keep believing there can be some sensible connection? Based on a gut feeling? A hunch? Despite what has been pointed out numerous times now?
    If you can't for whatever reason accept my input, at the least contact known experts in GR and get their honest feedback. It won't be encouraging., but it should save further waste of time effort and money.
     
  19. RJBeery Natural Philosopher Valued Senior Member

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    The Nordberg experiment was a positive result - I mimicked the setup and observed the same thing he did. It was his explanation of those results which was faulty. The reason I did the experiment was because he didn't strike me as a hoaxer, his video as I recall seemed very sincere. I knew at the time that his results seemed nonsensical and the only way to reconcile that was to do it myself.

    Same thing here. If there weren't plausible explanations which could circumvent the perpetual motion potential then I wouldn't bother, but doing the test myself will give me information either way.
     
  20. Q-reeus Valued Senior Member

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    Your choice. i won't try and dissuade anymore. Have you worked out a rough estimate of what this will set you back financially?
     
  21. RJBeery Natural Philosopher Valued Senior Member

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    I'm still gathering info on equipment. There's a place called Soudan Lab in Minnesota which is a half-mile underground and currently unoccupied(!). I priced atomic clocks out in the 1000-2000 dollar range. No idea how I'm going to get my readings, I might run fiber down the shaft(?) and somehow transmit the signal topside. Gross estimate < $10k.

    Any suggestions on setup, by anyone, would be welcome.
     
  22. RJBeery Natural Philosopher Valued Senior Member

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    BTW, I'll tell you why the link you gave on uniform gravitational cavities was so concerning: if a lack of gradient still produces attraction (or, equivalently, if a body would indeed be attracted to an infinite wall) then my model may have a problem...but it may also give me a place to restructure it.

    As a test I buried a fishbowl in the back yard and have verified that gravitational effects were still present within it.*

    *I didn't really do this
     
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  23. Q-reeus Valued Senior Member

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    Recall the Newtonian definition: g = -∇φ, with φ = -GM/r the Newtonian potential. There is no lack of the gradient that matters - that of the potential φ.
    Right well if you had have, g = -∇φ would simply have been 'cleaned' of any tiny residual tidal field ∇g. Assuming a perfectly uniform and locally flat burial site that is. With no experimentalist near to gravitationally disturb such an ideally symmetric arrangement.
     

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