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Quantum vs relativity

  1. Sep 15, 2006 #1
    Ive seen a lot of comparisons between the conflict of electromagnetism and classical mechanics before relativity fixed it and the conflict of quantum mechanics and relativity. I know why classical mechanics and electromagnetism could not both be true (e.g. E&M says c is constant but CM doesnt). Are there any similar examples of things that are true in GR or QM but are not true in the other? All I know of is that QM says that when particles tunnel they travel at faster than c. However this isn't really impossible in GR as long as the mass is imaginary (which I believe it is while a particle is tunneling).
     
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  3. Sep 15, 2006 #2

    chroot

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    QM definitely does not state that quantum tunneling involves faster-than-light motion, nor do I understand why you think it does.

    - Warren
     
  4. Sep 15, 2006 #3
    Ive read multiple times that you get a speed faster than c for tunneling particles. There was some article about some group who made photons travel 4X c (sorry for the vagueness).

    and anyway, whether Im wrong or right it doesnt have anything to do with my question.
     
  5. Sep 15, 2006 #4

    JesseM

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    Well, the old solution was that E&M was only exactly true in the rest frame of the ether, and that if you were traveling at some velocity v relative to the ether, light waves would move at c+v in one direction and c-v in the opposite one. If the Michelson-Morley experiment had verified this, then that would have shown that electromagnetism and classical mechanics could be reconciled, it's just that the laws of E&M would be specific to a particular inertial frame.
    I don't know if there are any situations where they both make clear predictions that contradict each other, but see here for a discussion of one of the main problems in figuring out how to reconcile them, having to do with the fact that the uncertainty principle would seem to allow for huge uncertainty in energy at sufficiently small scales, but in GR big energies cause significant curvature of spacetime, and my understanding is that physicists only know how to make predictions in quantum field theory if they have a specific known background spacetime.

    I guess another more general conflict is that quantum field theories treat the other set of forces using a common set of rules, but if you try to apply these rules to gravity you get infinities which can't be "renormalized" as in the case of the other forces. Of course, I suppose it is logically possible that gravity would just work in a fundamentally different way than the other forces, so this in itself might not be the sort of conflict you're looking for.
     
    Last edited: Sep 15, 2006
  6. Sep 15, 2006 #5

    chroot

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    They created a signal with a group velocity greater than 4x. This is nothing surprising, nor does it mean any information was actually transmitted faster than light. The phase velocity, the velocity at which information is propagated, was the speed of light.

    This is the equivalent of pointing a laser pointer to the south sky, then suddenly turning and pointing it at the northern sky, and claiming that the laser beam travelled thousands of times faster than c.

    - Warren
     
  7. Sep 15, 2006 #6
    are you sure? I remember reading specifically that this wasnt just speeding up group or phase velocity. They made photons tunnel through some gas which made it go faster than c. and isnt it theoretically possible anyway? how fast do you think things tunnel?
     
  8. Sep 15, 2006 #7

    chroot

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    Please provide a reference, then. Good luck. Tunneling does not occur faster than light.

    - Warren
     
  9. Sep 15, 2006 #8
    I googled tunnel faster than light and this was the first result.
     
  10. Sep 15, 2006 #9
    ok I found some sites that said that the evanescent waves can't carry information and its impossible to use this FTL travel to make FTL information (which I dont rly get..). But the fact is, tunneling is faster than light. supposedly it is a constant speed for light no matter how thick the barrier.
     
  11. Sep 15, 2006 #10

    chroot

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    I guess you didn't read the whole thing, then, eh?

    That's exactly what I'm saying. Phase velocity is always less than c, even though group velocity may exceed it. This very basic misunderstanding is at the heart of 99% of "faster than light" claims.

    Good try, though, chap.

    - Warren
     
  12. Sep 15, 2006 #11
    find me a reference that says this is the same thing as group velocity.
     
  13. Sep 15, 2006 #12

    chroot

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    Give me a break, dude. You make a stupid claim, and you get the burden of proof. Do your own homework, I've already done mine.

    - Warren
     
  14. Sep 15, 2006 #13

    ZapperZ

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    M. Buttiker and S. Washburn, Nature v.422, p.271 (2003).

    They presented what I thought to be an excellent explanation on why such claims of superluminal motion is highly misleading. They explore what we actually mean by a pulse of light, when we actually define where the location of a pulse is, and what happens during a tunneling process that severely attenuates this pulse.

    As with the NEC experiment, no part of the pulse actually travelled faster than c. And the speed of information in such a system can actually be slower than c. See M.D. Stenner et al., Nature v.425, p.695 (2003) or http://physicsweb.org/articles/world/16/12/3.

    Zz.
     
  15. Sep 15, 2006 #14
    thanks zapper
     
  16. Nov 25, 2006 #15
    I thought it was the other way around? That group velocity is always less than c and that phase velocity can be greater than c.
     
  17. Nov 25, 2006 #16

    robphy

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    http://www.math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html says
    "5. Phase velocity
    ...
    Look at this wave equation:
    Code (Text):

       d2u         d2u
       --    -  c2 --   + w2 u = 0
       dt2         dx2
     
    This has solutions of the form:
    u = A cos( ax - bt )
    c2 a2 - b2 + w2 = 0
    These solutions are sine waves propagating with a speed,
    v = b/a = sqrt(c2 + (w/a)2)
    But this is faster than light, so is this the equation for a tachyon field? No it is the usual relativistic equation for an ordinary massive scalar particle!

    The paradox is resolved by distinguishing this velocity which is known as the phase velocity vph from another velocity known as the group velocity vgr which is given by,
    vgr = c / vph
    If a wave solution has a frequency dispersion it will take the form of a wave packet which travels at the group velocity which is less than c. Only its wave trains travel at the phase velocity. It is only possible to send information with such a wave equation at the group velocity so the phase velocity is yet another example of a speed faster than light which cannot carry a message."
     
  18. Nov 25, 2006 #17
    I completely agree.
     
  19. Dec 12, 2006 #18
  20. Dec 12, 2006 #19

    ZapperZ

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    No, I wouldn't say that.

    At worse, all the theories SCALE with c. You are confusing possible variation with c over TIME, rather than possible variation with c under different situation at a given time. You still can't exceed c NOW.

    Furthermore, how does one throw "out the back door" theories that have been shown to work, and work very well, such as quantum mechanics? If the idea that c has changed over the history of our universe is true, does that suddenly make your computer stop working all of the sudden? The semiconductor that you use in modern electronics will suddenly cease to function just because we declare c has evolved over time?

    You'll note that we still use classical mechanics all the time (ask any structural enginner) even when we know it is only an approximation for our terrestrial condition. We certainly don't throw it out of the back door just because we realize that.

    Zz.
     
    Last edited: Dec 12, 2006
  21. Dec 12, 2006 #20
    Thanx Zap - I don't feel as baffled as before!
     
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