Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

B Einstein's relativity of simultaneity & quantum paradox.

  1. Jul 9, 2016 #1
    Einstein's relativity of simultaneity & quantum measurement paradox.

    Suppose a rocket traveling close to the velocity of light which emits a single photon from its midpoint at point A, illustrated below. The rocket is equipped with a single detector drawn in green at the front of the rocket. The velocity of light is independent of the velocity of the source, and thus an earthbound observer will note the photon's spherically-symmetric probabilistic wavefront expanding in the form of of the larger red circle C. An observer on the rocket will note the photon's spherically-symmetric probabilistic wavefront expanding in the form of of the smaller black circle D.

    Let us run this single-photon experiment numerous times. Because the detector illustrated in green occupies a larger portion of the smaller Circle D, the observer on the spaceship will see the photon detected more often by the detector than will the earthbound observer. Because the detector illustrated in green occupies a smaller portion of circle C, the earthbound observer will see the photon detected less often at the detector than the rocket's observer. OjcEC.jpg

    One could imagine surrounding both Circle C and Circle D with similar detectors along the entire circumference. One could perform the single-photon experiment numerous times on numerous trips, using only the detectors on Circle C or only the detectors on Circle D.

    On average, the earthbound observer will see the photon hit the illustrated green detector less often than will the observer on the rocket.

    Can both the observer on earth and the rocket be right?

    Paradox?
     
  2. jcsd
  3. Jul 9, 2016 #2

    Ibix

    User Avatar
    Science Advisor

    You've neglected relativistic aberration.

    Look that up and account for it. You'll find that the distribution of light around the ring is not uniform in the frame where the rocket is moving if it was uniform in the rocket's rest frame. The difference in the distributions will make your paradox disappear.
     
    Last edited: Jul 9, 2016
  4. Jul 9, 2016 #3
    So basically you are saying that "the distribution of light around the ring is not uniform in the frame where the rocket is moving if it was uniform in the rocket's rest frame." You are saying that the distribution of the light around the ring inside the spaceship varies with the motion of the spaceship. Thus an observer on the spaceship can detect absolute motion.
     
  5. Jul 9, 2016 #4

    PeterDonis

    User Avatar
    2016 Award

    Staff: Mentor

    Neither of these statements are correct. You are using a scenario in which relativity and QM are both relevant; that means you have to use quantum field theory (specifically quantum electrodynamics) as your theoretical framework. In QED, a photon's probability amplitude is not describable as a "spherically symmetric probabilistic wavefront expanding at the speed of light". In QED, photons have nonzero amplitudes to go faster or slower than light.

    A correct QED analysis of this problem would demonstrate that the photon field's amplitude at a given event in spacetime is a scalar invariant, i.e., it is the same in all reference frames. That means the probability of detection of a photon by a given detector at a given event in spacetime is also invariant. That is sufficient to dispose of your "paradox".
     
  6. Jul 9, 2016 #5

    Ibix

    User Avatar
    Science Advisor

    No. The distribution around the ring is uniform in the rest frame of the rocket. It is not uniform in the frame where the rocket is moving.
     
  7. Jul 9, 2016 #6

    PeterDonis

    User Avatar
    2016 Award

    Staff: Mentor

    What quantum-mechanical observable does this correspond to?
     
  8. Jul 9, 2016 #7
    Dear Peter,

    Please provide the correct QED analysis. Thanks! I have a Ph.D. in physics and studied QED with the best, so you can't win by just waving your hands here while throwing things you yourself do not understand at me. :) Let us see your "correct QED analysis of this problem." Educate us. Thanks! :)
     
  9. Jul 9, 2016 #8
    Yes the distribution around the ring is uniform in the rest frame of the rocket. That means that there is always an equal probability of the photon being detected at the green detector in the rest frame of the rocket.

    In the rest frame of the earth bound observer, the ring of light must also always be uniform, as there is no preferred fame. In the rest frame of the earthbound observer, there is less of a chance of the photon being detected at the green detector.
     
  10. Jul 9, 2016 #9
    What quantum-mechanical observables does Einstein refer to in his book on realtivity where he talks about photons? Are you saying that Einstein's relativity is bunk and BS because he does not mention your "quantum-mechanical observables"?

    I'm going to have to side with Einstein over you, who might or might not have a degree in physics even. :)
     
  11. Jul 9, 2016 #10

    Ibix

    User Avatar
    Science Advisor

    Probably none. I was treating his experiment as a circularly symmetric light pulse. He does refer to running the experiment multiple times to build up an ensemble, which more or less reduces to that case.
     
  12. Jul 9, 2016 #11
    Good eye Ibix!! :) Yes! The ensemble! To get around Peter Donis bullying with the QED he himself does not understand, as happens so often on these forums! :)
     
  13. Jul 9, 2016 #12

    Ibix

    User Avatar
    Science Advisor

    ...in which case my relativistic aberration objection resolves your paradox.
     
  14. Jul 9, 2016 #13

    PeterDonis

    User Avatar
    2016 Award

    Staff: Mentor

    Sorry, that's your job, you brought up quantum measurement. I'm simply pointing out that your analysis as it stands is incorrect, since you're using the term "quantum measurement" but not using the correct quantum theory, so it doesn't support your claim of a "paradox".

    (If your escape route is to say you didn't really mean "quantum", then Ibix's response is correct, so your claim of "paradox" is still not justified.)

    Then I fail to understand why "quantum measurement" is referenced at all anywhere in this thread.
     
  15. Jul 9, 2016 #14
    In Eisntein's Relativity he uses lightning bolts as sources of light which are measured by observers. Are you saying that no quantum processes take place in the generation of light from lightning bolts, and that no quantum processes take place in the measurement of said light? How do you personally measure or detect light without quantum mechanics? Please do share! :)
     
  16. Jul 9, 2016 #15

    PeterDonis

    User Avatar
    2016 Award

    Staff: Mentor

    It's your choice what theoretical framework you want to use. If you want to use quantum mechanics, then use it. In your OP you didn't, at least not correctly.

    If you don't want to use quantum mechanics, then don't object when someone (Ibix in this case) makes a reasonable classical approximation that works for the scenario you posed in your OP.

    In short, you can't have it both ways. Either you insist that QM is required for this scenario, in which case it's up to you to provide the correct QM math when it's pointed out, correctly, that your OP doesn't do that; or you agree that a classical approximation is OK, in which case you can't object when someone gives a classical resolution to your "paradox".

    Also, as you might have noticed, you have already received two warnings for your posts in this thread. They are because the attitude you are displaying is not conducive to productive discussion. Please take note.
     
  17. Jul 9, 2016 #16
    Dear Peter, please use relativity, quantum mechanics, or both to dispel the seeming paradox if you can. Whatever you use, please use math and physics instead of mere handwaving. Thanks!

    Nobody has yet given an resolution to the paradox, as I have seen no concrete math nor physics shared--only handwaving.

    Please do not delete this question for requesting concrete physics and math instead of mere handwaving! : )
     
  18. Jul 9, 2016 #17

    Ibix

    User Avatar
    Science Advisor

    Well, presumably you've got some maths to describe your thought experiment. Something like the integral of the light flux over the detector in both frames. Post it instead of hand-waving, as you put it, and then we can tell you where you've gone wrong.
     
  19. Jul 9, 2016 #18

    Ibix

    User Avatar
    Science Advisor

    Indeed.
     
  20. Jul 9, 2016 #19

    PeterDonis

    User Avatar
    2016 Award

    Staff: Mentor

    The only reason I am not issuing a further warning for this post is that you are new here and so I am willing to take a bit to explain how PF works.

    First, as to your claim that nobody has given a resolution: Ibix already answered your "paradox" as far as the classical approximation is concerned. The mathematics of aberration of light is well known and you should be perfectly capable of doing the analysis yourself--if you're not, then you don't know enough to make any claims of "paradox" to begin with. If you don't get the answer Ibix said--that the "paradox" disappears when aberration is taken into account in the classical approximation--you are perfectly free to post your math showing that and asking for further input. Your OP did not show any quantum "paradox" at all because it didn't use QM correctly. So there is nothing to answer as far as QM is concerned.

    More importantly: if you are coming to PF claiming a "paradox" in a well-established field of physics--two of them in this case, since your claimed "paradox" involves both relativity and QM--the burden is on you to provide the concrete math. Your OP does not do that. You drew a diagram that you claim properly represents how the photon looks in two different frames, but a diagram is not math. You gave some verbiage with terms like "one could imagine" to accompany your diagram, but that is not math either.

    Math would be you using well-known equations describing either wavefronts of light in a classical SR framework, or amplitudes for photons in QED, and showing that they give different answers in different frames. Otherwise your claim of "paradox" is nothing but, in your own terms, handwaving.

    If, instead of claiming "paradox", your OP had been along the lines of "it seems to me that different reference frames will predict different detection rates for photons in this scenario--obviously that can't be right because of the principle of relativity, so where have I gone wrong?", this would have been a very different discussion, because your attitude would have been conducive to productive discussion, whereas, as I've already said, it has not been in this thread as it actually happened. Even if you privately think you have found a "paradox" in a well-established field of physics, the odds are enormous that you are mistaken--that you have simply missed something that people with more knowledge of the field would have spotted. So your best bet, both to cover yourself if you are mistaken and to have a productive discussion in any case, is to at least post under the presumption that you have made a mistake somewhere, not to start out with claims of "paradox".

    Please do not post further unless you are willing to abide by the norms of discussion here on PF as I have explained them above. Further posts from you that do not do that will receive only a warning and a temporary ban.
     
  21. Jul 9, 2016 #20
    Thank you very much Peter Donis,

    Whenever you or anyone feels like adding a bit of math and physics to your copious words about the forum (instead of about the physics), I would welcome it very much!

    Please, let us keep this thread open and let us see some math and physics! Feel free to invoke the mathematics of quantum mechanics, physics, or both!

    I have faith that someone will soon step forth to contribute actual concrete math and physics pertaining to the paradox described above.

    Thanks to all!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Einstein's relativity of simultaneity & quantum paradox.
Loading...