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Bohmian Mechanics: Do photons travel faster than c in double slit experiment?

  1. May 10, 2009 #1
    In the double slit experiment, Bohmian Mechanics http://plato.stanford.edu/entries/qm-bohm/#2s" the paths of real particles traveling from the two slits to the detector to look like something like this:

    bohmian-path-double-slit.jpg

    The above image shows particles travelling in non-straight paths.

    The diagram below represents the double slit experiment.

    non-straight-path-of-real-photon-double-slit.jpg

    The two slits are at points A and B.

    A hypothetical real photon goes through the slit at A and is detected at point Y on the detector screen.

    Sp is a straight line from A to Y.
    Represent its length as “s”.

    Bp is a non-straight line from A to Y.
    Represent its length as “b”.

    b > s

    If the time it takes a photon to leave A and be detected at Y could be measured, and ...

    If this was found to be:

    s/c

    (c is the speed of light)

    Then would it be reasonable to conclude the following about the hypothetical real photon?

    Either:

    • The photon has in fact traveled in a straight line from A to Y - rather than in a non-straight line as depicted by Bohminan Mechanics

    Or:

    • The photon has at some point along its trajectory traveled faster than the speed of light

    I would appreciate comments and corrections regarding this hypothetical real photon scenario.

    Thanks. :smile:
     
    Last edited by a moderator: Apr 24, 2017
  2. jcsd
  3. May 10, 2009 #2
    The diagram you have provided is only supposed tp apply to electrons (particles with mass), not photons (which obviously have no mass).

    As far as I know Bohmian Mechanics does not describe photons, because to do that you need QFT, not just QM. This concurs with what is said in the link you posted:

    "Like nonrelativistic quantum theory, of which it is a version, Bohmian mechanics is incompatible with special relativity, a central principle of physics: it is not Lorentz invariant. Nor can Bohmian mechanics easily be modified to become Lorentz invariant."

    Therefore Bohmian Mechanics fails to describe the most important developments in the last 60 years of physics (those arising from Quantum Field Theory) and it surprises me that the moderators on these forums allow it to be discussed at all since it is so far outside the mainstream.
     
  4. May 10, 2009 #3

    Get over your anger, man. BM (including its QFT generalizations) is completely observationally compatible with relativity, which you would know if you didn't refuse to read about it on principle.

    Here is a paper "http://www.sciencedirect.com/scienc...1495569&md5=946c43811645f1f658f3c8f9b764731d"" by Ghose et al. which contains the correct diagram (indeed the one above is for electrons) and a full explanation for the original poster.

    Although it is difficult to make BM fundamentally Lorentz invariant, it is Lorentz invariant on the average (and therefore observationally indistinguishable from the usual stuff). One can just as logically conclude that Lorentz invariance fails at this deeper level (why not?). This very possibility is being actively considered in other contexts, in particular particle physics and quantum gravity, where some expect LI to fail at the Planck scale. There's a minor industry of "emergent relativity" with various tests going on (see e.g. http://arxiv.org/abs/0707.2673" [Broken] and refs. therein). Funny how there's much less dogma about this in some other areas of physics.

    Also - tell me again why the original question is a problem? Time of flight questions are meaningless in standard QM because the particles aren't there unless you look at them and therefore don't have trajectories (and you don't have a time operator). It is only in BM where the question makes any sense. Indeed one could in principle make deductions similar to what you say, but there is no experimental evidence whatsoever that "photons" travel in straight lines or at a speed different from c. Or am I missing something?
     
    Last edited by a moderator: May 4, 2017
  5. May 11, 2009 #4
    Good afternoon.

    Thanks to ExactlySolved and zenith8 for their helpful comments.

    The following image is from from the article, Bohmian trajectories for photons, by Partha Ghose, A.S. Majumdar, S. Guhab, J. Saub, Publication: 19 November 2001, Physics Letters A 290 (2001) 205–213 found @ http://web.mit.edu/saikat/www/research/files/Bohmian-traj_PLA2001.pdf

    Its accompanying caption says: "Fig. 2. Bohmian trajectories for a pair of photons passing through two identical slits. Note that there is no crossing of trajectories between the upper and lower half planes."

    photons-bohmian-trajectories-double-slit.jpg

    I look forward to studying this article in greater detail.

    I note that the photon trajectories - representing real particle photons according to Bohmian Mechanics - are clearly shown as being non-straight.
     
    Last edited by a moderator: Apr 24, 2017
  6. May 11, 2009 #5
    Pilot wave theory is not as far from the mainstream as you suggest. While it is not Lorentz covariant and needs a preferred frame, Lorentz covariant quantum theories can be described with pilot wave theories, some of them (in particular scalar fields and the EM field) even in a more or less straightforward way. Theories for fermions exist too.
     
  7. May 11, 2009 #6

    Demystifier

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    Nothing is difficult when you know how to do it.
    This refers to making BM fundamentally Lorentz invariant as well:
    http://xxx.lanl.gov/abs/0811.1905 [Int. J. Quantum Inf. 7 (2009) 595-602]
     
  8. May 11, 2009 #7

    Demystifier

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    Not necessarily:
    http://xxx.lanl.gov/abs/0811.1905 [Int. J. Quantum Inf. 7 (2009) 595-602]
     
  9. May 11, 2009 #8

    Demystifier

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    No it doesn't:
    http://xxx.lanl.gov/abs/0904.2287
     
  10. May 11, 2009 #9

    You say this like it's obvious that 'photon trajectories' should be straight in this situation. Did I misunderstand this, or do you have a particular reason for thinking so?
     
  11. May 12, 2009 #10

    Demystifier

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    PRODOS, in some situations the Bohmian velocities of photons may be larger than c. Nevertheless, this is not a problem. By using the general theory of quantum measurements, it can be shown that the Bohmian velocity of photons is exactly equal to c whenever you measure this velocity.
     
  12. May 12, 2009 #11
    Good afternoon zenith8,

    No, I don't think it's at all obvious that the photon trajectories are straight.

    My statement was intended to "update" my initial post which pictured Bohmian electron particle paths instead of photon particle paths.

    i.e. To indicated that ...

    Although the photon trajectories look different from those of electrons, since they're still "non-straight" my question remains unaffected.

    For clarity, I'd better present the question again with the correct picture ....
    I'm interested in this issue because I'm trying to understand and compare the various physics theories, models, and interpretations.

    That's basically why I registered for PhysicsForums.com in the first place. I would like to also mention that, as well as the wonderful resources, and diverse perspectives available @ PF, what clinched it for me was reading the posts of https://www.physicsforums.com/member.php?u=323" His calm, fair, thoughtful approach appealed to me greatly.

    I agree with your earlier note, that ....
    Thanks.

    Best Wishes,

    Prodos
    Melbourne, Australia
     
    Last edited by a moderator: Apr 24, 2017
  13. May 12, 2009 #12
    DrChinese I have noticed as well is very understanding of the layman's curiosity. I read an article on quantum entangled particles and became interested out of curiosity if it would ever lead to FTL communication via digital signal. He was very understanding of my question and helped me understand what it was I was looking into. This also opened a Pandora's box of other questions for me as well. Some of the greatest physicists of our "time" have described some of these kinds questions as being "Impossible to comprehend fully" "Beyond the reach of metaphor, visualization, or even language itself."
    Take the two slit experiment for example.
    You watch/observe the particle and it passes through like a bullet.
    No one watching and it acts like a wave that can go crazy and pass through both slits at the same time.
    Now if this kind of thing baffles these guys how am I ever to play catch up?

    The number 1 question I had was ... "Why do these particles/photons act this way?" Its as if they are smiling for the camera.
     
  14. May 12, 2009 #13

    Hi Belzy,

    I think this is precisely the point of the de Broglie/Bohm interpretation. Questions like yours can be given perfectly natural, even obvious answers, formulated in terms of fully visualizable continuously existing entities and with precisely-defined mathematics. And given that it is entirely observationally equivalent to the standard viewpoint, one might as well teach it that way in particular so that beginners don't get so confused. It simply is not necessary to make QM (particularly the non-relativistic kind) into the 'weird, mysterious discipline that nobody understands' of popular legend.

    In the case of the two-slit experiment:

    While each particle track passes through just one of the slits, the wave passes through both; the interference profile that consequently develops in the wave generates a similar pattern in the particle trajectories guided by the wave.

    It is interesting to compare Feynman's commentary ("Nobody knows any machinery" etc.) with that of John Bell's:

    "Is it not clear from the smallness of the scintillation on the screen that we have to do with a particle? And is it not clear, from the diffraction and interference patterns, that the motion of the particle is directed by a wave? De Broglie showed in detail how the motion of a particle, passing through just one of two holes in the screen, could be influenced by waves propagating through both holes. And so influenced that the particle does not go where the waves cancel out, but is attracted to where they cooperate. This idea seems to me so natural and simple, to resolve the wave-particle dilemma in such a clear and ordinary way, that it is a great mystery to me that it was so generally ignored."
     
    Last edited: May 12, 2009
  15. May 12, 2009 #14
    If you mean that I am not as understanding as our worthy Oriental friend, then you are right. I try, but he knows much more than I do.

    My original reply stated:
    What I was trying to say at the end there is simply - 'Yes, Bohmian mechanics makes time-of-flight predictions (that standard QM doesn't), and yes this in principle constitutes an experimental test of it, but I am not aware of any such experiments'. What I should perhaps have made clearer is that this is because I am not at all familiar with the experimental literature on this subject. Can anyone summarize what has been done on this?
     
    Last edited: May 12, 2009
  16. May 12, 2009 #15
    Its not that, I was just showing appreciation to his understanding of my personal curiosity is all.
     
  17. May 13, 2009 #16
    Good evening Demystifier. Thanks for your comments.

    Do you mean “moderately” faster-than-c velocities as in the Bohmian photon trajectories of the double slit experiment? (Is it reasonable to refer to these photon speeds as "moderately" faster than c or does that misrepresent them in some fundamental way?)

    Or do you mean the many-times-faster-than-light velocities that are sometimes put forward to account for nonlocality in EPR type experiment?

    Or both?

    If you mean “moderately” faster-than-light, a la double slit experiment, could you possibly indicate the kinds of situations where, according to Bohmian Mechanics, this occurs or might occur, please?

    Is the application of the general theory of quantum measurement to these cases a recent development in Bohmian Mechanics or is it an established/standard aspect of Bohmian Mechanics?

    Thanks for your help.

    Best Wishes,

    Prodos
    Melbourne, Australia
     
  18. May 13, 2009 #17

    Demystifier

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    PRODOS, this velocity can be many times faster than c. In fact, it can even be infinite. Nevertheless, it has nothing to do with nonlocality in EPR experiments because the exchange of photons is NOT the mechanism of communication between entangled particles.
    A typical situation in which such ultra-high velocities occur is a wave function which is a superposition of two different frequencies.

    Concerning the application of quantum measurements to such situations, I would say that it is a standard aspect of BM, although it has been explicitly stated relatively recently.
     
  19. May 13, 2009 #18
    Unfortunately, the trajectories of BM are unobservable, so, while time of flight makes sense as really existing, we cannot observe it. At least not in quantum equilibrium.

    Any experimental literature claiming to have made experimental tests between BM and QM is based on bad theory. All what follows from the accurate interpretation is that we have yet another common confirmation of BM as well as QM.
     
  20. May 13, 2009 #19

    Demystifier

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    Let me further explain it. To measure time, we need a clock. But any measurement, including a measurement by a clock, is actually a measurement of the position of something (e.g., the needle of the clock). On the other hand, measurements of positions in BM allways give the same results as those in standard QM.
     
  21. May 14, 2009 #20
    Good evening.

    According to Bohmian Mechanics, the velocity of a particle photon – under some circumstances – can be many times greater than c. Correct?

    Okay. That’s an important point. Thanks for making it very clear.


    Such a superposition of different frequencies is happening in the region between the slits and the detector in the double slit experiment. Correct?

    Question: Stepping away from the double slit experiment for a moment ... Is it the case that, when we can plot a non-straight photon trajectory, we can infer a faster-than-light photon? But when we can plot a straight-line photon trajectory we infer an exactly-c-velocity? (I’m excluding photons being refracted, reflected, scattered, etc.)

    Question: In the specific case of a typical photon double slit experiment, is it possible to indicate the approximate range of photon velocities that might be specified by Bohmian Mechanics? For instance: "more than c, but less than twice c"? (I understand that if we took an actual measurement at any point between slits and detector we would always measure c.)

    Many thanks. :smile:
     
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