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Double-slit experiment with photons vs electrons

  1. Nov 29, 2013 #1
    Both photons and electrons give the same kind of interference pattern in the double-slit experiment, but while in the case of electrons this carachteristic interference pattern is due to the probabilistic complex wavefunction of the Schrodinger equation within NRQM, for photons no such non-relativistic Schrodinger wavefunction exists, and apparently the interference pattern can be accounted simply by the classical real as opposed to complex EM wave, and I'm centering here just on the interference pattern, surely photons have particle properties such as the compton and photoelectric effects that are not justified by the classical wave theory, the important thing here is that these kind of properties in the case of electrons are justifies simply thru the NRQM wavefunction.
    Is there a simple way to understand how such different mathematical entities as Schrodinger wavefunction and Maxwell EM waves produce the same experimental outcome?
     
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  3. Nov 29, 2013 #2

    bhobba

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    Of course - the standard way.

    Both have wave or wave-like solutions in certain situations.

    But like many things in physics, that's the simple, elementary way of looking at it. If you delve deeper its more complex.

    BTW, Maxwell's equations are not really applicable when the light intensity is so low you only have one photon creating interference - you need a QM description - although you may get away with it at a superficial level.

    Thanks
    Bill
     
  4. Nov 30, 2013 #3

    Jano L.

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    Do you have a reference for such extraordinary claim?
     
  5. Nov 30, 2013 #4

    bhobba

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    You mean that Maxwell's equations predict quanta?

    I thought it was utterly obvious. Maxwell's equations predict the intensity can be lowered below that of a single photon - which of course is not what's going on when the intensity is such that only a single photon is present - you get a build up of 'spots' on the screen as single photons arrive - not the continuous result classical theory predicts.

    Thanks
    Bill
     
    Last edited: Nov 30, 2013
  6. Nov 30, 2013 #5
    Ok, Bill, my fault; so let me rephrase my question: is there a more complex way to explain it?:wink:


    This statement might be misleading, my question arose from the fact that there is really no good NRQM-standard QM description of the photon, one has to move on to QED and even there there are some weird caveats(for reference see Cthuga's posts in the" size of the photon" thread or the long discussion about interpretation of the single photon's "wavefunction":is the wave function real or abstract statistics?" thread where it was made clear that one can only talk about "single particle in a statistical way. ).

    Also as noted by Jano L. even though certainly Maxwell equations don't predict the quantum particle features of photons they are enough to account for their propagation as a wave features that show up in the quantum interference and diffraction experiments with photons, aren't they?
    References taken from stackexchange.com:Photon wave function. Iwo Bialynicki-Birula. Progress in Optics 36 V (1996), pp. 245-294, where it is implied that a classical EM plane wavefunction is a wavefunction (in Hilbert space) of a single photon with definite momentum (c.f section 1.4), and Neumaier's comment:"As explained by Iwo Bialynicki-Birula in the paper quoted, the Maxwell equations are relativistic equations for a single photon, fully analogous to the Dirac equations for a single electron. By restricting to the positive energy solutions, one gets in both cases an irreducible unitary representation of the full Poincare group, and hence the space of modes of a photon or electron in quantum electrodynamics."

    The bottom line is how can photons, that is, quantum particles, have their propagation behaviour explained by a classical theory, while other quantum particles need the whole QM apparatus of the Schrodinger or Dirac equation?
     
  7. Nov 30, 2013 #6

    bhobba

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    I am not sure exactly what he meant - I thought what I said was utterly obvious.

    I don't know what you mean by 'account for their propagation as a wave features that show up in the quantum interference and diffraction experiments with photons'

    Maxwell Equation's describe the behavior of EM fields - not the quanta of those fields - photons. QM - specifically QED - is required for that.

    In the double slit experiment if you lower the intensity of the light so only a single photon is ever present then Maxwell's equations have broken down - they do not predict the observed behavior. At a 'superficial' level if you wait long enough the bands you get is exactly what classical theory predicts - but that's only because of the bulk statistical nature of how they behave is the same.

    To be honest I don't even really understand what your question is on about. There is no mystery classically, its only QM that is the issue. And, obviously for QM, well you need QM.

    What you mean by Maxwell's equations for a single photon has me flummoxed as well.

    Added Later:

    Had a look over on Stackexchange and here is what I found:
    http://physics.stackexchange.com/qu...describes-the-wavefunction-of-a-single-photon
    There is a slight confusion in this question. In quantum field theory, the Dirac equation and the Schrödinger equation have very different roles. The Dirac equation is an equation for the field, which is not a particle. The time evolution of a particle, ie, a quantum state, is always given by the Schrödinger equation. The hamiltonian for this time evolution is written in terms of fields which obey a certain equation themselves. So, the proper answer is: Schrödinger equation with a hamiltonian given in terms of a massless vector field whose equation is nothing else but Maxwell's equation.

    If that's what you mean - sure. But that's a rather advanced sophisticated view eg you need to write the EM field in their complex form - and that is most definitely not their standard form.

    Thanks
    Bill
     
    Last edited: Nov 30, 2013
  8. Nov 30, 2013 #7
    As I specified I'm leaving aside things like the photoelectric and Compton effects that are obviously not predicted by Maxwell equations but what you comment here is not well brought up here, and IMO might be misleading, you are referring here to the way the measurements are visualized wich is complex in itself, as most know each spot can be produced by many photons wich prevents identifying spots with single photons in a naive way, and even if one manages to send "one photon at a time", that is achieved only in a statistical or ensemble sense, and measurements are discrete by their very nature, a "single" measurement is always a local thing. Anyway we are here into "collapse" territory that I wanted to stay away from as much as possible.





    The link is invalid.

    Surely I'd rather stick to the "sophisticated" view than going on with views so simple that are wrong like:
    Surely there Maxwell equation would break down but this is not an accurate description of how a "single photon" (with all the the caveats I alluded above allow to even talk about a single photon) is obtained( I mean that lowering the intensity is not the advanced explanation of how the "single photon" measured is achieved), and also the the classic EM theory is not even concerned with single photons, so how could it predict anything about them. That is why I insisted on talking about propagation of photons in plural, and how they produce the interference pattern.
     
    Last edited by a moderator: May 6, 2017
  9. Nov 30, 2013 #8

    bhobba

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    All I was pointing out is the bleeding obvious - that Maxwell's Equations aren't really applicable - but somehow that was of concern.

    Sorry - fixed it up.

    Ok - if that's what you are thinking about then, yes, I do recall it is possible to write Maxwell's equations in complex form and it looks like Schrodenger's equation (I think John Baez did it in a book I got of his) and I did find a link to it (see equation 521):
    http://www.nist.gov/pml/div684/fcdc/upload/preprint.pdf

    Just to be sure we are on the same page, are you talking about this formal connection?

    Thanks
    Bill
     
    Last edited: Nov 30, 2013
  10. Nov 30, 2013 #9

    Jano L.

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    Why do you think such situation implies intensity cannot be lowered below that of single photon?

    Maxwell's equations by themselves are not able to predict whether the pattern on the screen is made of continuous color variation or spots. For that another assumptions are necessary, like the fact that the screen is made of grains of matter - atoms or molecules, and model of them that would be able to describe interaction with light. Then the build up of interference pattern made of "spots" does not in any way disprove Maxwell's equations. It may only disprove some simplistic model of matter, like matter made of continuous gelatine that shines continuously every time it is under action of electric field.

    By the way, spots on screen or CCD detector are not manifestations of photons. You will find explanation in any good book on modern optics. I recommend

    Knight, P.L., Allen L., Concepts of Quantum Optics, Pergamon Press, 1983

    which contains also preprints of original papers on this subject.
     
  11. Nov 30, 2013 #10

    bhobba

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    Errrr.

    Come again. That doesn't make any sense.

    To reconcile the concept of 'intensity' of whatever you have in your wave equation, and that of a single particle, which has a fixed 'intensity', energy or whatever, you must resort to a statistical like interpretation of the 'whatever' that you are using the word 'intensity' to describe.

    In that case you are way beyond what Maxwell's equations are saying.

    I did manage to dig up some literature on rewriting Maxwell's equations in a form the same as Schrodinger's equation, which is a rather interesting fact, but EM fields are not the same thing as a wavefunction, which is the expansion of a state in terms of position eigenvectors. They literally are fields, whose definition is in terms of forces on test particles. They are entirely different things.

    That's not my contention - its interpreting the EM field in a classical manner for radiation that is of very low intensity, so low only one photon can ever be in the double slit experiment.

    Of course the single flashes we get in the double slit experiment is not the only evidence we have that's because its a single particle - that comes from a myriad of experimental and theoretical evidence so strong no one seriously doubts it.

    Thanks
    Bill
     
    Last edited: Nov 30, 2013
  12. Dec 1, 2013 #11

    Jano L.

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    By "intensity" I mean electrical intensity. Any application of Maxwell's equations needs another assumptions. When you calculate field inside wire, you are also way beyond Maxwell's equations, because you need to assume boundary conditions and material properties of the wire and air (conductivity). Still, Maxwell's equations are part of the theory. Nothing implies that "Maxwell's equations are not really applicable". Similarly for low intensity light.

    Perhaps you can find support for your quoted claim in literature. I would be very interested if you could provide reference.

    Single flashes in low intensity light are not described by single photon field states. The latter has to be prepared in a special way. Still, such states do not disprove Maxwell's equations. You may interpret the equations in many ways, some of which are far from the view of classical physics, but nevertheless the equations are still the same.

    The only way of disproving Maxwell's equations I heard of is to show that nonlinear phenomena exist in vacuum, like scattering of light wave off another light wave, which I believe has not been observed yet.
     
  13. Dec 1, 2013 #12

    bhobba

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    A reference for what?

    Maxwell's equations need to be quantizied to explain the existence of photons.

    QED explains photons - not Maxwell's equations.

    I would be very interested in a reference that says otherwise.

    It would overturn the discovery of photons because its well known from the history of physics it was impossible, utterly impossible, to explain black-body radiation with Maxwell's equations:
    http://en.wikipedia.org/wiki/Rayleigh–Jeans_law

    If you know a way to do it with an actual reference, in a peer reviewed journal then that would be extremely interesting - not to mention likely to earn an immediate Nobel prize - it would be an earth shattering discovery.

    So have you a reference to explain black body radiation classically?

    Thanks
    Bill
     
    Last edited: Dec 1, 2013
  14. Dec 1, 2013 #13

    Jano L.

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    For this claim of yours:

    In interference experiment, besides the field, there is also matter with complicated behaviour. If something is hard to explain, it makes no sense to blame only Maxwell's equations. The matter equations are also important, more complicated and much less understood.

    Matter drops out from the picture only in vacuum, hence my reference to possible scattering of light wave off another light wave. If observed, it would be compelling evidence that Maxwell's equations are not quite right. But what happens in a complicated experiment with mirrors, beam splitters and background radiation is hard to use to disprove Maxwell's equations, since in such situation, they predict very little by themselves.
     
  15. Dec 1, 2013 #14

    bhobba

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    It doesn't matter how you cut and dry it, there is no way, absolutely no way, to explain the full behavior of light classically via Maxwell's equations. That includes black body radiation and the photoelectric effect.

    All my claim was is that when the radiation intensity is so low that just one quantum is present then Maxwell's equations are not enough. To doubt that you would need to overturn a massive amount of evidence.

    Thanks
    Bill
     
  16. Dec 1, 2013 #15

    Jano L.

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    Sometimes history of physics can be very misleading. Rayleigh-Jeans result was important problem, but it did not disprove Maxwell's equations. This is because the R-J derivation assumes many things that are not implied by Maxwell's equations alone:

    1) that there exists cavity made of perfect reflector of EM radiation

    2) that energy is given by quadratic function of the total field

    3) that the Boltzmann distribution is applicable to states of the EM field.

    Besides that these assumption do not follow from the Maxwell equations, they are all questionable.

    If you read Planck's treatise The theory of heat radiation (you can find on the Internet Archive), you will find out that one can actually go very far by quantizing only matter oscillators. In both his first and second derivation of the spectrum of thermal radiation, Planck assumed that the Maxwell equations are always satisfied and derived his spectral function.

    Every derivation has its caveats, so people did not stop to think about thermal radiation and invented many others. Some use quantization of the EM field (like Debye's which is often taught to students), some do not.

    An example of the latter:

    http://prola.aps.org/abstract/PR/v182/i5/p1374_1

    There are more papers with similar view, you can find some on PROLA.
     
  17. Dec 1, 2013 #16
    Yes, that is the kind of approximation that I referred to in the reference by Bialynicki-Birula, but I was using it as an example of something that is intended as a "photon's wavefunction" in the QM sense but it doesn't quite make it IMO basically because of the reasons you've given.

    We all agree about this, of course. One has to introduce quantized energy and Planck's h for that.

    I don't think anyone is trying to "disprove" anything here, just defining the range of validity of theories, and certainly energy quantization is out the Maxwell's equations range. I believe everyone acknowledges that QED is beyond Maxwell's equations even if there is not yet clear empirical evidence of photon-photon scattering, it is within QED theory the expectation that beyond Schwinger's limit the vacuum is not linear.

    I didn't fully realized it myself when writing the OP(so it was to be expected that it was hard to guess what I was getting at) , but I suppose my question was headed towards this nonlinear vacuum issue. When talking about the wave-particle duality in QM it is clear that neither the classical waves nor the classical particles are valid concepts, but it is hard not to wonder why the nonlinear wave concept hasn't apparently been fully explored to explain quantum phenomena.
     
  18. Dec 2, 2013 #17

    Cthugha

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    A single flash at a single detector is of course indeed not an indicator for the presence of single photons. But a single detection event at one of two detectors placed at the output ports of a beam splitter which has a single photon state at the input port is (when repeated many times). Maxwell's equations predict a certain probability that both detectors will show a detection event simultaneously at low intensities, while this will not happen when a single photon state is used.

    For completeness: One can avoid assuming single photons in this setup by instead assuming pretty strange "conspiracy detectors", but that is just not convincing and usually also not consistent with other experiments.
     
  19. Dec 2, 2013 #18
    Not that I'm fully sympathetic to it, but Khrennikov et al. have actually proposed such a model where the calibration of detectors plays a major role for the production of non-classical statistics. I was surprised when I came across this. Interestingly, his model is testable as it predicts violations of Born's rule under certain experimental situations. I've hi-lited some of the more interesting passages:
    Born's rule from statistical mechanics of classical fields: from hitting times to quantum probabilities
    http://arxiv.org/pdf/1105.4269.pdf

    Towards violation of Born’s rule: description of a simple experiment
    http://arxiv.org/pdf/1007.4677.pdf


    More details on this model can be found in this paper:
    Subquantum detection theory—SDT
    http://www.sciencedirect.com/science/article/pii/S1386947709002021
     
    Last edited: Dec 2, 2013
  20. Dec 2, 2013 #19

    Cthugha

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    In my opinion Khrennikov is often pretty much on the fringe.

    His claim "Surprisingly the role of detectors and the detection procedure in the problem of hidden variables has not yet been properly analysed." (in the first of the three papers) has no substance. One of the main topics of quantum optics is detector theory and a lot has been done since the 60's. One of the standard quantum optics books (Vogel/Welsch) has quite some focus on that and Vogel's work still focuses on detector theory.

    The third paper celebrates a sensitivity of hypothetical detectors sensitive to the fourth order of the field to some dispersion in random fluctuations. These detectors are not hypothetical. This is for example realized in plain two-photon absorption. And indeed two-photon absorption is well known to be sensitive not only to the mean photon number, but also to the photon number noise. This has been known for quite some time. He considers that as a deviation from the Born rule, which is quite odd. I think that paper would not have made it to a real peer-reviewed journal (it has been published in some conference proceedings which usually do not have strict peer review).

    Some authors go ahead and design some hypothetical threshold detectors which are able to show features considered as non-classical for "standard" detectors and then jump to conclusions. One of the main lessons quantum optics taught us is that detector theory is of prime importance and every detector has its own set of non-classicality conditions. Therefore, the correct way would be to start from an exact description of the detector actually used - which is well known for standard detectors like APDs - instead of starting from the results and designing a detector which might create them.
     
  21. Dec 2, 2013 #20
    Khrennikov is not on the fringe. He also has numerous peer-published papers and books and has directed a number of international conferences involving world-renown researchers in foundations of probability and QM:

    http://lnu.se/employee/andrei.khrennikov?l=en
    http://web.up.ac.za/sitefiles/file/48/2058/12695/Andrei%20Khrennikov%20CV.pdf [Broken]
     
    Last edited by a moderator: May 6, 2017
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