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Photons, particles and wavepackets

  1. Feb 9, 2007 #1
    I have some trouble making sense out of photons. I have numerated some key questions in the following story, so that giving answers to specific questions could be easier.

    Suppose I had created double slit experiment with light successfully. I would then change the set up as follows. I would replace one light source with two, and place a wall between the two slits so that light from one source reaches only the one slit, and from the other source the other slit. Question is then, do I still have interference pattern?

    (I'm not sure if that explanation was sufficient, so I'll explain it with two dimensional coordinates in better detail. First light source was in location (0,-5), there is a wall on line (x,0), and two slits in positions (-1,0) and (1,0). I'll then place a new wall into between points (0,0)...(0,-3), and replace old light source with two that are in positions (-2,-5) and (2,-5). Light from (-2,-5) doesn't reach point (1,0), and light from (2,-5) doesn't reach point (-1,0).)

    If I think this classicaly, then why not? Electromagnetic fields should be summed even though they came from different sources. So I should have interference. Also if this experiment was carried out using water waves, the interference would remain.

    If I instead think of this with quantum mechanical particles, it is a different story. It is absolutely important, that a wave function of a single particle goes through the both slits, in order to interference appear. If a single particle goes through only one slit, then its propability distribution is going to consist of only one peak. And if I have one million particles, that all have a propability distribution of a one peak, there won't be interference appearing in macroscopic intensity.

    So is there interference or not? (1) I would be happier if there were not, because when classical and quantum theory contradict, the quantum one should be more correct. But what about reality? Is there interference in physical experiment? I have never heard of experiment of this kind. Has anyone here?

    But things get more confusing. I have often got impression, that we are supposed to consider photons as electromagnetic wavepackets. If photons are quantum mechanical particles, then claiming them to be actually wave packets of macroscopic electromagnetic field doesn't make any sense. If I have a wave packet of classical electromagnetic field, does this wave packet have anything to do with photons? (2)

    I've read, that laser is coherent light. Coherent seems to mean, that individual wave packets have the same frequency and no such phase difference, that they could cancel each others. But if I have large amount of photons, each of them carrying some energy, I would assume their total energy to be the sum of the energies of photons. Sounds simple? But if the total energy is simply sum of the energies, then no phase differences should have any effect on the total energy. The idea that energy of light could be lesser if photons canceled each others, seems to assume that photons are indeed wave packets of macroscopic electromagnetic field. If that thought is incorrect, then does the coherent light mean anything? Is it only a confusing way to say that energy spectrum of photons is a sharp peak? (3) If so, does the phenomena of interference have anything to do with light being coherent? (4)
    Last edited: Feb 9, 2007
  2. jcsd
  3. Feb 9, 2007 #2


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    No, except if you have very special light sources. I think I've read about experiments in which two separate light sources have been made to interfere, but they're difficult to do.

    When you do this with water waves (for example producing the waves by dipping mechanical oscillators into water), you have a single continuous wave coming from each source. This is very difficult to do with light sources, which usually contain many many atoms, each of which is a separate light source. Even lasers do not produce perfectly monochromatic light. Accrding to the optics text that I'm looking at right now (Pedrotti, Pedrotti and Pedrotti, Introduction to Optics, 3rd ed.), you can model this non-monochromaticity by letting the phase of each wave vary with time, which causes the amount of interference to vary with time as the waves drift in and out of phase. This variation is slow compared to the wave frequency, but is usually very rapid compared to the time scales of most real detectors.

  4. Feb 25, 2007 #3
    Okey, thanks, I didn't fully understand, but got a feeling, that I could understand if I read more. But I just happened to hit into this quote else where in these forums
    (By Pieter Kuiper in Photon Self-Interference thread)

    Just to mix the mess even more :smile: Frankly, these statements seem to contradict. Doesn't make fully sense to me yet.
  5. Feb 25, 2007 #4
    If you have two coherent sources of light, and a photon strikes a screen, you really can't tell which source the photon came from. Regardless of whether the sources are just separate slits or completely separate emitters, the two "paths that the one photon may have taken" interfere and Dirac's statement is justified (otherwise we would expect the pattern to change when we reduce the intensity so that there aren't two photons present simultaneously). However, if the separate light sources don't stay coherent/synchronised, then their phase difference will slowly drift (continually shifting the interference pattern), and the pattern will become completely washed out (so if you want to see interference from cheap lasers, make sure both possible photon paths are from the same laser).

    Don't think I've really described any quantum process here yet..
    Last edited: Feb 25, 2007
  6. Feb 25, 2007 #5
    What then if the phase difference would not drift? Should the interference then appear? If I understood Dirac correctly, the answer is no. Since photons from different sources don't interfere, the phase difference of two sources should not matter at all.
  7. Feb 25, 2007 #6
    Sorry cesiumfrog, I may have missed the point in the beginning of the reply. Are you saying, that a single photon could be created so that it has non-zero amplitudes for initially being in both emitters? Sounds striking :smile: I'm not sure if that's correct, or what you meant.

    (Adding with edit:)

    No, cesiumfrog, in fact I think I disagree with this
    When photon is emitted from some particular emittor and passes through two slits, the reason why you can't tell which slit it passed through, is that there is a non-zero amplitude for the photon to pass through both slits. Instead, when there is two emittors, A and B, a photon either comes from A or from B. In this case you can't tell where the photon came from for practical reasons, not because of nature of quantum mechanics. The "not knowing where photon came from" is of different nature in these cases.
    Last edited: Feb 26, 2007
  8. Feb 26, 2007 #7
    Have you read anything on QED. A good qualititave explanation can be found in Feynman's book of he same name.
    I think that would answer all of your questions.
  9. Feb 26, 2007 #8
    If I place a high relative permittivity/refractive index material in front of the slits in a normal double slit experiment, do I get an interference pattern? If so, how is that reconcilable with

    if the material slows the photons down (i.e. interacts with them)? Does the material not act as a measuring device, collapsing the wavefunction and destroying the interference pattern? If not, why not? I have seen a double slit experiment carried out in air, so I don't see why you wouldn't get an interference pattern if epsilon_rel was larger... My guess is it is something to do with the non commutativity of x and p, but I really don't see exactly how it would work.
  10. Sep 25, 2007 #9
    My first thread! :smile:

    The old problems are the best. I still don't understand this, but I think I can explain the paradox more clearly now.

    The Dirac's message is still quite clear.


    I remain skeptical about such experiments, until I really see the evidence. Even if the small difference in the frequency of two different lasers would destroy the interference pattern, that should not be the true reason for the lack of interference. The true reason is what Dirac says. Different photons don't interfere.

    On the other hand, we know that electric field is something we can sum. The electric field around two charges is the sum of the electric fields of them both separately. If we oscillate some charge, then the electric and magnetic fields around it will start oscillating too, and this is electromagnetic radiation. Since the radiation is merely electric and magnetic fields, which can be summed, we conclude that the electromagnetic radiation is summable, and radiation from different sources will interfere. For example, radio waves from different sources interfere.

    As we know, the visible light and radio waves are fundamentally the same thing. The just have different frequency.

    Then consider this: The light waves from different sources don't interfere. The light waves are the same thing as radio waves, except with a different frequency. The radio waves from different sources interfere.

    Well that's the paradox!

    I can see that the most popular solution to this is to ignore the Dirac's message, and believe that light waves from different sources would interfere. I cannot accept such solution attempt, because I cannot see how it would not be in contradiction with the quantum theory, and particle nature of radiation.

    Other direction where the solution could be tried, is to deny the interference of the radio waves. But that is unacceptable too, because we could start slowing down the frequency arbitrarily, and eventually we would be claiming that almost static electric fields were not summable at all.

    Hence I'm forced to conclude that radio waves and visible light are fundamentally different. That means, that the frequency is not the only difference, but there is more to it. This is in contradiction with what all books tell, but I don't think that is immediately absurd claim. After all, the birth mechanism of visible light and radio waves is fundamentally different too. The visible light originates from quantum mechanical systems, and the radio waves originate from oscillating charges.

    Maxwell was wrong? :biggrin: (to mentors: please, no locking without warnings first)
  11. Sep 25, 2007 #10


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    One should not mix electromagnetic field with the 1-photon wave function. They satisfy the same Maxwell equation, yet they are different. In particular, the former is real while the latter is not. Nevertheless, they both can be expressed as c-numbers originating (in DIFFERENT ways!) from QED.
    It seems to me that all confusion comes from mixing these two different concepts.

    So, can 2 photons interfere with each other? Yes they can. However, their common wave function lives in the 2X4=8 dimensional configuration space, not in the ordinary 4 dimensional spacetime. Therefore, they do not interfere in the ordinary spacetime. Still, the electromagnetic field associated with this 2-photon state lives in the 4 dimensional spacetime. Essentially, it is the average value of the EM field operator in the 2-photon state. This c-number valued EM field interferes in the ordinary 4 dimensional spacetime.
    Last edited: Sep 25, 2007
  12. Sep 25, 2007 #11


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    I think quantum mechanics is not that different from classical field theory. Classical electrodynamics can be easily expressed in the language of hermitean operators. It's mainly because QFT describes infinitely many more degrees of freedom that QFT seems so complicated. Where in classical field theory you consider only one field configuration in spacetime, in QFT you consider all field configurations (even classically forbidden ones) and their respective probability amplitudes. This is how the functional integral approach describes QFT.

    Having said this, let's go back to single particle quantum mechanics: don't think of a particle as a little black spot somewhere in space. If you send an electron beam (with 1 "particle" on average) onto a double-slit, there isn't any particle in this beam. It behaves completely utterly like a wave and nothing else ... until it hits the screen - then it behaves like a little black spot.

    Do you know about Occam's razor ? It says that we ought to find the most economic description of nature. Of course you might imagine that there is also a little black spot riding on the wave or something. But with your current experiment you are totally unable to detect that little black spot - until it hits the screen. So what is more economic ? A little black spot surfing on a wave (probably with a grin on its face...), which you cannot detect in your experiment however, or just a wave the effects of which you detect in your experiment ?

    So if you say something like "If a single particle goes through only one slit" you fool yourself by implying that a single particle cannot go through both slits. No ! It's the wave that goes through both slits if you don't cover one of them. And that's absolutely the same thing as for the photon. In either case you get an interference pattern if the input was monochromatic.

    No, a photon in the true sense of the word is a monochromatic plane wave of definite polarisation, and as such it covers all space, from here to infinity. In theory one creates a photon by applying the ladder operator of one single wave vector. A wave packet consists of many wave vectors, so photons are not wave packets. Again the impression cannot be avoided that you fool yourself by thinking of photons as little black spots.
    Last edited: Sep 25, 2007
  13. Sep 25, 2007 #12
    OOO, I'm afraid you did not understand my point. Did you understand the part where I explained the experiment being modified by an extra wall? I don't have problems with a wave function passing through two slits simultaneously, but in this (mind) experiment I was forcing the particles to go through only one slit.

    I remember seeing an electron being described like this somewhere. There was a picture of the electron, and it had a text "artist's impression".
  14. Sep 25, 2007 #13
    Hanbury Brown-Twiss (HBT) intensity interferometer. R. Hanbury Brown and R.Q. Twiss, Nature,177, 27 (1956).

    Are you ask questions or provide explanations? I find your explanations beautiful.

    I guess that the most popular solution to this is presented by A.Einstein, Phys.Zeit. 10,185,(1909). The first term is “the Dirac's message” and the second is due to intensity fluctuations (Maxwell).

    Regards, Dany.
    Last edited: Sep 25, 2007
  15. Sep 25, 2007 #14


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    There are a few experiments where photons coming from different sources have been shown to interfere.
    See e.g,. Kaltenback et al PRL 96, pp 240502 (2006) which also gives are good background to the topics.

    The conditions are essentially that the two sources are well synchronized and that the photons are indistinguishable when they arrive at the detector.
  16. Sep 25, 2007 #15


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    I think I did.

    But I can't see your problem. As others have said, its a matter of phase correlation. If you don't believe it, replace your light sources by two microwave emitters and scale the experiment respectively. If you're able to control the phase correlations between them by means of an electronic circuit then you will see an interference pattern, otherwise not.

    If you try the same with thermal light sources or even lasers you won't succeed for practical, not theoretical reasons.

    Maybe it helps you if you read again what cesiumfrog has said about it.
  17. Sep 25, 2007 #16
    I coloured in blue what I repeat from a lot of time; I was also hardly criticized for having said it.
    Hope you will have more lucky.
    Last edited: Sep 25, 2007
  18. Sep 25, 2007 #17


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    I'll try hard. :wink:
  19. Sep 25, 2007 #18
    No, you didn’t. It is better to use the correlation terminology. You talking about the quantum (phase) correlations, but Jostpuur talking about also the classical intensity correlations.

    Is it news for you? And you can’t explain the black body radiation curve without that. In addition, I consider your post #11 absurd.

    Regards, Dany.
  20. Sep 25, 2007 #19


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    Thank you very much for explaining to me what I was talking about.

    I certainly didn't claim to be able to explain black body radiation with a double slit experiment. So much for absurdity.
  21. Sep 25, 2007 #20
    You don’t understand OP questions, it is about photons and their properties, QED vs CED and not once again about double slit. Change diskette. In addition, if you don’t want to know, nobody force you.

    Regards, Dany.
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