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Feynman's double-slit experiment

  1. May 21, 2009 #1
    Here's my puzzle...

    Electrons through a single slit one at time - standard distribution
    Electrons through a double slit one at a time - interference pattern
    Set up a detector to observe which slit the electrons passed through - back to a standard distribution.

    This is all well and good. In searching for the origin of this story I found it comes from Feynman's Lectures On Physics. Nice one, Richard.

    The problem I have is this. The description given by Feynman appears to be a mere thought experiment. However, the result is quoted in many places as an actual result. I've tried to find the relevant papers which might have shown this result but have so far failed.

    My question is then, does anybody know where this result has been shown to hold? And if nobody has actually shown this result, why is the story constantly told (especially in awful popular media - I'm looking at you Wikipedia) that this is the great lesson of the double-slit experiment?

    Any ideas?

    Pete
     
  2. jcsd
  3. May 21, 2009 #2

    Born2bwire

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  4. May 21, 2009 #3
    I'm terribly sorry, I've been totally unclear!

    The result I'm calling into question is the breakdown of the interference pattern once the electrons are being detected as going through one slit or the other.

    Feynman's thought experiment suggests a light source hidden behind the metal plate with the slits in it and between the slits, the sort of place you'd expect to be able to bounce photons off each electron as it passes through. My question is, has anybody done this? (and I suspect not!)
     
  5. May 21, 2009 #4
    What do you expect? That the pattern remains regardless (vindicating realism afterall)?

    It's been done, in different ways. The ten-dollar way is to replace the electrons with photons, and mark which slit each went through by rotating its polarisation or not; cross-polarised light doesn't interfere, but you can erase the marking and recover the pattern by putting a diagonal polariser in front of the screen. See "quantum eraser" on "google scholar".
     
    Last edited: May 21, 2009
  6. May 21, 2009 #5

    Demystifier

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    It has been done many times. It's actually considered too trivial to make explicit reports in the literature.
     
  7. May 21, 2009 #6
    I don't know what variations on the experiment have been carried out since Feymann's Lectures were published in 1964, but I'm quite sure that at the time he was describing a thought experiment, as the OP suggests.
     
  8. May 21, 2009 #7

    DrChinese

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    As Demystifier says, you really already know the exact answer.

    You knew there was an interference pattern with 2 slits. Now cover up the left one. What do you get? It's just a one slit pattern (as mentioned, no interference). Now cover up the right slit (leaving left open).

    Since neither
    nor
    show any interference, obviously [both open] is not equal to
    +
    . That's 'bout it.​
     
  9. May 21, 2009 #8
    But surely there are other ways of detecting which slit the electron went through then simply covering up one slit? When you cover a slit up it's no longer a double slit, so why would you even do that?

    I've been wondering this myself... Is the disappearance of an interference pattern a truly quantum effect (because interference cannot occur) or is it merely because we somehow 'block' the electron (by covering up a slit, or by other means)? Or is that really the same thing?
     
  10. May 21, 2009 #9

    DrChinese

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    Yes, there are other ways too. For light, you use polarizers set orthogonally (crossed). The interference pattern disappears. You can also put a detector behind one slit. But really, if you think the particle went through a specific slit, then closing off one slit entirely should be enough.

    [Now, please note that there are interpretations (Bohmian) in which the particle goes through a specific slit while the hypothetical guide wave goes through both slits. These do not make any difference to the predicted outcome, however.]
     
  11. May 21, 2009 #10
    Thanks very much to those that replied. That cross polarisation experiment with photons was the sort of thing I was looking for.

    In response to some of the other omments, my question was much more subtle than I originally let on. I have no doubt that detection of which slit the particle went through will destroy the interference pattern. I'm concerned about how one should read Feynman's comments.

    If Feynman is quoting a result from an experiment he knew of and then giving an ontological explanation, this is quite different from proposing what he thinks would happen if such an experiment were carried out. If the latter is the case, then any discussion of the interpretation of quantum mechanics would not need to account for such a result in the body of evidence which needs explaining - simply because there would be no evidence indicating that that might be the case.

    I suspected the quantum eraser experiments might address the same issue but I was especially interested find out if anyone had used anything but photons to show the effect.
     
  12. May 21, 2009 #11
    Actually, it is misleading to claim that path knowledge definitely disturbs the interference. At the very least, the jury is still out but here are some experiments which prove otherwise:
    * R. Sillitto, and C. Wykes, Phys. Lett. A 39, 333 (1972): two slits with only one open at a time. Interference fringes clearly observed
    * E. Fonseca, P. S. Ribeiro, S. Padua, and C. Monken, Phys. Rev. A 60, 1530 (1999): complete path knowledge was obtained for all photons and interference persisted
    * L. Basano, and P. Ottonello, Am. J. Phys 68, 245 (2000). Two laser sources, photons from each can only pass through a single slit. Path knowledge complete yet interference obtained.
    * C. Santori, et al., Nature 419, 594 (2002): Complete path knowledge, interference obtained

    Oh, and the above experiments together with a hand full of others rule out self-interaction which is the current dogma. For example:
    * Yu. Dontsov, and A. Baz, Sov. Phys - JETP 25, 1 (1967). Interference disappeared when the photon flux was drastically reduced by placing neutral density filters before the slits but not by placing filters after the slits.
    * Y.-H. Kim, et al., Phys. Rev. A 61(R), 051803 (2000). By making sure only one photon was in the system at a given time and controlling the interval between successive photons, the appearance/disappearance of interference was heavily dependent on the time interval.
     
    Last edited: May 21, 2009
  13. May 21, 2009 #12
    mn4j, I picked the reference for which your description sounded the strongest, but it appears your interpretation is false. In that experiment the interference is occurring because there is no way to know which slit of effective-aperture A1A2 the photons go through.
     
    Last edited: May 22, 2009
  14. May 21, 2009 #13
    One means that would not destroy phase information until after the passage of the electron is by measuring the recoil imparted to the slit. Good luck with that. As far as the cross polarizers goes, it requires that the observer not be entangled with information as to the orientation of the polarizers until after the electron has passed. I haven't been following along with this stuff. What you might be interested in might go by the name delayed choice.

    Earlier than Feynman, Bohr invoked the double slit which-way thought experiment in his reply to EPR.
     
    Last edited: May 21, 2009
  15. May 22, 2009 #14
    Of course you fail to realize that there is no effective aperture. There are two apertures (A1 and A2) and each photon passes only through one but not the other. There are also two separate detectors, one for each aperture and it is obvious from the experiment which aperture the photon went through, yet by considering coincident counts between the apertures interference fringes can be obtained from the results, even though simply adding up the results of both does not give interference. What you call "effective aperture" is not an aspect of the experiment but a method of interpreting the results of the experiments. Unless you have a penchant for mysticism you will not suggest that the photons knew how the results would be interpreted.

    This experiment clearly casts doubts to suggestions that knowing the path of the photons somehow disturb the interference. In case you are tempted to suggest that the interference is due to not knowing which side of A2 it the photon passed through, realize that D2 alone did not give an interference pattern without considering the coincidence counts at D1 (see Fig 5).
     
  16. May 23, 2009 #15
    If there is no effective aperture, why do the experimenters go to such length in reporting its characteristics? (I don't have the article in front of me today, but you'll no doubt see that it is the slit separation of the effective aperture which determines the angles of the interference maxima.)

    Are you aware that the pair of photons produced in the crystal are momentum-entangled? This means they both go through complementary positions of their respective apertures. In other words, by selecting only coincidences (where neither photon has been blocked by its respective aperture) it is guaranteed that both photons have gone through the doubly-restricted space of the effective-aperture (and you could confirm this using detection rates).

    Of course there is no raw pattern at D2, this is an entanglement experiment after all: If a lens is placed in front of D1 then (Wheeler's CCD at) D1 could tell exactly which part of each aperture was traversed by both photons (including the one to D2, which would contradict quantum interfering of possible paths, a la Cramer's discredited FTL communicator. Another way of viewing this is that the spontaneously emitted photon pair does not have the coherence of a laser: neither beam alone could be used directly to produces raw double-slit interference because it would not reach both sides of the aperture in constant phase). Rather, the geometry has been chosen such that D1 measures the phase difference of the possible paths (e.g., coincidence with D1 selects the photons at D2 which, in equal phase, could have traversed paths through both slits of the effective-aperture, and hence produce a sinc pattern).
     
    Last edited: May 23, 2009
  17. May 23, 2009 #16

    Cthugha

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    I do not know about the other papers, but I know this paper very well and it is about indistinguishability of consecutive photons from a single quantum dot. What they use to show this indistinguishability is Hong-Ou-Mandel interference, which is a consequence of the bosonic nature of photons: two photons incident on a 50-50 beamsplitter with perfect overlap will always leave the beamsplitter together at the same exit ports. This is an intrinsic two-photon interference effect, which should not be mixed up with the single photon interference pattern you get in a double slit experiment. In fact Zeilinger even showed that single photon interference and two photon interference are complementary. You cannot have both at the same time with good contrast. So in fact any demonstration of two-photon interference when the path is known shows directly that there is no single photon interference present.

    After a brief look at the other references it seems to me, that they are about two photon interference, too, although I need to take some time to be sure. However, it seems your argument is void. A lot of people do not get the difference between single photon interference and two photon interference. This topic is covered very well in the bible of quantum optics ("Optical coherence and quantum optics" by Mandel and Wolf).
     
  18. May 23, 2009 #17
    You keep talking about effective aperture as if there is ever a single aperture. There are two, period. When superimposed, they become equivalent to a double slit. So what you call "effective aperture" is not anything the photons care about but a result of post-processing of the data. Every photon that went through A1 went ONLY through A1, and every photon that went through A2 went only through A2. Every photon detected at D1 went ONLY through A1 and every photon detected at D2 went only through A2. Note that, when D2 is kept fixed and D1 is moved, you get interference and vice versa. Consider the former situation, note that A1 is equivalent to a single slit and that D1 only measures photons which have gone through A1. It is therefore obvious that there is complete path knowledge for every photon arriving at D1.

    See the following for similar experiments without the "indistinguishability loophole":
    * Z. Y. Ou, X. Y. Zou, L. J. Wang, and L. Mandel, Phys. Rev. Lett. 65, 321-324 (1990).
    * P. G. Kwiat, et al., Phys. Rev. A 41, 2910-2913 (1990)


    This clearly casts doubts to the idea that path knowledge has anything to do with appearance or disappearance of interference and also points to the fact that interference is a multi-photon phenomenon. You can argue that entanglement is involved, which doesn't obviate the fact that more than one photon is involved.
     
    Last edited: May 23, 2009
  19. May 23, 2009 #18
    I challenge you to show me a single experiment where single photon interference was confirmed. In order to prove self-interference, the experiment must meet the following criteria:

    1 It must ensure that photons do not overlap in transit
    2 The coherence time of the source must exceed the interval between two photon emissions
    3 with 1, and 2 valid, interference fringes must be obtained for arbitrary intervals between any two detections. In other words, the interval between durations should not matter.

    So my challenge is for you to show me an experiment which met all three criteria above, failing which you can not claim self-interference has been experimentally verified. I've given you two examples which rule out single photon-interference or what is also called (self-interference), see the Dontsov and Baz paper I quoted above for a start. Self-interference is a myth.

    I will wait for you to show me convincing evidence of self-interference or what you call single photon interference.
     
    Last edited: May 23, 2009
  20. May 23, 2009 #19
    If there were no single photon interference, quantum mechanics would be wrong.
     
  21. May 23, 2009 #20

    Cthugha

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    I do not see, why these conditions should be necessary to prove self-interference. In fact 1) and 2) even contradict each other because coherence time is a measure of the time during which several photons are indistinguishable. While I agree that 1) is necessary, 2) must be converted to the opposite: (first order) coherence time must be shorter than the interval between two photon emissions. Otherwise you can never verify that you produced a Fock state. The further process is then very easy. You just need to do a HBT-experiment on your light source to demonstrate that antibunching is present by showing that the equal time intensity correlation function is zero. Then you direct this emission towards a double slit, where the slit seperation is still small compared to the coherence length of the emission. Additionally you have to ensure that the recoil of the photon emission does not give any information about the photon path. Although this is rather trivial maybe someone thought of it as interesting enough to publish it. I will check when I have access to the library of my university again.

    This paper is not quoted very often and two of the quotes are articles called "How to judge flawed science" and "'Pseudo-Effects' in Experimental Physics: Some Notes for Case-Studies", which makes this article look very suspicious. However, I will have a look at it when I am back in the office. Now I do not have access to that paper.

    edit: If I remember correctly "Experimental Evidence for a Photon Anticorrelation Effect on
    a Beam Splitter: A New Light on Single-Photon Interferences." by P. Grangier, G. Roger and A. Aspect should do the trick: Europhys. Lett., 1 (4), pp. 173-179 (1986)

    They use a cascaded decay instead of a quantum dot and a Mach-Zehnder interferometer instead of a double slit, but that should not change anything.
     
    Last edited: May 23, 2009
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