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Quantum Mystery #1 - Complementarity Principle

  1. Apr 21, 2005 #1
    Quantum Mystery #1 - Complimentarity Principle

    Hi all - Making sense of the standard double-pinhole experiment is
    not easy for the layman! In order for me to better understand complimentarity, an experiment is proposed. What is wrong with this thought experiment? Please view (you may need to scroll horizontally):


    The Photon Delay device is just a series of mirrors that reflect the
    beam and elongates the path, causing the photon to arrive with a delay.

    A single photon is sent to the half mirror and then the full mirror. An
    interference pattern should be statistically detected at D, and
    visibility of the pattern is V = 1. Assume we record the time t that it takes the photon to travel the path (the difference in the time of emission and absorption).

    If t = t_1 (t_1 is measured by replacing M_h by M_f), then we know the
    photon has taken path 1. If t = t_2 (t_2 is measured by removing
    M_h), then we know the photon has taken path 2. Therefore, the
    which-way information is known sharply, and K = 1. This would
    contradict the Complimentarity Principle.

    Question - What is the value of t (when V = 1)? What is wrong with the picture?

    TIA -Zak
    Last edited: Apr 21, 2005
  2. jcsd
  3. Apr 21, 2005 #2
    Quick view and short answer:

    Same problem as in the classical double slit experiment, just replace your mirrors by slits and ask the same questions:
    If I close slit A, I detect a photon on the screen, therefore I know the which slit the photon passed through;
    If I close slit B, same stuff.
    Now, if I open the 2 slits, which slit the photon passes through?

    Nothing contradicts the complementary principle in this experiment. Your assumption that you can detect the "which path" by measuring the delay of the photon arriving at the detector when the 2 mirrors are present is simply wrong as this delay has nothing to compare with the delay when only one mirror is present.

  4. Apr 21, 2005 #3
    Yes, it is quite like the double slit experiment with both slits open and the photons one-by-one building up an interference pattern on the screen. :smile:

    You have two possible paths for a photon to one point on the screen. One path through one slit is longer than the other path through the other slit when a photon is detected at any other point on the screen other than the middle. The photon is travelling at the speed of light, so it would seem obvious as to which path the photon took if you time the emission and detection of a single photon.

    But something must be wrong with this picture too, as the two possible paths are interfering with each other and there is no single path for the photon.

    The answer must be that something about the time which must not be telling us which path is which. The time when there are interference effects building up on the screen must have a different value from those two possible paths when only one slit is open. But why is it different? I keep meaning to find out. :blushing:
  5. Apr 21, 2005 #4
    Quick answer:
    Just go back to the double slit experiment. And ask the 2 questions:

    1) at what time the event "a photon hit the screen when the 2 slits are open" occur ?

    2) at what time the event "a photon hit the screen when one slit is open" occur ?

    (After the event "emission of a photon at time t=0)

    And finaly, do these 2 events types define a path for the photon?

  6. Apr 21, 2005 #5
    I am not sure if I understand seratend -

    Are you saying that t (time with double slits open) is nondeterministic and t_2 <= t <= t_1 ?

    If lets say t = t_1 half the events, or t = t_2 the other half of events, then I suppose it could be concluded that we have knowledge of which-way information.

    Question: What is the value of t (if the experiment was conducted)?
  7. Apr 21, 2005 #6
    How can you conclude that? It has only a meaning (relatively to you) if each photon has a "classical path". If it is the case, closing one slit should not change the interference pattern (you should get holes in the spatial distribution of the hits in the screen).

    In other words, if I say "all the photons detected on the top of screen “passes” through the slit A when the two slits are open". Do you believe that it is the case? I think no. Your statement is of the same sort: As long as you are not able to define exactly what a quantum path for a single photon is for you, concluding that 2 events (the emission of a photon and the detection of a photon) identify this undefined path is totally irrelevant (i.e. you can say what you want). Thereafter, claiming that this experiment contradicts the HUP is completely nonsense.


    P.S. Quickly for the timing of the double slits (has been a long time I have studied this topic): we recover, for the wave function, mainly the same results as with the classical em waves because the free propagator of the wave function (of the SE) is the same as the free propagator of em waves (helmotz equation).
    Therefore, for each position on the screen and photon, we may have 2 possible delays if we neglect the size of the slits and these delays are analogue to a classical particle going through one of the slits (but please do not say that the photons has gone through a given slit! this just a timing not a path).
    Last edited: Apr 21, 2005
  8. Apr 21, 2005 #7
    I suspect we get a speed and time from emission and detection of the particle which comes the interference of the longer paths that go through the slits that makes it seem as if the particle had taken the shorter paths through the screen with the slits. :smile:

    It's a sum-over-histories without the most direct paths, just the paths to either side of the most direct paths creating an effect as if there were direct paths. And the time and speed are very similar to what we'd expect from these nonexistent direct paths.
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