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Feynman's Interference Experiment: Detector versus Photon Source

  1. Aug 4, 2008 #1

    I was reviewing Feynman's description of an interference experiment of electrons, where he has used a light source to "see" the electrons and a detector which produces a "click" sound when an electron strikes it.

    In the course of the description, he states that the electric field of the light beam will exert a force on the electrons and their motion is altered. I understand that the presence of the light source will disturb the measurement as momentum from the photons will be transferred to electrons and the final outcome is the smoothed (no interference) probability distribution.

    In conclusion, the light source disturbs the measurement.

    But now, consider the case when there is no light source. The detector is still supposed to click when an electron strikes it, but does it have no other role to play? That is, does the detector--evidently a measuring instrument too, in this case--not affect the experiment at all?

    Is it possible to mathematically express the effect of the detector and show that (if at all it has no effect on the measurement) its 'operation' on the electron wavefunction produces the same wavefunction, whereas for the photon source, the wavefunction changes?

    I can see that expressing this measurement operation mathematically for the photon source should be possible, but how does one write an "operator" for the detector? In other words, how can I analyze the effect of the detector on the interference pattern itself?

    Theoretically, I am not supposed to "measure" or "observe" the pattern in order to get a true interference, but suppose I have different kinds of tones for different positions on the detector, I can in principle reconstruct the interference pattern without having disturbed the measurement (assuming again that the detector plays no role here). But is this really correct?

    Thanks in advance.


    EDIT: I put some more thought into it. I haven't edited anything above, but a re-read of my own post makes me believe that the question is somewhat ill-posed and reflects a misconception about the role of the detector. We have defined the interference pattern as one that detector records and the diffraction of electrons takes place at the slits, so thinking intuitively, the physics ends there. The detector is merely a ground where a distribution of the electrons evolves with time, and so just takes a snapshot, without disturbing the whole situation. But I was wondering if one can put all this down in a better way, perhaps mathematically?
    Last edited: Aug 4, 2008
  2. jcsd
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