Feynman's Interference Experiment: Detector versus Photon Source

[maverick280857]

Hi

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.

Cheers
Vivek

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?

 

[eljose79]

Dear Vivek,

Thank you for your post and for bringing up an important aspect of the interference experiment with electrons. You are correct in your understanding that the presence of the light source does disturb the measurement and alters the final outcome. However, even without the light source, the detector still plays a role in the experiment.

To answer your question about mathematically expressing the effect of the detector, it is indeed possible to do so using quantum mechanics. The detector can be represented by a quantum mechanical operator, just like the photon source. This operator would act on the electron's wavefunction and produce a new wavefunction that reflects the measurement. This new wavefunction would be different from the one produced by the photon source, as the detector is not just passively observing, but actively interacting with the electron.

In this sense, the detector does affect the interference pattern, but it is not the same kind of disturbance caused by the photon source. The detector's role is to collapse the electron's wavefunction to a specific position in space, whereas the photon source alters the electron's momentum. So, in a way, the detector is also a source of disturbance, but of a different kind.

As for your point about reconstructing the interference pattern without disturbing the measurement, that is not possible in quantum mechanics. The act of measuring or observing the electron's position will always disturb its wavefunction, and therefore the interference pattern. This is a fundamental principle in quantum mechanics known as the observer effect.

I hope this helps clarify your questions. If you have any further doubts or would like to discuss this further, please let me know.

 

[denian]

I would like to clarify that Feynman's interference experiment involves the interference of electrons, not photons. This may have been a typo in the question, but it is important to note the distinction between the two.

Regarding the role of the detector in the experiment, it is true that the presence of the detector can potentially disturb the measurement. This is due to the interaction between the detector and the electrons, which can alter the electrons' motion and ultimately affect the interference pattern.

To mathematically express the effect of the detector, we can use quantum mechanics and the concept of wavefunction collapse. The detector can be represented as an operator that acts on the electron's wavefunction, causing it to collapse into a particular state when the electron is detected.

Whether or not the detector has a significant effect on the interference pattern depends on the specific setup and conditions of the experiment. In some cases, the detector may have a negligible effect and the interference pattern can still be observed. In other cases, the detector may significantly disturb the measurement and alter the interference pattern.

In terms of reconstructing the interference pattern without disturbing the measurement, it is possible in principle but may be difficult to achieve in practice. This is because any measurement or observation inherently involves some interaction with the system being measured, which can potentially disturb it.

In conclusion, the role of the detector in Feynman's interference experiment is not just to record the interference pattern, but it can also potentially affect the measurement itself. The exact mathematical expression of this effect would depend on the specific experimental setup and conditions.