Physics Asked by Matteo Lorenzini on October 19, 2020
I am always surprised by the subtleties that are embedded in the wave/particle dualism. That is why I read again and again the paragraph in the Dirac’s classical text dealing with the single photon interference. Here, it is clearly stated that any measurement of the kick-off of a mirror would cause the photon wave function to collapse, then completely spoiling the quantum interference of the probability distribution. So I wonder if here some ad hoc definiton of measurement is assumed, since in general terms, no matter how I chose to support the mirror, that support will experience a momentum transfer (or radiation pressure) therefore its kick-off will be definitely measured. To be precise, I found no reason to assume that, provided I have a sensitive enough device, I could not measure the single photon radiation pressure (gravitational wave interferometers actually can do that). So the point is that I could, but I don’t do it? Subsequent inspections of the Dirac’s text unfortunately did not improve my understanding.
I am not sure if I understood the doubt. The problem is about being able to measure the reflected photon? In principle, if the photon is reflected by the mirror it can be detected. However in this case there will be no interference (You know the path of the photon). The wave function between the mirror and the photon become entangled and so the mean value of the one body operator will have no interference
Answered by Fabio Paolini on October 19, 2020
Firstly, let's just separate science from philosophy. The idea of quantum collapse is philosophy, not science, because there is no known experiment that can establish whether it really happens.
As far as the science is concerned, let's consider an interferometer such as a Mach-Zender interferometer where the light are directed along two paths with the aid of mirrors. As Dirac explained, the interference that is observed here (called first order interference) can be seen as each photon interfering with itself. (This kind of interference is not considered to be "quantum interference.")
But what happens when the photon is reflected by a mirror? Strictly speaking there is a momentum transfer. So if the photon is in a superposition of different momentum states (different plane waves) then the photon will effectively become entangled with the mirror. Since we do not measure the mirror momentum, the photon now represents a mixed state. As a result, it should destroy the interference, right? Then how can one ever observe any interference with such an interferometer?
Well, the thing is that the mirror is very heavier. As a result, the momentum transfer is extremely tiny - too small to be noticeable. In other words, it does not "completely spoil" the interference. Although the photon is in a mixed state, it is only slightly mixed - still very close to being a pure state. Therefore, one can observe the interference.
Hope I've managed to address your question.
Answered by flippiefanus on October 19, 2020
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