Photon interference

Hello, could anyone help me with this question?
We have a mental experiment consisting in a source S that sends two plane waves of light that propagate in one direction and collide in a photo-detector (PD). It is important to note that the propagation of each wave is in one-dimension, so that there are no waves arriving out from the PD. It can be considered as a kind of interferometer.
Well, if the waves arrive out of phase at the PD then the amplitude of the resulting wave is zero at the PD. And, as the propagation is in a given direction, there are not interferences out from the point at which the PD is placed.
In this case, if we change the waves by photons, we have that, while S is sending photons the PD does not detect any photon.
Is this result correct? If so, what happens with the photons? Does not the mass conserve?

Thank you very much
 
If you revise this for clarity you might get more replies...
 
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If you revise this for clarity you might get more replies...
The question is perfectly clear and it is a very important question. Everybody who has studied physics has to come up against this question sooner or later. Understanding the answer to this question is a significant step in anyone's physics education.

(edit) Of course it's really a question about waves: trying to analyze it in terms of photons contributes no helpful insights as far as I know...
 
Hello, could anyone help me with this question?
We have a mental experiment consisting in a source S that sends two plane waves of light that propagate in one direction and collide in a photo-detector (PD). It is important to note that the propagation of each wave is in one-dimension, so that there are no waves arriving out from the PD. It can be considered as a kind of interferometer.
Well, if the waves arrive out of phase at the PD then the amplitude of the resulting wave is zero at the PD. And, as the propagation is in a given direction, there are not interferences out from the point at which the PD is placed.
In this case, if we change the waves by photons, we have that, while S is sending photons the PD does not detect any photon.
Is this result correct? If so, what happens with the photons? Does not the mass conserve?

Thank you very much

We will assume that we have a Mach-Zehnder interferometer with only one detector. The wave description is different from the photon description, so we will consider them one at a time.


In the wave description, the two waves must travel different paths so that there is a phase difference of 180 degrees before recombining at the second beamsplitter. No light enters the detector. Usually, there are two detectors employed, and, if we insert the second detector, all the light is found there. If we have destructive interference on one side of a beamsplitter, then we always have constructive interference on the other side. This is classical wave optics. You are correct. The light does not just disappear!

In the photon description, quantum mechanics allows us to calculate the probability that the photon will be detected. When the probability is zero, no photon ever reaches the detector. However, when this occurs, the probability of reaching the second detector is one; all the photons are found in the second detector.

Rest assured, the light energy (wave or photon) is always conserved. I am not sure that this is the kind of experiment you have in mind, but the above results are always true; if the light is not found here, then it is someplace else. I assumed only that there is no transformation of the light energy into other energy forms.
Best wishes.
 

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