Which path information for a photon reflecting from a mirror as in Feyman's QED

[Colin Mitch]

I would like to know whether it is possible to determine which path information for a photon reflecting from a mirror as shown in the book QED by Feynman page 40 and 43 (or available by googling mirror reflection Feynman or similar) if photons are fired one at a time from the source (unaimed) and I use a directional photomultiplier detector aimed so that the field of view is a particular spot on the mirror (say 1mm of the mirror) eg use a long tube with the detector at one end and a small hole in the other end.
Feynman uses summing over paths to get the result that it is most probable photons take the path where the angle of incidence equals the angle of reflection. However there is a small probability a photon could take an alternative path.
If I aim my detector at the centre of the mirror no doubt I will observe a lot of the photons because there the angle of incidence equals the angle of reflection. However if I point my detector down at one end of the mirror (say at K) and wait a long time when I finally observe a photon can I deduce (assuming that it is overwhelmingly probable the photons travel in straight lines) that this particular photon took the path less traveled and reflected from K where the angle of incidence does not equal the angle of reflection?

 

[eljose79]

Thank you for your question about determining the path information of a photon reflecting from a mirror. I am happy to provide you with some information and insights on this topic.

Firstly, let me clarify that photons are quantum particles and their behavior is governed by the laws of quantum mechanics. This means that they do not follow a predictable path like classical particles, such as billiard balls. Instead, they exist as a probability wave, and their position and momentum can only be described in terms of probabilities.

With that being said, it is indeed possible to determine the path information of a photon reflecting from a mirror, but it requires careful experimental setup and data analysis. The experiment you described, using a directional photomultiplier detector aimed at a specific spot on the mirror, is a good starting point.

As you mentioned, Feynman's sum-over-paths approach shows that the most probable path for a photon reflecting from a mirror is the one where the angle of incidence equals the angle of reflection. However, there is a small probability that the photon could take an alternative path. This means that even if you aim your detector at the center of the mirror, you may still observe some photons that took alternative paths.

Now, if you aim your detector at a specific spot on the mirror, such as K, and wait a long time, you may observe a photon that took the less traveled path and reflected from K. But this does not necessarily mean that the angle of incidence at K is different from the angle of reflection. It could be that the photon took a slightly different path, but still reflected at the same angle.

To conclusively determine the path information of a photon reflecting from a mirror, you would need to perform multiple experiments and analyze the data statistically. This would involve measuring the positions and angles of the reflected photons and comparing them to the expected values based on the laws of quantum mechanics.

In summary, it is possible to determine the path information of a photon reflecting from a mirror, but it requires careful experimental setup and data analysis. I hope this helps answer your question. If you have any further inquiries, please do not hesitate to reach out.