If you take Feynmann's path integral formulation, phase is proportional to action.
Holography is done by aiming two coherent light sources at one-another then recording their phase relationships on film.
Suppose we create a hologram using only two photons: one photon from each light source. How does QM explain phase in this regard? Send enough photons from both lasers at the holographic film and we'll end up with a hologram (a micrograph of the film shows a characteristic grating--bands of transparency and opacity where the photons interfered constructively and destructively). But, sending just two photons at the film--one photon from each laser--and we end up with _________ ?
Since phase is explained away with a classical wave equation in the hologram, how can we explain phase when we emit only one photon? This is where I'm encountering my problem.
What's phase from a QM standpoint?
Are you talking about the phase of a wave function or the phase of light (when acting classically)? These two are not the same thing.
No, you start with a single light source, split the beam into two parts using a beamsplitter, let one beam fall on the object that you want to make a hologram of, then let the light reflected from the object combine with the second beam on the film. Each photon from the source goes one way (first beam to object to film) or the other way (second beam to film), but if we can't tell which photon goes which way, we get interference and a hologram.
If you have two distinct sources, such that you can tell which one emits which photon, you don't get interference. The photon coming from the first source arrives at the film or detector with the same probability distribution that it would have if only the first source were operating; and similarly for the photon coming from the second source.
It is possible to set up a situation in which the two sources interfere... but then you can't tell which source a particular spot on the film or detector comes from!
We can't explain phase for only one photon. Phase requires reference and reference is another oscillator with the same frequency i.e. another photon.
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