How to find the photon's path?

[jk22]

Let be given the ##\vec{E}(r,\theta,\phi,t)## and ##\vec{B}(r,\theta,\phi,t)## fields that are solution of Maxwell equations in vacuum.

How to find the trajectory of the photons ?

Is the photon moving along the Poynting vector, like ##\vec{S}=\vec{E}\times\vec{B}## at the speed of light ?

 

[PeroK]

Photon? What photon?

 

[hilbert2]

Let be given the ##\vec{E}(r,\theta,\phi,t)## and ##\vec{B}(r,\theta,\phi,t)## fields that are solution of Maxwell equations in vacuum.

How to find the trajectory of the photons ?

Is the photon moving along the Poynting vector, like ##\vec{S}=\vec{E}\times\vec{B}## at the speed of light ?

Photons appear only after treating those as quantum fields, and they don't have a classical trajectory. Actually, they don't even have a position operator, unlike electrons.

 

[jk22]

So this question would need a quantum treatment.

There is no frame attached to the photon but could this question be asked in the lab frame ?

 

[PeroK]

So this question would need a quantum treatment.

Yes, the photon is a QM particle. There is no photon in classic EM.

 

[jk22]

Ok. So basically what would the protocol be : one should take the initial electromagnetic field and quantize this by projecting onto the number operator basis ? (Like a wave-packet)

Then computing an average ?

Or does no position operator mean that the photon is everywhere ?

 

[PeroK]

one should take the initial electromagnetic field and quantize this by ...

https://en.wikipedia.org/wiki/Quantization_of_the_electromagnetic_field#Quantization_of_EM_field

 

[hilbert2]

Or does no position operator mean that the photon is everywhere ?

The photon creation and annihilation operators of QED really do affect the whole EM field everywhere in space. Unless you think of the field as contained in some finite box, but then only a discrete set of photon wavelengths are allowed.

 

[vanhees71]

Ok. So basically what would the protocol be : one should take the initial electromagnetic field and quantize this by projecting onto the number operator basis ? (Like a wave-packet)

Then computing an average ?

Or does no position operator mean that the photon is everywhere ?

A photon is not a particle in any sense. It does not even allow to introduce a position observable. In other words it cannot be located at all from first principles. The only way to describe photons is relativistic quantum field theory and the only observables are defined as photon detections by some measurement device. Usually photons are detected using the photoelectric effect. So all you can calculate in theory and observe in nature are the probabilities to detect a photon given the state it's prepared in.