What is wave of photon? oscillation of something in space?

[Geometry_dude]

I hate to tell you that I'm not an instrumentalist and thus I have trouble with accepting these principles as fundamental principles of nature. It is quite interesting though.
Apart from those philosophical issues, those principles are not enough to specify the time evolution of a quantum system, which requires a description of a classical Newtonian or special-relativistic system and a quantization step to get to the corresponding quantum description. Getting rid of that is the true art.

 

[jostpuur]

Everytime I have attempted to discuss the wave functions of relativistic particles, the physicists change the topic to the creation and annihilation of particles and the particle collisions.

Operationally how do you measure velocity classically? And exactly how would you apply that to a photon? I think you will find that any observation with a photon that happens at a position destroys it making that determination rather difficult

So the topic was changed to the particle annihilation. How surprising.

 

[rubi]

Your problem seems to be that you insist on the existence of well-defined quantum theories of relativistic particles. That might be mathematically desirable, but it's not physically relevant, because our best theories just aren't particle theories. Instead, they are field theories. Of course you could ask, what the quantum analog of a hypothetical classical relativistic massless particle was. But such an object is just not physically realized, so the question is purely academic. The relevant classical theory that we need to consider is classical electrodynamics. It is a field theory and it's quantum analog is quantum electrodynamics, which is a field theory as well. That means that the observables of the theory aren't position $x$ and momentum $p$, but rather the field $A_\mu(x)$ and it's conjugate $\pi_\mu(x)$. Position $x$ isn't an observable in classical electrodynamics either, so there's no reason to believe that such a concept needs to appear in the corresponding quantum theory. The notion of photons doesn't refer to particles. Instead, we have a bosonic Fock space built from the Hilbert space of an irreducible massless helicity=1 representation of the Poincare group and a photon is just a vector in such a Hilbert space. It's a well-defined mathematical concept, but it doesn't refer to a particle, although many poor textbooks want you to think of it that way and the "-on" suffix just encourages you to do so.

 

[bhobba]

Apart from those philosophical issues, those principles are not enough to specify the time evolution of a quantum system, which requires a description of a classical Newtonian or special-relativistic system and a quantization step to get to the corresponding quantum description. Getting rid of that is the true art.

You should read chapter 3 of Ballentine - QM - A Modern Development:
https://www.amazon.com/dp/9810241054/?tag=pfamazon01-20

It actually follows from the POR ie symmetry - specifically the probabilities are frame independent.

Thanks
Bill

 

[Geometry_dude]

That is indeed very nice, I wish my quantum theory course would have been like that. Thank you for the recommendation.