enotstrebor said:
Mathematically? That is not the question? The question is what is the physic(al)s object we term the photon?
The problem is that the present mathematics is a model of behavior not a model of the photon.
So you are replacing the well defined term photon with a fuzzy one that represents your idea of a photon. Sorry the name is taken, you may call your photon the enotstrebor-photon, and define it any way you like.
The present theory can not tell you if the EM mathematical description is a description of the photon (a property of the particle) or a description of the interaction of the photon (a property of the interaction - an inter-particle property) and thus lacks clearity.
It is a description of a state of the em field. Just like an electron is a state of the electron field. Your apparent disparity does not appear to me. I agree that introductory texts into particle physics, which don't use QFT are misleading, but once you read some dedicated Quantum optics books things should clear up.
That the EM description is likely not the photon is also evidenced by the fact that these can not be used when one tries to combine the photon and matter particles (QED), but requires the use of the vector potential.
Photons are excitations of the A-Field (aka vector potential). This is why we do quantum
field theory. Electrons are also an excitation of the electron particle field. Still no contradictions.
This unification can not be done using the EM description.
Whatever that EM description might be. Maybe you are trying to tell us, that the fact that we use the Lorenz gauge in QFT which is something we are free to choose in classical EM. This still doesn't show that we don't understand photons.
Lastly the EM photon fields rise and fall together and thus do not continuously conserve total field energy.
I thought there were no photon fields in EM. If you are talking about QFT again, than I assure you that the em field conserves energy just like anything else in QFT.
To quote Einstein, ``Today every Tom, Dick and Hary thinks he understands the photon but they are wrong.''
And he liked dreaming, and had a lot of stupid ideas too:
I am enough of an artist to draw freely upon my imagination. Imagination is more important than knowledge. Knowledge is limited. Imagination encircles the world.
Albert Einstein
To summarize: We know the photon pretty well by now. Phenomenological textbooks and many QFT intros suck for reasons I don't understand, and this confuses many people, but once you have quantized the A field by hand and checked out things like quadrature squeezed states, I think you will have a better grip on the photons.
Many people falsely believe, that photons can only be measured by absorption, this is not the case. Theory gives no reason to assume this, and there are new experiments which manage to do these http://www.nature.com/nature/journal/v448/n7156/abs/nature06057.html". Half truths stated here are state of physics research many years ago. We have progressed people, photons are real and not just some clicks in a photomultiplier.