But you did not show that the photon is a particle. In string physics a particle is a tiny string. In ordinary physics a particle is a point. But you just said that the photon has length. You also said that a photon can be a spherical em wave, a wave function. Well, if you redefine the properties of a photon that way, I cannot disagree with you, except to say that those are not the properties of what most of us would call a particle.
On the other hand(OTOH) I think that at times, instants of time, em waves collapse into tiny objects that we ordinarily think of as particles. For example, take your spherical photon. It occupies a huge amount of space, especially when you also take the incoherence length into account. Yet a tiny detector can collect photon events. And this is the closest we can ever come to the actual realization of a photon as you pointed outin earlier posts. And we can collect many photons in the time it takes a coherence length of em waves to pass by the detector.
So, and this is just common sense that anyone can understand- no physics education needed- somehow the photons which you just said occupy 3-D space with spherical symmetry in a shell the thickness of a coherence length, can squeeze into a tiny detector.
Most physicists have reasoned that photons must be like electrons, and must be point particles with spin that are just accompanied by em waves which act like quantum wave functions and determine the probability of where the point photon particle is. If you read the double slit literature, you see evidence of this thinking. Always wondering which slit the photon went through.
But that is incorrect thinking. I am pleaseed that your viewpoint is more sophisticated than that. Your view is quite close to mine. The math is in exact agreement. Our difficulty is semantic. You just call em waves photons. That's OK but not customary thinking of what a particle is.
But we still have a physics disagreement on "how the large photon can fit into a tiny detector". I claim that this can only happen from collapse of the wave function- one that is real and not just probability waves. You do not seem to think that collapse exists. But there is no theory for the collapse. Perhaps it will come from string theory, but there the concentration is so much on particles rather than fields that a change in basic thinking seems required.
My apologies to Alexander if I have misunderstood your thinking on collapse. But we are close to resolving our differences, at least with regard to photons. If we can come to some kind of agreement with photons, then we can go on to condider electrons, which I think are analogous to photons- that is they are mostly fields that act like particles occasionally, like when they become entangled with photons.
The current thinking that everything is composed of strings rather than fields, and that the fields are just probability waves, is a paradigm that is hindering the present development of physics. Do you agree?