Dear Constanin,
Thank you for taking the time to read my essay. It is my privilege to defend the points that you raised.
1. "Photons are the carriers of causality - it is not correct, we can also send causal signals using neutrino, gravitation waves, beams of protons, neutrons, electrons, and so on."
Protons, neutrons and electrons can all be annihilated by their anti-partner. Upon annihilation, there is a release of gamma rays, but no particle fragments. Gamma rays are photons. With current technology, we do not have the ability to signal using gravity waves. But if we did, I would argue that we would use frequency shift photons to generate them. I am working on that right now by looking for a transfer function. As for neutrinos, some have suggested that a neutrino-anti-neutrino pair forms a photon, however, I don't think they've gotten it work out. Until they can prove otherwise, I assume that neutrino-anti-neutrino pairs will annihilate one another into gamma rays. Let me know if anyone proves otherwise.
2. "Distance and time are defined with photons - we can define distance and time also using coherent beams of atoms or electrons. " But atoms and electrons can be decomposed into photons. We can define distance and time with rulers and stopwatches, however, (a) the international community uses photon transitions in Cesium atoms and (b) photons are fundamental (more fundamental than atoms or electrons). If someone succeeds in decomposing a photon into a neutrino-anti-neutrino pair, then we can define time and distance in terms of neutrinos, if we can find them.
3. The wave function is the set of solutions to the Schrodinger equation. The difference between wave-functions and other mathematical objects is that wave-functions can be of the form:
[math]\Psi = A e^{i(kx-\omega t)}[/math]
\Psi = A e^{i(kx-\omega t)}
Coincidentally, plane waves, including polarized electromagnetic plane waves, are of the same form. Wave-functions offer the ability to describe any quantum system while still remaining very general. It made sense to commit Photon theory to the requirement of describing everything in physics with photons and wave-functions. Even now, I am looking for a solution to the Schrodinger Equation (and Hamiltonian Mechanics) for a gravity field. It was a strategic decision that I am happy with.
4. Defining particles as wave-functions with photons trapped inside has not been a popular decision. The advantage of doing so is that F=ma implies that the trapped photons within the mass have to undergo a change in frequency. A change in frequency requires a change in photon energy. Therefore, when someone asks why rocks are heavy, it's because the photons trapped inside have to convert frequency energy into potential energy. I hope that makes sense. If not, then pin me down on that point.
If you don't like the idea of a cluster of wave-functions with trapped photons, you can interpret that as an energized wave-function.
