Dear Lev-
Thanks for your interesting essay. It is well written and I liked the quoted text on page 2 and your suggestion for a very different approach towards unification. However, I feel that your suggestion of a different formalization will not bring us closer to a unified theory of physics. The likelihood for success ('to hit the target') is extremely small, since there are an infinite number of possible formalizations. The 'chosen one' should not be a matter of personal preference. The best starting point is nature, which is no formalism. I would like to give you specific feedback to illustrate my points and also areas of agreement. For this, I relate to the essay that I submitted for the contest, which is based on Kirilyuk's work on Quantum Field Mechanics, and my own extensions.
Page 1, Abstract:
a. I differ in opinion on the usefulness to start out with a formalism. See comment above.
b. Making a distinction between temporal and spatial aspects is appropriate, but they could be highly related and, therefore, prioritizing them could be inappropriate. In fact, see my QFM essay in which it is suggested that such 'primacy' is inappropriate.
Page 1, second paragraph: 'numeric road': I would call it the formal road using abstract spaces and operations.
Page 1, 3rd paragraph: "Thus, what is not so well understood is that the needed paradigm change might be of much more radical nature than physicists and even mathematicians have been prepared to think about." I completely agree.
Page 1, 3rd paragraph" "Relational generalization" See mutual protofield attraction in QFM.
Page 2, Schrodinger's comments: Read these observations again after you have gone through the my essay, and then you can see that they are really appropriate comments. It is formal discreteness that has been forced upon us. QFM uses continuous protofields from which discreteness emerges dynamically, which is caused by protofield attraction. In other words, continuity and discreteness coexist, and discreteness emerges from continuous behavior.
Page 2, Schrodinger's comments: "So the facts of observation are irreconcilable with a continuous description in space and time . . . . On the other hand, from an incomplete description from a picture with gaps in space and time one cannot draw clear and unambiguous conclusions; it leads to hazy, arbitrary, unclear thinking and that is the thing we must avoid at all costs! What is to be done? The method adopted at present may seem amazing to you. It amounts to this: we do give a complete description, continuous in space and time without leaving any gaps, conforming to the classical ideal description of something. But we do not claim that this 'something' is the observed or observable facts; and still less do we claim that we thus describe what nature (matter, radiation, etc.) really is. In fact, we use this picture (the so called wave picture) in full knowledge that it is neither."
At the level of human observations, space and time appear to be continuous. However, according to QFM they are really discrete. The observed continuity follows because the quantum of time is equal to 10^(-20) sec and the quantum of space (Compton's wavelength) is of the order of 10^(-12) meters. Both are too small for normal observation, although the quantum beat frequency of 10^20 Hz has been observed in an experiment conducted in France (see [4] in my essay).
Page 2, Einstein in a letter to Infeld: "I tend more and more to the opinion that one cannot come further with a continuum theory." This is incorrect, QFM shows that this is possible: discreteness can emerge from continuous interaction as a consequence of pulsation.
Page 3, section 2: Yes: most fundamental. The representational part, I don't agree with since it becomes formal, and is not necessarily related to nature. In fact, in my opinion, it would be surprising if it would.
Page 8, figure: Interesting figure, showing temporal and spatial aspects. However, QFM demonstrates that the two are really combined into one single unceasing continuous process and cannot be separated although they a produce discretization as a consequence of continuous random pulsating motion.
Page 8, section 3: "The particle-wave duality can probably be explained by the possible forms of interaction between a quantum process and its environment." In QFM, the particle wave duality is a consequence of the pulsation of the particle such that two types of states exist, a weakly bound state and one or more strongly bound states. The average of the weakly bound states is the wave function.
Page 8, section 3: "The resulting quantum process always depends on the external events that are allowed to intervene in its construction during its generation." This statement seems to imply environmentally induced quantum behavior, i.e., decoherence. In QFM, this is far more subtle since no distinction van be made between particle and environment. The mutually attractive protofields are the environment that causes the existence of particles by the pulsating behavior. Quantum entanglement occurs within a particle by the simultaneous pulsation and rotation in both protofields, such that they protofields get intertwined. Entanglement can also occur between particles (see Kirilyuk's work).
Page 10, conclusion: " we should be seeking fundamentally new formal schemes and structures that would be more effective." I agree with seeking a new scheme, not the formal part of it. We should be using nature as the starting point.
Anyway, this is my perspective.
