A.A. Derkachov, Ph.D.

Well-known is Dirac's opinion that in the future perfected quantum mechanics, returning back to determinism, might possibly appear, supporting this way Einstein's position, and that this turning back to determinism would be possible at a price of refusal from some basic ideas which by then were admitted without even slightest doubt.

1. Relativistic Mechanics and Quantum-Mechanical Determinism

Special theory of relativity (STR), or relativistic mechanics of a single material particle, and general theory of relativity (GTR), being in fact the Einstein’s theory of gravitation for the case when one of two masses in the problem of two bodies is much greater than another one, have been successfully developed in the first quarter of the 20th century. This successful development was expressed in revolutionary review of a number of ideas and concepts of founded by Galilei, Newton and Lagrange classical mechanics. But this extremely important process was unjustly retarded and, actually, practically stopped due to the "boom" of indeterminism of quantum mechanics (the Heisenberg principle of indeterminism, the probability approach to solutions of Schroedinger equations, Dirac relativistic quantum mechanics, etc.).

As a result, in wide circles of physicists the conviction was formed that the relativistic determinism of STR and GTR has already accomplished its historical mission because such deterministic concepts as "the isolated, or closed, system of material particles". "the path of a material particle", had principally become behind of time due to switching of physics to such indeterministic concepts as "the ensemble of particles", "the operator of birth and death of particles", etc.

But, nevertheless, we must remember that such quantum-mechanical concepts as, for instance,” the Hamiltonian operator of energy “, “the operator of the moment of the momentum  ”, etc. would never have appeared in quantum mechanics unless their classical “predecessors" or their relativistic analogies existed. Consequently, before putting on a quantum-mechanical "hat" of the operator ^ , one has to posses that something to put this hat on. Still, may we doubtlessly affirm that by the moment of the powerful and successful boom in quantum mechanics all those, now classical, deterministic ideas and concepts of STR and GTR, which later on were subjected to further quantum-mechanical generalisation, have by that time been fully completed and understood? It is also worthy to pin that exaggerated hastiness in creating the image of purity and perfectness, obviously serving bad to further development of the Great Idea of Relativity.

As a result, Dirac's expectations of future, possibly peculiar, return to Einstein’s determinism (paying for that by refusing from some ideas and concepts that now seem to us absolutely doubtless) are so far vain. At the same time we may think: "If ninety years back the principal refusal from some "obvious" stereotypes of thinking has become so useful then why should one deny attempts to review at least some of those ideas and concepts which, following Dirac, by now are admitted without any doubt?"

Exactly such a "bridge" leading from deterministic neorelativistic mechanics into quantum mechanics, we are trying to create.