Can Young Talent Make Quantum Mechanics Complete and Deterministic?
Negative probabilities and negative energies are as real and yet as unobservable as negative money. This is what Paul Dirac wrote about negative probabilities, which he derived by transforming the equation of motion of Einstein’s special theory of relativity into Schrödinger’s wave equation of quantum mechanics. [1]
Eugene Wigner derived negative probabilities when he was transferring the quantum probability distribution from the Hilbert space to the classical configuration space used in thermodynamics. Wigner wanted to use this transfer to make corrections to the thermodynamic equilibrium for low temperatures. [2]
It is interesting that both solved the problems despite the presence of negative probabilities in their solutions. From a mathematical point of view, they could simply be ignored. Questions arose exclusively with their physical interpretation.
Dirac came up with a hypothetical antiworld, in which electrons were as rare as positrons (antielectrons) in our world. His antiworld hypothesis turned out to be suitable not only for leptons, but also for bosons, that is, for all known particles. [1]
Wigner saw a reality with the reverse flow of time. Accordingly, unitary operators turned into antiunitary operators in Wigner’s reality. [3]
Dirac and Wigner were the most prominent figures in quantum mechanics, but their ideas of antiworld did not take off perhaps because they explained already discovered things instead of predicting unknown ones.
Only Richard Feynman made an attempt to replace Dirac’s interpretation of positrons by his diagrams in which positrons were represented as electrons moving backward in time. [4]
In fact, I do not know why this happened. However, the most recent addition to the antiworld piggy bank was made by Gerard Hooft in 2020. When trying to create a mathematical formalism of a deterministic interpretation of quantum mechanics based on the states of particles with minimum energy levels, that is, a vacuum, he derived an antivacuum with maximum energy levels. [5]
What does this all mean? Einstein was sure that the fundamentally statistical nature of quantum mechanics is simply a consequence of the incompleteness of the description of reality given by Max Born’s interpretation of the absolute square of a wave function as a probability distribution . Schrödinger generally agreed with him. [6,7]
At the same time, it should be understood that for Schrödinger, objective reality was a phenomenon arising from the collective learning of agents (using Vitaly Vanchurin’s formulation in relation to gravity) [8] or “the intersection pattern of the determinations of many — indeed of all conceivable — individual observers,” in his own words. [7] In such a formulation, basic moral values can well be attributed to objective reality since they also arise from the collective learning of agents (determinations of observers).
However, moral values as constants or variables rather belong to the hypothetical antiworld of Dirac and Wigner because the reversal of time gives rise to an antibit, which can be equal to either zero or minus one. And the square root of minus one gives us not a real, but an imaginary number. An operator with such a number cannot be observed in our world, but this does not mean that it is unreal, if we follow Dirac’s logic.
If we accept moral values as real but unobservable parameter it will mean that Einstein was right that “the fundamentally statistical character of the (quantum) theory is simply a consequence of the incompleteness of the description” [6] of reality in the interpretation of quantum mechanics that modern physics still uses, and which no one questions nowadays, by and large. Looks like this problem is too challenging to modern well established science. Also its solution, if it exists, can turn modern physics upside down. That will be good for the progress of science but not necessarily as good for physicists who committed to its incremental development their entire careers. What can be done about it?
Einstein was 26 when he sent to the Annals of Physics his papers on the photoelectric effect, Brownian motion, and special relativity, as well as his then recently defended doctoral thesis on the size of molecules, one of his most cited papers to this day. Heisenberg was his age when he created quantum mechanics. Dirac was a year younger when he discovered antimatter.
Today, scientists of their age, yet without a PhD or disdainfully called postdocs, have virtually no opportunity to publish their own original theories. They are all combed under the comb of conformism, where the main thing is to stay in the mainstream. The clearest minds with the greatest potential are used for the most pointless activities.
The last leader of the famous Moscow School of Mathematics Nikolai Luzin counted his students’ own publications towards passing an exam. Those who wanted to think, not cram, seized on this opportunity. If you want to know where this led, take an interest in the Moscow School of Mathematics. It seems that the Luzin tree is still hanging on the website of the Physics and Mathematics Department of Moscow State University.
I am writing all this because, on the one hand, I do not believe that the task of creating a working deterministic interpretation of quantum mechanics can be solved by modern venerable scientists. On the other hand, I am sure that a lot of absolutely talented guys suffer from the inability to prove themselves.
It would be great to hold a competition among them for the best solution to the incompleteness of quantum mechanics. To do this, we need to somehow get to them and make sure that participation in this competition is not constrained by the framework of conformism and does not put their careers at risk, but on the contrary, gives them an acceleration. Perhaps the prize in such a competition should be an offer of work in a new research center for the creation of a scientific platform for the technologies of life. And only the participants of the competition will be able to get a job in such a center. Not necessarily the authors of the winning works, but those who completed the task with great curiosity and enthusiasm.
References:
- Dirac, P. A. M. Bakerian Lecture. The Physical Interpretation of Quantum Mechanics. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, vol. 180, no. 980, 1942, pp. 1–40. JSTOR,
- Wigner, E. P. On the Quantum Correction For Thermodynamic Equilibrium. Phys. Rev. 40, 749 — Published 1 June 1932
- Wigner, E. P. (1931). Group Theory and its Application to the Quantum Mechanics of Atomic Spectra, New York: Academic Press (1959).
- Feynman, R. P. (1949) The theory of positrons. Physical Review, 76 (6). pp. 749–759. ISSN 0031–899X. doi:10.1103/PhysRev.76.749. https://resolver.caltech.edu/CaltechAUTHORS:FEYpr49b
- t ‘Hooft, Gererd, Deterministic Quantum Mechanics: The Mathematical Equations, Front. Phys., 29 July 2020, Sec. Statistical and Computational Physics, Volume 8–2020 | https://doi.org/10.3389/fphy.2020.00253
- Einstein’s letter to Schrödinger, 1950
- Schrödinger’s letter to Einstein, 1950
- Vanchurin, Vitaly. (2025). Neural Relativity. 10.13140/RG.2.2.36422.79689.
