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ON THE NATURE OF QUANTUM NONLOCALITY

Aleksandr V. Belinsky, A. K. Zhukovskiy

Published Dec 15, 2025• 0 citations
Publisher

Abstract

An example of a thought experiment for an isolated quantum system is considered, which testifies in favor of the existence of the principle of reciprocity of the coordinate and momentum descriptions that permeate space-time. The fundamental connection between the symmetry of space-time and the conservation laws in physics is considered. The question of what is the root cause is analyzed: isotropy and homogeneity of space-time or the conservation laws themselves. Binary relations of coordinate and momentum descriptions proposed by Professor Yu.S. Vladimirov are discussed, including the thesis on the determining role of momentum space.

DOI
10.22363/2224-7580-2025-4-43-53

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An example of a thought experiment for an isolated quantum system is considered, which testifies in favor of the existence of the principle of reciprocity of the coordinate and momentum descriptions that permeate space-time. The fundamental connection between the symmetry of space-time and the conservation laws in physics is considered. The question of what is the root cause is analyzed: isotropy and homogeneity of space-time or the conservation laws themselves. Binary relations of coordinate and momentum descriptions proposed by Professor Yu.S. Vladimirov are discussed, including the thesis on the determining role of momentum space.
Abstract Quantum entanglement and quantum nonlocality are examined in the context of the fundamental relationship between spacetime symmetry and conservation laws. It is established that quantum nonlocality arises from the very structure of spacetime. Arguments are presented in favor of the secondary nature of the spacetime continuum relative to more fundamental principles and concepts of the microworld. An example is given of a closed quantum entangled system, which demonstrates that such a system behaves as an indivisible whole: its particles are inseparably linked through the conservation of momentum. Physically, this manifests as strict correlations in measurements—correlations that must be nonlocal in nature. This supports the idea that there exist deep mechanisms of coordination, such as the principle of reciprocity between coordinate and momentum representations, and binary relations permeating the fabric of nonlocal spacetime. To understand the coherent behavior of such systems, it is necessary to move beyond local reductionism and accept the objective reality of global connections that bind the elements of the system into a unified ensemble.
Symmetry in space and time lead to the conservation laws of energy and momentum,which are a general principle across all fields of physics So.it is of great importance to study symmetrization and conservation laws of mechanical system,While in most of general literatures and textbooks the derivations of conservation of momentum for quantum systems are made by infinitesimal translations in space,by approximate expansion of wave functions as the first order,or by means of the Lie symmetries.In this paper,the conservation of momentum is derived from the picture Schrdinger and the wave functions belonging to the translations in space are made to expand in power series and with the help of Lie symetries,the conservation of momentum is obtained.It is more precise than that in the literatures.
In the course of classical and theoretical mechanics, there exists a relation between the laws of conservation (integral or constant of motion) and the property of the symmetry of space and time https://www.w3.org/1998/Math/MathML"> t https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003273073/d236e21f-f9f6-4e42-b186-ef1c50f0a68b/content/math3_1.tif" xmlns:xlink=" https://www.w3.org/1999/xlink "/> . It has been shown that the law of conservation of momentum follows from the isotropy of space and time https://www.w3.org/1998/Math/MathML"> t https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003273073/d236e21f-f9f6-4e42-b186-ef1c50f0a68b/content/math3_2.tif" xmlns:xlink=" https://www.w3.org/1999/xlink "/> . So any property of space and time symmetry should correspond to a conservable physical quantity . This theorem is true for quantum mechanics.
@As a way of honoring Professor Wheeler on his sixtieth birthday, I propose to take this opportunity to elaborate upon certain somewhat speculative ideas which I have tried to hint at on occasion, concerning the possible nature of a quantized space-time. The reader will not need to be too discerning to recognize some substantial dierences between the ideas I am proposing here and those which Professor Wheeler has on many occasions so eloquently and forcefully put forward. Nonetheless, there is little doubt in my own mind as to the very great inspirational inuence that Professor Wheeler’s own views have had in the development of several of the thoughts which I am expressing here. To begin with, let me make clear that I do not necessarily mean by \quantized space-time something which could be obtained by applying standard (or even non-standard) techniques of quantization to Einstein’s general theory of relativity. What I wish to say has its roots in something which is really more primitive than either quantum theory or relativity as such. This is the question of the fundamental role played by the mathematical concept of continuum in virtually the whole of accepted present-day physical theory. Not only does the continuum occupy a basic position in our mathematical models of space and time (with the concomitant implication of a continuous nature for many related physical concepts such as velocity, energy, momentum, temperature, etc.), but so also does present-day quantum theory rest crucially on a continuum concept, namely on the two-dimensional complex continuum of probability amplitudes, this being the continuum which also occurs in the superposition law. Let me say at the outset that I am not happy with this state of aairs in physical theory. The mathematical continuum has always seemed to me to contain many features which are really very foreign to physics. This point = @ @
Introduction The application of group theory to study physical problems and their solutions provides a formal method for exploiting the simplifications made possible by the presence of symmetry. Often the symmetry that is readily apparent is the symmetry of the system/object of interest, such as the three-fold axial symmetry of an NH 3 molecule. The symmetry exploited in actual analysis is the symmetry of the Hamiltonian. When alluding to symmetry we usually include geometrical, time-reversal symmetry, and symmetry associated with the exchange of identical particles. Conservation laws of physics are rooted in the symmetries of the underlying space and time. The most common physical laws we are familiar with are actually manifestations of some universal symmetries. For example, the homogeneity and isotropy of space lead to the conservation of linear and angular momentum, respectively, while the homogeneity of time leads to the conservation of energy. Such laws have come to be known as universal conservation laws. As we will delineate in a later chapter, the relation between these classical symmetries and corresponding conserved quantities is beautifully cast in a theorem due to Emmy Noether. At the day-to-day working level of the physicist dealing with quantum mechanics, the application of symmetry restrictions leads to familiar results, such as selection rules and characteristic transformations of eigenfunctions when acted upon by symmetry operations that leave the Hamiltonian of the system invariant.
One of the fundamental questions in physics concerns the relation between spacetime and quantum entanglement. The spacetime is usually considered as a fixed background physical space, and the quantum entanglement is usually manifested as a ``spooky action at a distance" or the existence of ``nonlocality" in nature. Here, we propose the flat-space isotropy and homogeneity principles as the fundamental criteria for determining the maximum degree of nonlocality of nature. More specifically, we consider abstract and deterministic nonlocal-box models which have stronger correlations than in quantum mechanics, whereas therein instantaneous communication remains impossible. We impose space-symmetry group structures on these models and derive a measure for the degree of space symmetries. Surprisingly, there is a tradeoff or inconsistency between the degree of space symmetries and the degree of nonlocality, where this inconsistency is exactly lifted at the Tsirelson bound, as predicted by quantum physics and also predicted in the experiments. Moreover, we prove this result in the general framework of deterministic nonlocal models and conclude that the probabilistic interpretation of the nonlocal box models is an emergent property of the flat-space symmetries.