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arXiv:physics/0006037

Quantum mechanics can be led by metrics in Minkowski's time-space world

Takashi Sakai

Published Jun 16, 2000• 0 citations
arXivHTMLPDF

Abstract

A body of theory is completely different between relativity theory and quantum mechanics. Most targeting physical phenomena are different between them as well. Despite that both theories describe our time-space world, no one has succeeded in arriving at one of these theories by using the other one, deductively. Fusion of these two theories produced quantum field theory. However this theory impresses us as a theory that was made by merging the two theories by force. So this theory cannot indicate the reason why both relativity theory and quantum mechanics exist in this world at the same time. Here I show you that quantum mechanics can be led by the equation of Minkowski's metrics, which stands up in the relativistic world of space and time. This is the first report proving mathematically that quantum mechanics can be born reductively in our relativistic world.

DOI
10.48550/arxiv.physics/0006037

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A body of theory is completely different between relativity theory and quantum mechanics. Most targeting physical phenomena are different between them as well. Despite that both theories describe our time-space world, no one has succeeded in arriving at one of these theories by using the other one, deductively. Fusion of these two theories produced quantum field theory. However this theory impresses us as a theory that was made by merging the two theories by force. So this theory cannot indicate the reason why both relativity theory and quantum mechanics exist in this world at the same time. Here I show you that quantum mechanics can be led by the equation of Minkowski's metrics, which stands up in the relativistic world of space and time. This is the first report proving mathematically that quantum mechanics can be born reductively in our relativistic world.
The picture of space-time that Minkowski created in 1907 has been followed by two important developments in physics not contained in the original picture: general relativity and quantum mechanics. We will argue that the use of concepts of those theories to construct space-time implies conceptual modifications in quantum mechanics. In particular one can construct a viable picture of quantum mechanics without a reduction process that has outcomes equivalent to a picture with a reduction process. One therefore has two theories that are entirely equivalent experimentally but profoundly different in the description of reality they give. This introduces a fundamental level of undecidability in physics of a kind that has not been present before. We discuss some of the implications.
In general, a physical theory is based on some fundamental principles concerning space, time, matter, and the laws prescribing how matter is distributed in space and how it evolves in time, and even how spacetime itself changes in response to the changes of matter. The spectrum of the known theories is very diverse, since they are based on different assumptions. Some theories assume that space and time are totally independent, some that they are warped in a continuum named "spacetime", and some even that there are more dimensions than the usual 3+1. Most theories consider that space and time are continuous, but many recent theories consider them to be discrete. Most dynamical laws of fundamental Physics are deterministic, but apparently Quantum Mechanics shows that they may have an indeterministic component. Despite these distinctions between various theories, our intuition and experience tells us that they have a lot in common. In this paper I will try to capture the common features in a single mathematical structure. This is not a Theory of Everything, but only a mathematical structure which is common to most physical theories known so far. We will see that these theories can be obtained as particular cases of this structure, which I will call "world". In particular, the worlds described by the Classical Mechanics, the Theory of Relativity and the Quantum Mechanics are examples of worlds according to this definition, but also some theories attempting to unify gravity and QM, like String Theory. The purpose of this distillation is to provide a mathematical common background to both physical and metaphysical discussions about the various theories of the World.
Relativistic quantum theories are equipped with a background Minkowski spacetime and non‐relativistic quantum theories with a Galilean space‐time. Traditional investigations have distinguished their distinct space‐time structures and have examined ways in which relativistic theories become sufficiently like Galilean theories in a low velocity approximation or limit. A different way to look at their relationship is to see that both kinds of theories are special cases of a certain five‐dimensional generalization involving no limiting procedures or approximations. When one compares them, striking features emerge that bear on philosophical questions, including the ontological status of the wave function and time reversal invariance.
The implications of the relativistic space-time structure for a physical description by quantum mechanical wave-functions are investigated. On the basis of a detailed analysis of Bell's concept of local causality, which is violated in quantum theory, we argue that this is a subtle, as well as an important effort. A central requirement appearing in relativistic quantum mechanics, namely local commutativity, is analyzed in detail and possible justifications are given and discussed. The complexity of the implications of wave function reduction in connection with Minkowski space-time are illustrated by a quantum mechanical measurement procedure which was proposed by Aharonov and Albert. This procedure and its relativistic implications are explicitly analyzed and discussed in terms of state evolution. This analysis shows that the usual notion of state evolution fails in relativistic quantum theory. Two possible solutions of this problem are given. In particular, it is shown that also a theory with a distinguished foliation of space-time into space-like leafs - accounting for nonlocality - makes the right predictions for the Aharonov-Albert experiment. We will repeatedly encounter that an analysis of the wave-function alone does not suffice to answer the question of relativistic compatibility of the theory, but that the actual events in space time, which are predicted and described by the theory, are crucial. Relativistic versions of quantum mechanical theories which precisely describe actual processes in space-time are briefly described and discussed in the appendix.
A theory with a simple physical model gives logical and reasonable answers to all the strange phenomena and difficult-to-understand problems in modern physics, from the theory of relativity, quantum mechanics QM, and up to the field of cosmology. It is a theory suitable for explaining phenomena from small particles to large bodies such as stars, galaxies, and the entire universe. In this article, we will define in an innovative manner how space-time is seen and we will give a different graphical representation to the special theory of relativity. We will show how the Lorentz transformation equations and the space-time interval are obtained from it, how light behaves in space-time, and according to it, how to obtain relativistic Doppler formulas. The most important thing in this article is that just as two bodies can be in two different times, according to the theory of relativity, they can also be simultaneously in two different locations. According to it, Heisenberg's uncertainty principle and quantum superposition can be explained. We will present for the first time a very common physical phenomenon, but unknown up to this day, which we will call "leap set". According to it, we will logically and deterministically explain the double-slit experiment of electrons and we will show that the result of the experiment is not a wave interference because the electron does not pass through the slits, but it performs a leap set to possible locations on the screen. Also, according to the same model, we will see the conditions and reasons for quantum entanglement and how it is obtained. We will also show the expansion of the universe and Hubble's law according to this theory and model, the Casimir effect as a cosmological phenomenon. We will discuss the possibility of the existence of a mirror world completely identical to our world, located at a distance of 2x13.8Gly in the space-time and we will prove that the material mass energy of the universe is zero.