Relativistic quantum mechanics and relativistic quantum statistics based upon a novel perspective on relativistic transformation

TL;DR

This paper introduces a novel perspective on relativistic transformation leading to a new formulation of relativistic quantum mechanics and statistics, resolving longstanding anomalies and providing new insights into particle confinement and thermal properties.

Contribution

It proposes a new relativistic quantum mechanics and statistics framework based on a novel relativistic transformation perspective, addressing key anomalies and deriving new particle confinement and thermal results.

Findings

Eliminates negative probability density and energy states in relativistic quantum mechanics.

Establishes a lower bound on particle confinement size related to the Compton wavelength.

Derives a relativistic speed distribution differing from Jüttner distribution at high temperatures.

Abstract

A novel perspective on relativistic transformation recently-proposed provides an insight into the very meaning of the principle of relativity. With this novel perspective and Bell's theorem, we argue that special relativity, instead of quantum theory, should be radically reformulated to resolve inconsistencies between the two theories. A new theory of relativistic quantum mechanics is formulated upon this novel perspective. This new relativistic quantum mechanics is free from such anomalies as the negative probability density, the negative-energy states, Zitterbewegung, and the Klein paradox deep-rooted in the current relativistic quantum mechanics. Moreover, a remarkable result is found that a particle can not be confined within an infinite square well of width less than half of the Compton wavelength. As implications in nuclear physics, there is a lower bound on the size of atomic nucleus. Neither an electron, nor a positron, can be confined inside the nucleus by whatever interaction. Furthermore, we argue that the postulates of non-relativistic quantum statistics fulfill the principle of relativity, as extended to the relativistic realm. A new theory of relativistic quantum statistics is formulated such that the probability distribution functions are the same as the three well-known probability distribution functions in non-relativistic quantum statistics. A relativistic speed distribution of a dilute gas is then derived by the new relativistic quantum statistics and the new relativistic quantum mechanics. This relativistic speed distribution reduces to Maxwell speed distribution in the low temperature region. Yet, this relativistic speed distribution differs remarkably from J\"uttner speed distribution in the high temperature region. Also, thermal properties of a dilute gas are studied by the new relativistic quantum statistics.