School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Document Type
Article
Publication Date
7-11-2024
Abstract
This article studies the breaking of the Lorentz symmetry at the Planck length in quantum mechanics. We use three-dimensional ℘-adic vectors as position variables, while the time remains a real number. In this setting, the Planck length is 1/℘, where ℘ is a prime number, and the Lorentz symmetry is naturally broken. In the framework of the Dirac-von Neumann formalism for quantum mechanics, we introduce a new ℘-adic Dirac equation that predicts the existence of particles and antiparticles and charge conjugation like the standard one. The discreteness of the ℘-adic space imposes substantial restrictions on the solutions of the new equation. This equation admits localized solutions, which is impossible in the standard case. We show that an isolated quantum system whose evolution is controlled by the ℘-adic Dirac equation does not satisfy the Einstein causality, which means that the speed of light is not the upper limit for the speed at which conventional matter or energy can travel through space. The new ℘-adic Dirac equation is not intended to replace the standard one; it should be understood as a new version (or a limit) of the classical equation at the Planck length scale.
Recommended Citation
Zúñiga-Galindo, W. A. 2024. “\wp-Adic Quantum Mechanics, the Dirac Equation, and the Violation of Einstein Causality.” Journal of Physics A: Mathematical and Theoretical 57 (30): 305301. https://doi.org/10.1088/1751-8121/ad5cab
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Publication Title
Journal of Physics A: Mathematical and Theoretical
DOI
https://doi.org/10.1088/1751-8121/ad5cab
Comments
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.