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HYPOTHESIS AND THEORY article

Front. Phys.
Sec. Cosmology
Volume 13 - 2025 | doi: 10.3389/fphy.2025.1537461

The Euclidean Model of Space and Time, and the Wave Nature of Matter

Provisionally accepted
Radovan Machotka Radovan Machotka *
  • Institute of Geodesy, Faculty of Civil Engineering, Brno University of Technology, Brno, Olomouc, Czechia

The final, formatted version of the article will be published soon.

    The aim of the paper is to show the fundamental advantage of the Euclidean Model of Space and Time (EMST) over Special Relativity (SR) in the field of wave description of matter. The EMST offers a unified description of all particles of matter as waves moving through four-dimensional Euclidean space at the speed of light. Unlike the usual description in three dimensions, where the group and phase velocities of a particle differ, in four-dimensional space the wave and the associated particle can be treated as a single object. The paper deepens understanding of the EMST as a viable alternative to SR. The EMST clarifies the origin of relativistic phenomena and at the same time explains the apparent mysteries associated with the wave nature of matter. From the broader perspective, the EMST has all the prerequisites to become the starting point for the mutual combination of "relativistic" and "quantum" physics into a single physical theory.

    Keywords: special relativity, Euclidean relativity, Euclidean metric, wave-particle duality, de Broglie waves

    Received: 30 Nov 2024; Accepted: 14 Jan 2025.

    Copyright: © 2025 Machotka. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

    * Correspondence: Radovan Machotka, Institute of Geodesy, Faculty of Civil Engineering, Brno University of Technology, Brno, 602 00, Olomouc, Czechia

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