Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

A Tentative Correction to the Inappropriate Application of Mathematical Theory to Physics — and A Correction to the Assumptions underlying Probability Theory

Version 1 : Received: 13 July 2022 / Approved: 14 July 2022 / Online: 14 July 2022 (11:29:39 CEST)

How to cite: Qin, S. A Tentative Correction to the Inappropriate Application of Mathematical Theory to Physics — and A Correction to the Assumptions underlying Probability Theory. Preprints 2022, 2022070213. https://doi.org/10.20944/preprints202207.0213.v1 Qin, S. A Tentative Correction to the Inappropriate Application of Mathematical Theory to Physics — and A Correction to the Assumptions underlying Probability Theory. Preprints 2022, 2022070213. https://doi.org/10.20944/preprints202207.0213.v1

Abstract

For a long time, physicists always directly use mathematical tools to deal with physical problems, and few people pay attention to the difference between mathematical theory and physical theory. Just like the dilemma that physicists once faced when dealing with the problem of blackbody radiation function.By analyzing the difference between the theoretical basis of mathematics and the theoretical basis of physics, this paper draws the following conclusions: (1) The theoretical basis of mathematics and the theoretical basis of physics are different, so when we use mathematical tools for physics research, we need to be very careful. (2) Finiteness and discreteness should be the basis of the whole physical theory; This paper points out that it is not advisable to use infinite " " and infinitesimal "0" without restriction and demonstration in physics, as well as the continuity of functions, which will bring a lot of trouble to physical theory.At the same time, through the analysis of Banach-Tarski paradox and Bertrand paradox, this paper proposes that if we revise the basic assumptions of probability theory: assuming that "points" have quantized sizes, and "lines" also have quantized widths. After the correction, we can not only avoid the troubles caused by Bertrand paradox, but also make probability theory better for practical application.

Keywords

infinity; infinitesimal; continuity; finiteness; discreteness; Banach-Tarski paradox; Bertrand paradox

Subject

Physical Sciences, Mathematical Physics

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