Why finite mathematics is the most fundamental and ultimate quantum theory will be based on finite mathematics

Abstract

Classical mathematics (involving such notions as infinitely small/large and continuity) is usually treated as fundamental while finite mathematics is treated as inferior which is used only in special applications. We first argue that the situation is the opposite: classical mathematics is only a degenerate special case of finite one and finite mathematics is more pertinent for describing nature than standard one. Then we describe results of a quantum theory based on finite mathematics. Implications for foundation of mathematics are discussed.

Finite Mathematics, Finite Quantum Theory and a Conjecture on the Nature of Time

“…As noted in Refs. [3,4] and Sec. 2, from the point of view of quantum theory, the notions of infinitely small/large, continuity etc.…”

“…In Refs. [2,4] we called the quantity p the constant but in those references the problem of time has not been discussed. A possibility that p may be related to time has been first discussed in Ref.…”

“…As noted in Secs. 3 and 4, for IRs of the so (1,4) algebra it is possible to find a basis such that all representation operators have only discrete spectrum. This is important for understanding the relation between standard theory and FQT.…”

“…A detailed discussion of FQT has been given in Refs. [2,3,4]. Here we describe only basic facts needed for further presentation.…”

“…As shown in Refs. [2,3,4], FQT sheds a new light on fundamental problems of gravity and particle theory. In the present paper we discuss how FQT can be applied for solving such a fundamental problem of quantum theory as the problem of time.…”