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Computing Fuzzy Time FunctionFuzzy Time and the impacts of it on Science [4]

Farzad Didehvar

Published Mar 1, 2022• 0 citations
OpenAlex

Abstract

We consider time as a fuzzy concept. Based on this, the Fuzzy Time-Particle interpretation Of Quantum Mechanics is introduced as an interpretation of Quantum Mechanics [4],[5],[6]. Here, we show how to compute the function associated to Fuzzy time.

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In this paper we consider physical systems and the concept of their states in the context of the theory of fuzzy sets and systems. In section 1 we give a brief sketch on the fundamental difference between the theories of classical physics and quantum mechanics. In section 2 and 3 we introduce very shortly systems and their states in classical and quantum mechanics, respectively. Section 4 presents the concept of fuzzy systems. We propose to fuzzify the classical systems in section 5 and quantum systems in section 6. In section 7 we start to consider a fuzzy interpretation of the uncertainty principle.
In this paper, an attempt is made to synthesize fuzzy mathematics and quantum mechanics. By using the method of fuzzy mathematics to blur the probability (wave) of quantum mechanics, the concept of fuzzy wave function is put forward to describe the fuzzy quantum probability. By applying the non-fuzzy formula of fuzzy quantity and Schrödinger wave equation of quantum mechanics, the membership function equation is established to describe the evolution of the fuzzy wave function. The concept of membership degree amplitude is introduced to calculate fuzzy probability amplitude. Some important concepts in fuzzy mathematics are also illustrated.
The goal of this study is to integrate fuzzy mathematics and quantum mechanics to seek deeper cosmic principles. The concept of fuzzy wave function is proposed to represent the fuzzy quantum probability by utilizing fuzzy mathematics to blur the probability (wave) of quantum mechanics. By applying the non-fuzzy formula of fuzzy quantity and the Schrödinger wave equation of quantum mechanics, the membership function equation is constructed to describe the evolution of the fuzzy wave function. The concept of membership degree amplitude is introduced to calculate fuzzy probability amplitude, and the membership degree amplitude equation is derived. Some important concepts in fuzzy mathematics are also illustrated.
Recently we proposed the linguistic Copenhagen interpretation (or, quantum language, measurement theory), which has a great power to describe both classical and quantum systems. Thus we think that quantum language can be viewed as the language of science. Further, we showed that certain logic (called quantum fuzzy logic) works in quantum language. In general, it is said that logic and time do not go well together. Then, the purpose of this paper is to show that quantum fuzzy logic works well with time. That is, quantum fuzzy logic has the advantage of being able to clearly distinguish between implication and causality. In fact, we will show the contraposition of the proposition “If no one is scolded, no one will study” (or the negation of “John is always hungry”) can be written in quantum fuzzy logic. However, “time” in everyday language has various aspects (e.g., tense, subjective time). Therefore, it is not possible to understand all of the “time” of everyday language by the “time” of quantum language.