Book Publisher International (a part of SCIENCEDOMAIN International)

Quantum Theory of Fuzzy Events—Reformation and Redevelopment of Quantum Theory

Wenbing Qiu

Published Sep 1, 2022• 0 citations

Abstract

The goal of this study is to extend quantum theory to the field of fuzzy phenomena. Using the idea and method of fuzzy mathematics, the quantum probability theory of fuzzy event is proposed, with the form of fuzzy event route integral, membership degree amplitude, fuzzy field function, Green function, physical quantity and fuzzy diagram. This theory changes quantum mechanics, making it a special instance of the former. Under some conditions, this theory breaches unitarity, gauge invariance, probability conservation, and information conservation, rendering these concepts approximate. This new theory, which does not require renormalization and can naturally produce meaningful results that are consistent with the experiments, is the proper theory for describing microscopic high-speed phenomena, whereas quantum mechanics is only a proper theory for describing microscopic low-speed phenomena. Because this theory is not divergent under the conditions that there is no renormalization and an infinite number of offsetting terms, it can constitute the theoretical framework required for gravity quantization.

DOI: 10.9734/bpi/nfpsr/v1/7776f

Related papers

Fuzzification of Feynman Path Integral and Its Effect on Field Theory and Quantum Gravity—Reformation and Redevelopment of Quantum Theory

Wenbing Qiu

The quantum probability theory of fuzzy event is suggested by using the idea and method of fuzzy mathematics, giving the form of fuzzy event path integral, membership degree amplitude, fuzzy field function, Green function, physical quantity and fuzzy diagram. This theory reforms quantum mechanics, making the later become its special case. This theory breaks unitarity, gauge invariance, probability conservation and information conservation, making these principles become approximate ones under certain conditions. This new theory, which needs no renormalization and can naturally give meaningful results which are in accordance with the experiments, is the proper theory to describe microscopic high-speed phenomenon, whereas quantum mechanics is only a proper theory to describe microscopic low-speed phenomenon. This theory is not divergent under the condition of there being no renormalization and infinitely many offsetting terms, thereby it can become the theoretical framework required for the quantization of gravity.

Journal of Modern PhysicsJan 1, 20200 citations

Fuzziness in Quantum States—Breaking through the Framework and the Principle of Quantum Mechanics

Wenbing Qiu

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.

Book Publisher International (a part of SCIENCEDOMAIN International)Jun 15, 20220 citations

There Also Can Be Fuzziness in Quantum States Itself—Breaking through the Framework and the Principle of Quantum Mechanics

Wenbing Qiu

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.

Journal of Modern PhysicsJan 1, 20203 citations

Can Fuzzy Sets Be Useful in the (Re) Interpretation of Uncertainty in Quantum Mechanics?

Rudolf Seising

New scientific theories have been and will always be required for the progress of science. Two examples of new theories that were advanced in the 20th century are quantum mechanics and fuzzy set theory. Both deal with the concept of uncertainty and both use mathematical tools that are essentially different from those used in classical probability theory. In both, the introduction of new concepts (theoretical terms) was necessary because phenomena and processes observed in the real world could not be explained with existing mathematical concepts. This paper examines the possibilities of (re)interpreting uncertainty in quantum mechanics with the aid of fuzzy sets and systems

Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS)Jun 1, 20067 citations

New wave function and its new differential equation in quantum physics. The fuzzy logic and fuzzy sets theory of Lutfi Zadeh

It is known the quantum mechanics is different from the classical mechanics.The reason is the principle of Heisenberg's Uncertainty in quantum mechanics.The uncertainty as principle of mechanics result in wave function in it, square of which is probability.Therefore principal stochasticity of microworld which noted Bohr in famous dispute with Einstein about a God playing dice results in the quantum logic.In frame this logic the Schrodinger cat is alive and dead the same time.The probability theory with its elementary events in its topological probability space cannot extend its definitions.Fuzzy logic and fuzzy sets of Zadeh with focal elements in topological possibility space can makes it.

Engineering mechanicsJan 1, 20240 citations

A New Approach to The Quantum Mechanics

Yulei Feng

In this paper, we try to give a new approach to the quantum mechanics(QM) on the framework of quantum field theory(QFT). Firstly, we make a detail study on the (non-relativistic) Schrödinger field theory, obtaining the Schrödinger equation as a field equation, after field quantization, the Heisenberg equations for the momentum and position operators of the particles excited from the (Schrödinger) field and the Feynman path integral formula of QM are also obtained. We then give the probability concepts of quantum mechanics in terms of a statistical ensemble, realizing the ensemble(or statistical) interpretation. With these, we make a series of conceptual modifications to the standard quantum mechanics, especially propose a new assumption about the quantum measurement theory which can solve the EPR paradox from the view of the QFT. Besides, a field theoretical description to the double-slit interference experiment is developed, obtaining the required particle number distribution. In the end, we extend all the above concepts to the relativistic case so that the ensemble interpretation is still proper. Two extra topics are added, in the first one, an operable experiment is proposed to distinguish the Copenhagen interpretation from the ensemble one via very different experimental results. While the second topic concerns with the extensions of the concept of coherent state to both the Bosonic and Fermionic field cases, to obtain the corresponding classical fields. And in the concluding section, we make some general comparisons between the standard QM and the one derived from the QFT, from which we claim that the QFT is the fundamental theory.

arXiv:1210.6418Oct 24, 20121 citation