I want to apply fuzzy theory to quantum physics as a theoretical approach and experimentally apply it to quantum computing utilizing fuzzy logic to construct quantum algorithms. Use features like bookmarks, note taking and highlighting while reading quantum physics, fuzzy sets and logic. The road from fuzzy sets to definable causality and. This leads naturally to a new look at quantum gravity. Since relations between fuzzy sets and infinitevalued logic are the same as. Quantum logic and quantum probability theory represent important. Quantum physics, fuzzy sets and logic steps towards a. Quantum measurement, fuzzy logic, fuzzy set theory. One of the purposes of this paper is to bring together fuzzy logic and quantum mechanics. Quantum measurement, fuzzy logic, fuzzy set theory pacs. What does quantum mechanics imply for classical logic.
Soleimani2, shahidan radiman1 1school of applied physics, universiti kebangsaan malaysia 43600 ukm, bangi selangor, malaysia email address. Birkhoffvon neumann quantum logic as infinitevalued lukasiewicz logic. Quantum physics, fuzzy sets and logic springerlink. Pdf the manyvalued logic of quantum mechanics researchgate. In this paper we study quantum computation from a complexity theoretic viewpoint. Piron considers for example a point particle, for which the set of states. In the fuzzy logic approach, the conjunction and disjunction of propositions are interpreted as in classical logic except that the truth values, expressed. This unique compendium represents important action of fuzzy systems to quantum mechanics. One attempts to build up classical physics, including classical logic, on these quantum foundations. In contrast to fuzzy logic, the logic is not based on membership values but on vector subspaces identified by projectors. Why everything you thought you knew about quantum physics. This article describes how methods of fuzzy logic apply to detection of critical production processes for the purposes of optimization and control of production and automated processes.
Currently i am a 2nd year undergraduate student in the physics department at utah state university. It is shown that quantum mechanics can be regarded as what one might call a fuzzy mechanics whose underlying logic is the fuzzy one, in contradistinction to the classical crisp logic. Steps towards a manyvalued interpretation of quantum mechanics springerbriefs in physics pdf, epub, docx and torrent then this site is not for you. The properties of a system correspond to sets of states. Tells me that you are not just regurgitating facts, but you also analyze them and ask appropriate questions. Quantum physics, fuzzy sets and logic steps towards a manyvalued interpretation of quantum mechanics. Pdf fuzzy logic is a wellestablished formalism in computer science being.
Download it once and read it on your kindle device, pc, phones or tablets. It begins with a short survey of main interpretations of quantum mechanics already proposed, as well as various models of manyvalued logics and. Quantum mechanics is a probabilistic theory, sure, but we still work within welldefined sets i. Reasoning in quantum theory sharp and unsharp quantum logics. Indeed, the marriage of quantum mechanics the physics of the very small with general relativity the physics of the very large is believed by some to be the crucial step in formulating a general theory of everything that will hopefully contain all the basic laws of nature in one package. Fuzzy theory applied to quantum physics and quantum. Read lukasiewicz operations in fuzzy set and manyvalued representations of quantum logics, foundations of physics on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. Also, the coverage often does not seem to be intended to emphasize understanding of the largerscale quantum system that a.
Quantum complexity theory siam journal on computing. Quantum physics is the study of the behavior of matter and energy at the molecular, atomic, nuclear, and even smaller microscopic levels. Quantum physics, fuzzy sets and logic steps towards a many. Is fuzzy logic used in science, and more specifically in. The only people who are paying attention to it are pure mathematicians who study different types of logic as mathematical structures quantum logics relation to orthomodular lattices and its relation to fuzzy sets, without paying any attention to the semantic or epistemic value of such nonclassical logics. Topics covered in this course include the general formalism of quantum mechanics, harmonic oscillator, quantum mechanics in threedimensions. Quantum structures and fuzzy set theory sciencedirect. Yet, the typical quantum mechanics texts for physics students are not written in a style that mechanical engineering students would likely feel comfortable with. Pdf on classical, fuzzy classical, quantum and fuzzy. In the early 20th century, scientists discovered that the laws governing macroscopic objects do not function the same in such small realms. Covers all topics, including wave particle duality, schrodingers cat, epr bell inequality, and the relationship between measurement and entanglement. One semantics of quantum logic is that quantum logic is the logic of boolean observables in quantum mechanics, where an observable p is associated with the set of quantum states for which p when measured is true with probability 1 this completely characterizes the observable.
Since, quantum computing works on qubits at a nanoscale, the behavior observed is very much dependent on laws of probability, like heisenbergs uncertainty principle. The prospective manyvalued interpretation of quantum mechanics is soundly based on a theorem concerning the isomorphic representation of birkhoffvon neumann quantum logic in the form of a special lukasiewicz infinitevalued logic endowed. He worked previously at nature for over 20 years, first as an editor for physical sciences for which his brief extended from biochemistry to quantum physics and materials science and then as a. Quantum logic was developed in the context of quantum mechanics. Our first result is the existence of an efficient universal quantum turing machine in deutschs model of a quantum turing machine qtm proc. Quantum logic and its role in interpreting quantum theory gelo noel m. This brief presents steps towards elaborating a new interpretation of quantum mechanics based on a specific version of lukasiewicz infinitevalued logic. Steps towards a manyvalued interpretation of quantum mechanics springerbriefs in physics on free shipping on qualified orders.
Fuzzy logic is something like, there is another possible way except 0 and 1. On the need for fractal logic in high energy quantum physics. In particular, the present authors integrated cantor sets and fractals as well as number. A concept that is intuitively similar to the principle of superposition in quantum computing is fuzzy logic. In this paper, we have implemented fuzzy logic on quantum computing technology to get better results. Assignments quantum physics i physics mit opencourseware. Quantum fuzzy logic mohammaed saed haj ali kinda altarbouch 2. Pdf on the relation between fuzzy and quantum logic. Using fuzzy sets, an element may belong to more than one set. There is a large body of literature on the application of fractals and deterministic chaos in quantum physics 169. In quantum mechanics, there is a possibility of finding an electron in more than one point, as the twovalued boolean logic eitheror does not apply in the range of subatomic processes. Fuzzy systems to quantum mechanics series in machine.
In the present work transfinite fractal sets and fuzzy logic are combined to enable the introduction of a new theory termed fractal logic to the foundation of high energy particle physics. Agenda quantum membership function based adaptive neural fuzzy inference system fuzzy quantum circuits to model emotional behaviors of humanoid robots 3. Freely browse and use ocw materials at your own pace. Although fuzzy logic and fuzzy mathematics is a widespread subject and there is a vast literature about. Steps towards a manyvalued interpretation of quantum mechanics springerbriefs in physics kindle edition by pykacz, jaroslaw.
Introduction quantum mechanics plays a fundamental role in physics for describing the universe. General systems, classical systems, quantum systems and fuzzy. Based on these considerations it is possible to arrive at the schroedinger equation directly from the hamilton. For example, the set of natural numbers n is a borel set, since one can take. From fuzzy sets to fuzzy systems, it also gives clear descriptions on the development on fuzzy logic, where the most important result is the probability presentation of fuzzy systems. This brief presents steps towards elaborating a new interpretation of quantum mechanics based on a specific version of. Fuzzy logic and quantum measurement formulation arxiv. Fuzzy set theory language and ideas are used to express basic quantum logic notions. Quantum mechanical approach to fuzzy logic modelling.
Quantum structures and fuzzy set theory it was argued that lukasiewiczs union and intersection of fuzzy sets or is morphic to them operations on fuzzy sets pointwisely generated by by nilp tent tconorms are, within the uncountable family of possible unionlike and intersectionlike operations on fuzzy sets, the only operations that. Quantum logic and its role in interpreting quantum theory. Lecture on fuzzy logic ppt free download as powerpoint presentation. The possibility of replacing probabilistic interpretation of quantum mechanics by interpretation based on infinitevalued logics and fuzzy set theory is outlined. Such likeness between fuzzy logic and quantum physics can be used for fuzzy modelling.
For instance, fuzzy set theory as logic is more mathematical than crisp sets, bipolar fuzzy set theory as logic is more mathematical than fuzzy sets, and fuzzy sets plus bipolarity naturally lead to definable causality, quantum cognition, and quantum intelligence see fig. Fuzzy time, a solution of unexpected hanging paradox a. The theory of fuzzy sets and systems also appeared as a theory that pertains to quantities that are not describable in terms of classical probability distributions. Finally, since fuzzy sets bear the same relation to infinitevalued logic as do tra.
Quantum physics, fuzzy sets and logic mathematical. A brief survey of main interpretations of quantum mechanics. On classical, fuzzy classical, quantum and fuzzy quantum systems. Editorial general systems, classical systems, quantum. Fuzzy sets and infinitevalued lukasiewicz logic in foundations of quantum. Fuzzy analysis of particle movement in quantum mechanics. They are like logic gates of classical computing world but unlike many classical logic gates, quantum logic gates are.
Hence, fuzzy logic defines appropriately behavior of the quantum computers. If youre looking for a free download links of quantum physics, fuzzy sets and logic. When zadeh established the theory of fuzzy sets and systems three years later, he. And this was very concerning to many physicists of that time. Fuzzy intuitionistic quantum logics called also brouwerzadeh logics represent to non standard version of quantum logic where the connective not is split into two different negation. This is just the beginning, where the predictability of classical physics was over turned by the potentiality of quantum physics. Find materials for this course in the pages linked along the left. We propose a mathematical model based on fuzzy logic methods to identify critical processes. Fuzzy logic models for detection of critical processes in. Similarity between quantum logic and fuzzy logic both quantum logic and fuzzy logic describe uncertainty. Therefore classical mechanics can be viewed as a crisp limit of a fuzzy quantum mechanics. We have tried to convey to students that it is the use of probability amplitudes rather than probabilities that makes quantum mechanics the extraordinary thing that it is, and to grasp that the theorys mathematical structure follows.