Fuzzy theory applied to quantum physics and quantum. Download it once and read it on your kindle device, pc, phones or tablets. Introduction quantum mechanics plays a fundamental role in physics for describing the universe. In contrast to fuzzy logic, the logic is not based on membership values but on vector subspaces identified by projectors. General systems, classical systems, quantum systems and fuzzy. Quantum logic was developed in the context of quantum mechanics. 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. Quantum physics, fuzzy sets and logic springerlink. Quantum measurement, fuzzy logic, fuzzy set theory. On classical, fuzzy classical, quantum and fuzzy quantum systems. 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. 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. Fuzzy analysis of particle movement in quantum mechanics. Fuzzy logic is something like, there is another possible way except 0 and 1.
Reasoning in quantum theory sharp and unsharp quantum logics. Studies quantum physics, logic and foundations of mathematics, and. Since, quantum computing works on qubits at a nanoscale, the behavior observed is very much dependent on laws of probability, like heisenbergs uncertainty principle. And this was very concerning to many physicists of that time. On the need for fractal logic in high energy quantum physics.
Quantum physics, fuzzy sets and logic steps towards a manyvalued interpretation of quantum mechanics. Hence, fuzzy logic defines appropriately behavior of the quantum computers. Quantum complexity theory siam journal on computing. Editorial general systems, classical systems, quantum. Pdf on the relation between fuzzy and quantum logic. Such likeness between fuzzy logic and quantum physics can be used for fuzzy modelling.
When zadeh established the theory of fuzzy sets and systems three years later, he. Quantum mechanical approach to fuzzy logic modelling. 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. Birkhoffvon neumann quantum logic as infinitevalued lukasiewicz logic. 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. Is fuzzy logic used in science, and more specifically in. Quantum logic and its role in interpreting quantum theory. 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. In particular, the present authors integrated cantor sets and fractals as well as number. 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. What does quantum mechanics imply for classical logic. This is just the beginning, where the predictability of classical physics was over turned by the potentiality of quantum physics. 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.
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. Quantum physics, fuzzy sets and logic mathematical. Find materials for this course in the pages linked along the left. Fuzzy logic and quantum measurement formulation arxiv. Yet, the typical quantum mechanics texts for physics students are not written in a style that mechanical engineering students would likely feel comfortable with. 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. Agenda quantum membership function based adaptive neural fuzzy inference system fuzzy quantum circuits to model emotional behaviors of humanoid robots 3. Steps towards a manyvalued interpretation of quantum mechanics springerbriefs in physics pdf, epub, docx and torrent then this site is not for you. Fuzzy sets and infinitevalued lukasiewicz logic in foundations of quantum. This leads naturally to a new look at quantum gravity.
There is a large body of literature on the application of fractals and deterministic chaos in quantum physics 169. Currently i am a 2nd year undergraduate student in the physics department at utah state university. Quantum measurement, fuzzy logic, fuzzy set theory pacs. Finally, since fuzzy sets bear the same relation to infinitevalued logic as do tra. Steps towards a manyvalued interpretation of quantum mechanics springerbriefs in physics on free shipping on qualified orders.
The properties of a system correspond to sets of states. The road from fuzzy sets to definable causality and. They are like logic gates of classical computing world but unlike many classical logic gates, quantum logic gates are. It begins with a short survey of main interpretations of quantum mechanics already proposed, as well as various models of manyvalued logics and. Fuzzy set theory language and ideas are used to express basic quantum logic notions. Our first result is the existence of an efficient universal quantum turing machine in deutschs model of a quantum turing machine qtm proc. A brief survey of main interpretations of quantum mechanics. Quantum mechanics is a probabilistic theory, sure, but we still work within welldefined sets i.
Piron considers for example a point particle, for which the set of states. Soleimani2, shahidan radiman1 1school of applied physics, universiti kebangsaan malaysia 43600 ukm, bangi selangor, malaysia email address. Since relations between fuzzy sets and infinitevalued logic are the same as. The possibility of replacing probabilistic interpretation of quantum mechanics by interpretation based on infinitevalued logics and fuzzy set theory is outlined. Fuzzy time, a solution of unexpected hanging paradox a. This brief presents steps towards elaborating a new interpretation of quantum mechanics based on a specific version of. Quantum physics is the study of the behavior of matter and energy at the molecular, atomic, nuclear, and even smaller microscopic levels. Pdf fuzzy logic is a wellestablished formalism in computer science being. A concept that is intuitively similar to the principle of superposition in quantum computing is fuzzy logic. 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. This brief presents steps towards elaborating a new interpretation of quantum mechanics based on a specific version of lukasiewicz infinitevalued logic.
Similarity between quantum logic and fuzzy logic both quantum logic and fuzzy logic describe uncertainty. Using fuzzy sets, an element may belong to more than one set. Use features like bookmarks, note taking and highlighting while reading quantum physics, fuzzy sets and logic. Quantum fuzzy logic mohammaed saed haj ali kinda altarbouch 2. If youre looking for a free download links of quantum physics, fuzzy sets and logic. Freely browse and use ocw materials at your own pace. Fuzzy systems to quantum mechanics series in machine. Pdf on classical, fuzzy classical, quantum and fuzzy. Also, the coverage often does not seem to be intended to emphasize understanding of the largerscale quantum system that a. Quantum physics, fuzzy sets and logic steps towards a many. Although fuzzy logic and fuzzy mathematics is a widespread subject and there is a vast literature about. Fuzzy logic models for detection of critical processes in. In the early 20th century, scientists discovered that the laws governing macroscopic objects do not function the same in such small realms.
Lecture on fuzzy logic ppt free download as powerpoint presentation. Quantum physics, fuzzy sets and logic steps towards a. Tells me that you are not just regurgitating facts, but you also analyze them and ask appropriate questions. For example, the set of natural numbers n is a borel set, since one can take. One of the purposes of this paper is to bring together fuzzy logic and quantum mechanics. Quantum logic and its role in interpreting quantum theory gelo noel m. Covers all topics, including wave particle duality, schrodingers cat, epr bell inequality, and the relationship between measurement and entanglement.
Pdf the manyvalued logic of quantum mechanics researchgate. 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. In this paper we study quantum computation from a complexity theoretic viewpoint. Quantum structures and fuzzy set theory sciencedirect. One attempts to build up classical physics, including classical logic, on these quantum foundations.
Quantum logic and quantum probability theory represent important. Why everything you thought you knew about quantum physics. 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. Steps towards a manyvalued interpretation of quantum mechanics springerbriefs in physics kindle edition by pykacz, jaroslaw. 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. Assignments quantum physics i physics mit opencourseware. Therefore classical mechanics can be viewed as a crisp limit of a fuzzy quantum mechanics. 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.