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World Journal of Neuroscience

A Clifford algebraic analysis gives mathematical explanation of quantization of quantum theory and delineates a model of quantum reality in which information, primitive cognition entities and a principle of existence are intrinsically represented ab initio

Elio Conte

Published Jan 1, 2013• 14 citations
Publisher

Abstract

The thesis of this paper is that Information, Cognition and a Principle of Existence are intrinsically structured in the quantum model of reality. We reach such evidence by using the Clifford algebra. We analyze quantization in some traditional cases of quantum mechanics and, in particular in quantum harmonic oscillator, orbital angular momentum and hydrogen atom. The results are confirmed analyzing human cognition behavior that evidences a very consistent agreement with the basic quantum mechanical foundations.

DOI
10.4236/wjns.2013.33021

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The thesis of this paper is that Information, Cognition and a Principle of Existence are intrinsically structured in the quantum model of reality. We reach such evidence by using the Clifford algebra. We analyze quantization in some traditional cases of quantum mechanics and, in particular in quantum harmonic oscillator, orbital angular momentum and hydrogen atom. The results are confirmed analyzing human cognition behavior that evidences a very consistent agreement with the basic quantum mechanical foundations.
The thesis of this paper is that Information, Cognition and a Principle of Existence are intrinsically structured in the quantum model of reality. There is an intrinsic “factor of knowledge” that supports its structure. We reach such evidence by using the Clifford algebra. In detail we analyze quantization in some traditional cases of interest in quantum mechanics and, in particular, in quantum harmonic oscillator, orbital angular momentum and hydrogen atom. We adopt the basic von Neumann results that projection operators represent logical statements and we demonstrated that are intrinsically structured in the cases of quantization that are taken in consideration. NeuroQuantology | March 2013 | Volume 11 | Issue 1| Page 34-46
First Paragraph... We retain important to add some further comments to our recent submission to NeuroQuantology (Conte, 2013a; Conte, 2013b; Conte and Todarello, 2013). The thesis of the paper is that Information, Cognition and a Principle of Existence are intrinsically structured in the quantum model of reality. There is an intrinsic “factor of knowledge” that supports its structure from its starting. We reach such evidence by using the Clifford algebra. In detail we analyze quantization in some traditional cases of interest in quantum mechanics and, in particular, in quantum harmonic oscillator, orbital angular momentum and hydrogen atom. We adopt the basic von Neumann results that projection operators represent logical statements and we demonstrate that are intrinsically structured in the cases of quantization that are taken in consideration. NeuroQuantology | September 2013 | Volume 11 | Issue 3 | Page 503-506
We review our approach to quantum mechanics adding also some new interesting results. We start by giving proof of two important theorems on the existence of the and Clifford algebras. This last algebra gives proof of the von Neumann basic postulates on the quantum measurement explaining thus in an algebraic manner the wave function collapse postulated in standard quantum theory. In this manner we reach the objective to expose a self-consistent version of quantum mechanics. We give proof of the quantum like Heisenberg uncertainty relations, the phenomenon of quantum Mach Zender interference as well as quantum collapse in some cases of physical interest We also discuss the problem of time evolution of quantum systems as well as the changes in space location. We also give demonstration of the Kocken-Specher theorem, and also we give an algebraic formulation and explanation of the EPR . By using the same approach we also derive Bell inequalities. Our formulation is strongly based on the use of idempotents that are contained in Clifford algebra. Their counterpart in quantum mechanics is represented by the projection operators that are interpreted as logical statements, following the basic von Neumann results. Using the Clifford algebra we are able to invert such result. According to the results previously obtained by Orlov in 1994, we are able to give proof that quantum mechanics derives from logic. We show that indeterminism and quantum interference have their origin in the logic.
The aim of such paper is to explain in detail the foundations of quantum cognition and to evidence the manner in which our pioneering experiments on quantum interference in humans should be correctly interpreted in the framework of a correct quantum mechanical elaboration. Often, studies on quantum cognition are elaborated from some authors evidencing that presently we have empirical evidence that the application of quantum rules gives better results respect to classical ones. Consequently, such studies are delineated as empirical tentative. It is not true. Quantum cognition is a scientific realization structured about robust quantum foundations and this is the reason because it gives such important results. Consequently, we discuss the evidence to correctly explain the foundations of this emerging discipline. In order to reach this objective we analyze the fundamental role of the abstract entity that is called quantum mechanical wave function. Soon after we describe the manner in which quantum operators must be entered in cognition studies by using the projectors that represent logic statements and thus relate directly our cognitive functions. We also discuss in detail the logical origins of quantum mechanics outlining that it does not represent a physical theory looking at the matter at microscopic level but a God Giano two faces looking simultaneously to material and to mental reality. We also discuss results establishing the nature of our consciousness and the unquestionable result that it obeys to the basic rules of quantum mechanics. We also give a further and pressing indication: in quantum cognition studies the quantum wave function must be intended as reconstructed experimentally a posteriori in our cognitive studies and cannot be confused with the standard examining elaboration that is used in usual textbooks of quantum mechanics. Also the question of the order effect is analyzed in detail using the important notion of reaction time of psychology. In substance, we give a total reformulation of the current quantum cognition studies evidencing that previous elaborations finalized to present the current status of this discipline as empirical tentative to characterize a quantum cognitive modelling result to be only approximate, incorrect and confusing prospects that damage the information about the robust structure of quantum cognition and therefore need to be rejected.
The conceptuality interpretation of quantum mechanics proposes that quantum entities have a conceptual nature, interacting with the material world through processes that are the physical counterpart of the meaning-based processes, which typically occur in human cognition. This interpretation emerged from the early developments in quantum cognition , a field that uses quantum mathematics to model human cognitive activity. It benefited from the specific approach taken by the Brussels research group , modelling concepts themselves as quantum entities and minds as measuring apparatus. The article sketches the essential steps of the intellectual journey, going from the first applications of quantum notions and formalisms to human cognition to the proposal of a potentially groundbreaking interpretation of quantum mechanics, offering profound explanations for major quantum phenomena. This was done by drawing numerous parallels with the human conceptual domain and suggesting the existence of a level of cognitive activity that would underlie our physical reality. This means that an increased cross-fertilization between the conceptuality interpretation and quantum cognition is to be expected in the future, both of which are synergistic in furthering our understanding of the nature of reality. This is the first part of a two-part article. In the second part, which can be read independently of the first, the successes of the interpretation will be described in a more systematic way, providing a brief overview of what has been achieved so far. This article is part of the theme issue ‘Quantum theory and topology in models of decision making (Part 1)’.