An Investigation on the Basic Conceptual Foundations of Quantum Mechanics by Using the Clifford Algebra
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Advanced Studies in Theoretical Physics 5 (11):485-544 (2011)
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 A(Si) and i,±1 N 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. In detail we realize a bare bone skeleton of quantum mechanics recovering all the basic foundations of this theory on an algebraic framework. We give proof of the quantum like Heisenberg uncertainty relations using only the basic support of the Clifford algebra. In addition we demonstrate the well known phenomenon of quantum Mach Zender interference using the same algebraic framework, as well as we give algebraic proof of quantum collapse in some cases of physical interest by direct application of the theorem that we derive to elaborate the i,±1 N algebra. We also discuss the problem of time evolution of quantum systems as well as the changes in space location, in momentum and the linked invariance principles. We are also able to re-derive the basic wave function of standard quantum mechanics by using only the Clifford algebraic approach. In this manner we obtain a full exposition of standard quantum mechanics using only the basic axioms of Clifford algebra. We also discuss more advanced features of quantum mechanics. In detail, we give demonstration of the Kocken-Specher theorem, and also we give an algebraic formulation and explanation of the EPR paradox only using the Clifford algebra. 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, as it is well known, are interpreted as logical statements, following the basic von Neumann results. Von Neumann realized a matrix logic on the basis of quantum mechanics. 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. Therefore, it seems that we may conclude that quantum mechanics, as it appears when investigated by the Clifford algebra, is a two-faced theory in the sense that it looks from one side to “matter per se”, thus to objects but simultaneously also to conceptual entities. We advance the basic conclusion of the paper: There are stages of our reality in which we no more can separate the logic ( and thus cognition and thus conceptual entity) from the features of “matter per se”. In quantum mechanics the logic, and thus the cognition and thus the conceptual entity-cognitive performance, assume the same importance as the features of what is being described. We are at levels of reality in which the truths of logical statements about dynamic variables become dynamic variables themselves so that a profound link is established from its starting in this theory between physics and conceptual entities. Finally, in this approach there is not an absolute definition of logical truths. Transformations , and thus … “redefinitions”…. of truth values are permitted in such scheme as well as the well established invariance principles, clearly indicate
|Keywords||Clifford algebra, foundations of quantum mechanics, wave function collapse, quantum mechanics and conceptual entities, von Neumann postulates on quantum measurement|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Elio Conte (2011). On the Logical Origins of Quantum Mechanics Demonstrated By Using Clifford Algebra. Neuroquantology 9 (2):231-242.
Elio Conte (2011). On the Logical Origins of Quantum Mechanics Demonstrated By Using Clifford Algebra: A Proof That Quantum Interference Arises in a Clifford Algebraic Formulation of Quantum Mechanics. Electronic Journal of Theoretical Physics 8 (25):109-126.
Elio Conte (2011). On the Logical Origins of Quantum Mechanics Demonstrated by Using Clifford Algebra. Electronic Journal of Theoretical Physics 8 (25):109-126.
Elio Conte (2010). A Preliminary Experimental Verification of Violation of Bell Inequality in a Quantum Model of Jung Theory of Personality Formulated with Clifford Algebra. Journal of Consciousness Exploration and Research 1 (7):831-849.
Ernst Binz, Maurice A. De Gosson & Basil J. Hiley (2013). Clifford Algebras in Symplectic Geometry and Quantum Mechanics. Foundations of Physics 43 (4):424-439.
Elio Conte (2012). What is The Reason to Use Clifford Algebra in Quantum Cognition? Part I: “It From Qubit” On The Possibility That the Amino Acids Can Discern Between Two Quantum Spin States. Neuroquantology 10 (3):561-565.
Elio Conte (forthcoming). Are Information, Cognition and the Principle of Existence Intrinsically Structured in the Quantum Model of Reality? Open Systems and Information Dynamics.
Elio Conte (forthcoming). Reconsideration of Quantum Foundations. Vaxjo University Conference ,15-18 June –2009 : A Clifford Algebraic Analysis and Explanation of Wave Function Reduction in Quantum Mechanics. [REVIEW] In Vaxio University -Sweeden (ed.), Proceedings Vaxjo Conference on Foundations of quantum mechanics.
Elio Conte, On Some Cognitive Features of Clifford Algebraic Quantum Mechanics and the Origin of Indeterminism in This Theory: A Derivation of Heisenberg Uncertainty Principle by Using the Clifford Algebra.
Elio Conte (2012). May We Verify Non-Existing Dispersion Free Ensembles By Application of Quantum Mechanics in Experiments at Perceptive and Cognitive Level? Neuroquantology 10 (1):14-19.
Elio Conte (2012). On Some Considerations of Mathematical Physics: May We Identify Clifford Algebra as a Common Algebraic Structure for Classical Diffusion and Schrödinger Equations? Advanced Studies in Theoretical Physics 6 (26):1289-1307.
Peter Kosso (2000). Quantum Mechanics and Realism. Foundations of Science 5 (1):47-60.
Elio Conte, A Proof That Quantum Interference Arises in a Clifford Algebraic Formulation of Quantum Mechanics.
Nicholas Maxwell (1976). Towards a Micro Realistic Version of Quantum Mechanics, Part I. Foundations of Physics 6 (3):275-292.
Added to index2012-11-13
Total downloads29 ( #65,832 of 1,139,990 )
Recent downloads (6 months)4 ( #48,755 of 1,139,990 )
How can I increase my downloads?