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Methodological Criteria for the Interpretation of Quantum Mechanics

Paolo Rocchi

Published Sep 2, 2023• 0 citations
Publisher

Abstract

Abstract Over a dozen constructions have been proposed to untangle the foundations of quantum mechanics (QM). The authors have spent a lot of energy in establishing formal solutions but, to the best of my knowledge, have not carefully examined the methodological problems that arise before beginning a theoretical construct in QM. This paper argues on the following methodological obstacles: 1. The definitional and computational formulas. 2. The different theories of probability. We have also tried to solve problems 1 and 2, but the complete illustration of this attempt exceeds an article’s length, so this paper is limited to presenting 1 and 2, and discussing the intellectual and formal assumptions that should be necessary to unify the theories of probability.

DOI
10.21203/rs.3.rs-3302699/v1

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Abstract Over a dozen constructions have been proposed to untangle the foundations of quantum mechanics (QM). The authors have spent a lot of energy in establishing formal solutions but, to the best of my knowledge, have not carefully examined the methodological problems that arise before beginning a theoretical construct in QM. This paper argues on the following methodological obstacles: 1. The definitional and computational formulas. 2. The different theories of probability. We have also tried to solve problems 1 and 2, but the complete illustration of this attempt exceeds an article’s length, so this paper is limited to presenting 1 and 2, and discussing the intellectual and formal assumptions that should be necessary to unify the theories of probability.
(1) Background: Over a dozen constructions have been proposed to untangle the foundations of quantum mechanics (QM). So many irreconcilable schemes raise the suspect that methodological requisites should be discussed before beginning a theoretical construction in QM. In particular, we identify the ensuing issues of methods: formal definitions of particles and waves; incompatible probability theories and the single case problem. (2) Methods of the present inquiry: We tackle the second and third issue with a novel and comprehensive probability theory. Next it applies the theoretical results to quantum physics. (3) Results of the present inquiry: The new probability theory proves how some effects - the impossibility of measuring, the collapse of outcomes, non-locality and counterfactual definiteness - are not exclusive to quantum mechanics but can be observed also in classical context. (4) Conclusions: A probability-based interpretation of quantum mechanics is derived; innovative answers are put forward about quantum dualism, the measurement problem, collapse and the relations between classical and quantum physics.
This is an attempt to clarify certain concepts related to a debate on the interpretation of quantum mechanics, a debate between Khrennikov on the one hand and Stacey and Schack on the other hand. Central to this debate is the notion of quantum probabilities. I first take up the probability concept in the QBist school, as seen from my point of view, and then give my own arguments for the Born formula for calculating quantum probabilities. In that connection, I also sketch some consequences of my approach toward the foundation and interpretation of quantum theory. I discuss my general views on QBism as a possible alternative interpretation of quantum mechanics before I give some final remarks.
This chapter, based on the background information of the previous chapter, will review the formalism of quantum mechanics – its fundamental mathematical structure (the basic contents of Hilbert space representation and operator algebra representation) and physical assumptions (kinematics, dynamics, and measurement theory). These are the premise and foundation for discussing the quantum histories interpretation. Then, in combination with the viewpoints of some literature in recent years, we will explore what is the interpretation of quantum mechanics, analyze the relationship between the theory of quantum mechanics and its interpretation, and declare the author’s basic stance on these two issues. These two are the primary issues that all interpretive work in the philosophy of physics will face (not limited to the interpretation of quantum mechanics), and the necessary clarification here is also conducive to the subsequent discussion. Three common terms – theory, formalism, and interpretation – are explicated and differentiated by offering the necessary definitions of their meanings, based on the works of Acuña and Ruetsche. The clarification will help to make the subsequent related discussions more precise.
This paper calls attention to the current state of the probability (P) domain which presents weak points at the mathematical level and more significant flaws at the application level. Popper notices how fundamental issues raised in quantum mechanics (QM) directly derive from unresolved probabilistic questions. Endless philosophical debates create more problems than solutions, so the author of this research suggests going directly to the root of the issues and searching for the probability theory which formalizes the multifold nature of P. This paper offers a brief overview of the structural theory of probability, recently published in a book, and applies it to QM in order to show its completeness. The whole probability-based interpretation of QM goes beyond the limits of a paper and these pages condense a few aspects of this theoretical scheme. The double slit experiment is used to corroborate the theorems presented here.
Abstract This study calls attention to the current state of the probability ( P ) domain which presents weak points at the mathematical level and more significant flaws at the application level. Popper noticed how fundamental issues raised in quantum mechanics (QM) directly derive from unresolved probabilistic questions. Endless philosophical debates create more problems than solutions, so the author of this research suggests going directly to the root of the issues and searching for the probability theory which formalizes the multifold nature of P . This study offers a brief overview of the structural theory of probability , recently published in a book, and applies it to QM in order to show its completeness. The whole probability-based interpretation of QM goes beyond the limits of a paper and these pages condense a few aspects of this theoretical scheme. The double slit experiment is used to corroborate the theorems presented here.
It is argued that the traditional "realist" methodology of physics, according to which human concepts, laws and theories can grasp the essence of reality, is incompatible with the most fruitful interpretation of quantum formalism. The proof rests on the violation by quantum mechanics of the foundational principles of that methodology. An alternative methodology, in which the construction of sciences finishes at the level of human experience, as standard quantum theory strongly suggests, is then conjectured.