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Advanced Studies in Theoretical Physics

Two experiments from the perspective of the structural probability theory

Paolo Rocchi

Published Jan 1, 2025• 0 citations
Publisher

Abstract

Current literature presents about a dozen probability (P) interpretations: frequentist, Bayesian etc. Each one illustrates a partial aspect of indeterminism and turns out to be incompatible with the others on the logical plane. Basically, every model of P deals with a specific relation of P with the world and this fragmentary theorization inevitably has negative impact on quantum physics which is intrinsically indeterministic. Popper believed that the base issues of quantum mechanics cannot be untangled unless the unified probability theory is set up. So, we have conducted an attempt to integrate all the probability models and used the theoretical results to interpret quantum duality, wave collapse and measurement. The entire work, published in a recent book, exceeds the limits of this paper. Here we put forward a summary that concisely recalls the main definitions and five theorems out fifteen that have been proved. Finally, these theoretical tools will be used to discuss a thought experiment of Einstein and the Wheeler experiment. This proposal has the following features: (1) It addresses classical and quantum issues using the same theorems; (2) It develops a quantum interpretation that agrees with intuition and refutes disputable and bizarre views.

DOI
10.12988/astp.2025.92139

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Current literature presents about a dozen probability (P) interpretations: frequentist, Bayesian etc. Each one illustrates a partial aspect of indeterminism and turns out to be incompatible with the others on the logical plane. Basically, every model of P deals with a specific relation of P with the world and this fragmentary theorization inevitably has negative impact on quantum physics which is intrinsically indeterministic. Popper believed that the base issues of quantum mechanics cannot be untangled unless the unified probability theory is set up. So, we have conducted an attempt to integrate all the probability models and used the theoretical results to interpret quantum duality, wave collapse and measurement. The entire work, published in a recent book, exceeds the limits of this paper. Here we put forward a summary that concisely recalls the main definitions and five theorems out fifteen that have been proved. Finally, these theoretical tools will be used to discuss a thought experiment of Einstein and the Wheeler experiment. This proposal has the following features: (1) It addresses classical and quantum issues using the same theorems; (2) It develops a quantum interpretation that agrees with intuition and refutes disputable and bizarre views.
(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 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.
Waves and particles are alternative modes of being for the elements of atomic dimensions. This feature appears to be evident at the experimental level but remains a conundrum at the theoretical level. The squared wavefunction |Ψ|2 yields the probability of finding a particle at a particular position and time, namely, the wave is conceived as a derivation or a physical condition of the particle and not a condition of the quantum. What the wavefunction represents, whether it really exists, whether it is a purely formal representation and if the observer influences the wavefunction are the major arguments of quantum mechanics (QM). The double nature of electrons, photons, and so on has been clearly recognized, and the two natures should be established by precise formulations. This work adheres totally to this methodological criterion and puts forward two formal definitions. The measurement process and wave collapse problems are also discussed. Finally, we verify the theoretical conclusions using the double slit experiment and the photoelectric effect. Probability plays a crucial role in the quantum literature, and the definitions of the wave and the particle should be illustrated by exploiting the probability theory; however, the various probability theories are not univocal and propose irreconcilable views. Therefore, in a preliminary stage, we unify the ontological and epistemic interpretations of probability using four theorems that have been already published. In summary, this work is developed on the basis of two methodological criteria, which seek to improve the probability theory and fix the definitional formulas of QM.
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.
The interpretation of quantum mechanics has been disputed ever since the advent of the theory in the 1920’s. Famous are the discussions over long time between Einstein and Bohr. Einstein refused to accept the so‐called Copenhagen interpretation, where the wave function collapses at a measurement and where the outcome of the measurement is essentially accidental (“God does not play dice”). Alternative interpretations have appeared, but the Copenhagen school has dominated the thoughts throughout the decades. One interesting interpretation was formulated in 1957 by Hugh Everett at Princeton, a student of John Wheeler, which abandons the wave‐function collapse. In this model the universe is governed entirely by the Schrödinger equation, which does not allow for any collapse. In Everett’s model after a measurement the wave function is separated into different branches that do not interact. This model was left unnoticed for long time until Bryce DeWitt took it up in 1970 and termed it “Many‐Worlds Interpretation”, a term that in some sense is misleading. Everett’s model is incomplete, and it was later supplemented by the theory of decoherence, which explains how the different branches decouple as a result of the interaction with the environment. This extended model has in recent years gained increased respect, and some believe that it is the only model made available so far that is fully consistent with quantum mechanics. This interpretation can also shed some light on the development of the universe and, in particular, on the so‐called Anthropic principle, which puts human beings at the center of the development.