(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.
(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.
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.
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.
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.
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.
Quantum mechanics famously posits two distinct evolution rules for the state of a system: a deterministic, unitary time evolution under the Schr¨odinger equation, and a probabilistic “collapse” of the wavefunction upon measurement as dictated by the Born rule. The apparent inconsistency of these two dynamical laws – one continuous and one discontinuous – constitutes the quantum measurement problem. This foundational problem, which underlies the emergence of definite outcomes from quantum superpositions, has persisted since the theory’s inception. In this review, we present a comprehensive and rigorous examination of the measurement problem and survey the leading approaches that seek to resolve or circumvent it. We begin by formulating the measurement problem and its conceptual challenges. We then discuss in detail the major interpretations of quantum mechanics and theoretical frameworks addressing the problem: the Copenhagen interpretation, Everett’s many-worlds interpretation, de Broglie–Bohm pilot-wave theory, objective collapse models, the role of decoherence and environment-induced superselection, and epistemic approaches such as QBism. For each interpretation, we describe the core principles and mathematical formalism, assessing how (and whether) it attempts to solve the measurement problem. We also review modern developments and experiments relevant to quantum measurements, including tests of Bell inequalities, observations of decoherence and macroscopic superpositions, weak measurements and quantum eraser experiments, and thought experiments ‘a la Wigner’s friend. We highlight how these results inform the ongoing debate. Finally, we discuss open problems and challenges that remain in fully resolving the measurement problem.