It is argued that the Copenhagen Interpretation of Quantum Mechanics, founded ontologically on the concept of probability, may be questionable in view of the fact that within Probability Theory itself the ontological status of the concept of probability has always been, and is still under discussion.
The article discusses approaches to understanding the nature of probability in mathematics and physics with the consequences of these approaches, as well as the difficulties that arise. The ontological status of probability is discussed. It is shown that probability theory, contrary to R. Mises, should be classified as a mathematical science, using the definition formulated by A.N. Kolmogorov. The application of this definition in practice is provided within the framework of the classical approach, provided that the connection with physical reality is defined through the concept of equal opportunity. To do this, the concepts of simple and complex events are introduced, and the method of decomposing complex events into simple ones is explained. The point of view is substantiated, according to which a mathematical probability determined and related to physical reality in this way can be considered an objective probability, that is, existing independently of any tests. Various interpretations of quantum mechanics and approaches to understanding probability are also revealed. It is shown that in physics today the existing approaches to understanding the nature of probability contradict each other. In the Bohm interpretation, probability is an analogue of the classical approach – statistical objective probability, which has a mathematical formalization, and in quantum Bayesianism, probability quantifies the degree of reliability and depends on the subject conducting the experiment. The Copenhagen interpretation of quantum mechanics tries to eliminate the difficulties associated with combining the wave and corpuscular properties of light and electron beams into a single picture by giving the ontological status of probability, which leads to the problem of understanding physical reality. The article argues for the need for a new connection between the mathematical description of probability and physical reality. The empirical (frequency) approach of R. Mises is analyzed, which causes a lot of criticism, as it does not have a clear consistent formalization. The article argues that this approach is inconsistent with quantum mechanics. The probability given by M. Born in the Copenhagen interpretation of quantum mechanics is also considered, which formulates a new definition of probability, which does not exclude the difficulties associated with the physical interpretation of probability. Born’s approach is based on the classical approach and is reduced to a formal axiomatic definition, which assumes the interpretation of probability as a mathematical construct. The connection of probability with physical reality and the consistency of the statistical method of finding probability values remain unresolved problems, which creates a dualism of understanding probability: in mathematics – one thing, in physics – another. If in the mathematical approach, the solution of these problems is carried out through the connection of probability with physical properties, then in quantum mechanics, in the Copenhagen interpretation, problems persist, which is caused by giving the wave function an ontological status.
The aim of the article is to argue that the interpretations of quantum mechanics and of probability are much closer than usually thought. Indeed, a detailed analysis of the concept of probability (within the standard frequency theory of R. von Mises) reveals that the latter concept always refers to an observing system. The enigmatic role of the observer in the Copenhagen interpretation therefore derives from a precise understanding of probability. Besides explaining several elements of the Copenhagen interpretation, our model also allows to reinterpret recent results from 'relational quantum mechanics', and to question the premises of the 'subjective approach to quantum probabilities'.
The debate of all debates in modern physics has long been the question concerning the completeness of Quantum Mechanics, a controversy owing to the statistical mathematical treatment at its foundation. Because probability or statistical theory is overwhelmingly a numeric science with no contemplation or inference with regards to causation and determinants of action, physicists have always felt that the Quantum theory is at a miss when it comes to intimately intelligible interpretation of dynamic systems. Even the proponents from the Quantum School of Copenhagen felt that a philosophical justification was necessary in order to at least provide a view as to the analytic implications of the Quantum Theory, notwithstanding the pressure brought to bear onto them by compelling critics. Amidst this hurly-burly, little to no attention was ever paid to the dimension of discrete Quantum expression in the macrocosm thru the application of the same science of Probability Theory. In the following, we re-examine Probability Theory to show that it encloses a discrete ontological dimension that is universally applicable to all objects permeable to probabilistic treatment, thereby directly relating macroscopic dynamics to quantum dynamics on the basis of a unique Unification theory.
The aim of the article is to argue that the interpretations of quantum mechanics and of probability are much closer than usually thought. Indeed, a detailed analysis of the concept of probability (within the standard frequency interpretation of R. von Mises) reveals that this notion always refers to an observing system. Therefore the instrumentalist aspects of quantum mechanics, and in particular the enigmatic role of the observer in the Copenhagen interpretation, derive from a precise understanding of probability.
The Copenhagen interpretation of quantum theory is investigated from a philosophical point of view. It is justified the opinion that the philosophical attitude the Copenhagen interpretation is based on is in principle inevitable for a real comprehension of quantum theory. This attitude is mainly related to epistemological arguments. However, the measurement problem often seems not to be treated clearly enough within the interpretation. By referring to the property of the necessity to use macroscopic measurement instruments obeying classical concepts it is made the attempt to solve the measurement problem. According to this consideration the indeterministic character of quantum theory seems to have its origin in a lack of knowledge and thus it appears in a similar but more principle way than in statistical mechanics. It is emphasized the ontological character of the uncertainty relation and the related non locality of quantum theory suggesting that the existence of a position space is not as fundamental as the assumptions of general quantum theory.
Abstract Many theories and models from physics are probabilistic. This observation raises several philosophical questions: What are probabilities in physics? Do they reflect objective chances which exist independently of the human mind? Or do they only express subjective credences and thus capture our own uncertainty about the world? Finally, which metaphysical lessons, if at all, can one draw from the largely probabilistic character of physics? The chapters collected in this volume address these questions and provide a detailed philosophical appraisal of the status of probabilities in all of physics. Particular emphasis is laid upon statistical physics and quantum mechanics. Many chapters reflect a desire to understand probabilities from physics as objective chances. These chances are characterized, e.g., as time-averages, as probabilities from a best system in the terms of David Lewis, or using the Boltzmannian typicality approach. Other chapters are sympathetic to a Bayesian view of probabilities in physics. The chapters about quantum mechanics elucidate the peculiar characteristics of quantum correlations and discuss strategies to justify the Born Rule. Finally, the chapters of this volume demonstrate how closely interpretive issues about probabilities are entangled with other foundational problems of physics such as the Reversibility Paradox, the ontology of the quantum world and the question whether the world is deterministic.