The interpretation of quantum mechanics and of probability: Identical role of the observer

📝 Abstract

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’.

💡 Analysis

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’.

📄 Content

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The interpretation of quantum mechanics and of probability:
Identical role of the ‘observer’

Louis Vervoort University of Montreal,
louis.vervoort@umontreal.ca, louisvervoort@hotmail.com 17.06.2011

Abstract. 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‟.

1. Introduction.

A key element of the Copenhagen interpretation of quantum mechanics is the role played by the observer, or rather the observing system. The observing system, or the measurement, makes the wave function collapse. By the same token it causes the „measurement problem‟: why is an observing system any different from any „normal‟ physical system, e.g. the natural environment - which leaves the wave function of the system in its superposition state ? Bohr and Heisenberg are reputed to be the first to have recognized the 2

role of the observing system, giving an „instrumentalist‟ or „operationalist‟ flavor to quantum mechanics: to some, reality seemed to depend on, or be determined by, apparatuses. Since then a further shift in the interpretation of quantum mechanics has been proposed by several authors – a shift towards subjectivism, in which it is now the observer as a human being, including his or her mind, who plays the starry role: along with quantum information theory, Alice and Bob entered the scene. The degree of subjectivism is of course different for different authors, but the most radical of these interpretations (see Section 3.3.) almost impart the impression that quantum mechanics „happens in the head of the subject‟, and leave the reader wondering where the objective basis of science is gone. Besides the standard Copenhagen interpretation, we will in the following investigate some of the better known new interpretations of quantum mechanics, namely „relational quantum mechanics‟ of Rovelli and others [1-4], and the Bayesian or subjective interpretation of quantum probabilities of Bub, Caves, Fuchs, Schack and others [5-7]. As an excellent representative of the classical Copenhagen interpretation, we will use Peres [8-10], especially his textbook [8].

The aim of the present article is to show that the role of the „observer‟ in quantum mechanics is not new: it is exactly the same as he/she/it plays in classical probability theory. More precisely, we will argue 1) that a precise definition of probability (à la von Mises) always refers to an observing system, 2) that (as a consequence) the instrumentalist aspects of the Copenhagen interpretation stem from the probabilistic nature of quantum phenomena, and 3) that also other interpretations of quantum mechanics [1-7] can be re-interpreted, less radically, within the standard interpretation of probability. The „understanding‟ of quantum mechanics, beyond the formalism, would therefore heavily draw on the interpretation of the concept of probability.

Many a physicist will wonder whether anything new can be learned from the interpretation of probability. Is everything about probability not entirely said with Kolmogorov‟s simple axioms, dating from 1933 [11] ? Unfortunately not, else probability theory would not be termed the branch of mathematics in which it is easiest to make mistakes (Ref. [12], p. 4). Indeed, in order to apply probability calculus to the real world as it should one needs to know to which type of events exactly to apply it; in other words, one needs an interpretation of the concept of probability, beyond Kolmogorov‟s axioms. The most widespread interpretation in science is the relative frequency interpretation (in the limit of infinite trial series), which is generally attributed to Richard von Mises [13-14]. (References 3

[13-14] offer, in our view, the most rigorous treatment of all aspects of probability theory, both foundations and calculus, and in particular their link.) However, other interpretations such as the classical interpretation of Laplace, the propensity interpretation of Popper, and the subjective interpretation, associating probability with „degree of belief‟, exist (general references are [15-17] and the condensed [28] Ch. 4). As said, the subjective interpretation regains a vivid interest in the field of quantum mechanics [5-7].
As a matter of fact (and much to our own surprise), it appears that the notion of probability co

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