Questionable and Unquestionable in Quantum Mechanics

TL;DR

This paper explores the foundational differences between quantum mechanics and classical probability, proposing a broad operational framework that encompasses quantum theory without relying on traditional Hilbert space formalism.

Contribution

It introduces a general operational-probabilistic scheme for describing physical systems, contrasting it with quantum mechanics and examining their relationship.

Findings

Operational framework based on observable events and empirical laws

Quantum mechanics can be viewed as a special case of the broader operational theory

Highlights the conceptual distinctions between quantum and classical probabilistic descriptions

Abstract

According to the Kolmogorovian Censorship Hypothesis, everything that quantum theory says about the world in the language of the quantum mechanical Hilbert space formalism is actually about relationships between ordinary relative frequencies expressible in operational terms using classical Kolmogorovian probability theory. In other words, a quantum theoretical description of a system should in principle be translatable into a purely operational-probabilistic description. However, our goal in this paper is different; we do not want to deal with the problem how to translate the known theory of quantum mechanics into operational terms, or to reconstruct the theory from postulates which can be interpreted in operational terms. Our aim is somewhat broader and points in the opposite direction. We start with a general scheme for the operational description of an arbitrary physical system. The description is based solely on the notion of observable events (measurement operations and measurement results) and on general, empirically established simple laws concerning their relative frequency. These laws are so simple and fundamental that they apply equally to any physical system. In the first part of the paper, we outline the basic elements of such an operational-probabilistic theory. In the second part, we discuss how this operational-probabilistic description compares to the quantum mechanical description and to what extent the standard Hilbert space quantum mechanics can be regarded as a reformulation of the general operational-probabilistic theory.