Definition of Time in Non-Relativistic Quantum Mechanics from the Perspective of Bridgman’s Operationalism

M. Cavaglià, Александр Тихонович Филиппов, V. de Alfaro

Jakub Róg

Bridgman’s operationalism imposes a set of methodological requirements on its proponents, which become untenable when applied to the definition of time within the formalism of non-relativistic quantum mechanics. This paper explores the operational definition of time and investigates how far it can be aligned with the core principles of operationalism. To this end, Busch’s (2008) framework, which distinguishes three roles of time in the quantum mechanical formalism, is employed. One of these roles introduces demands that operationalism cannot meet without compromising its essential principles. As a result, it seems reasonable to conclude that operationalism and quantum mechanics are incompatible (at least in the context of the problem of time in quantum mechanics).

Marcos Amaku, Francisco Antônio Bezerra Coutinho, F. Masafumi Toyama

The usual definition of the time evolution operator e−iHt/ℏ=∑n=0∞1n!(−iℏHt)n, where H is the Hamiltonian of the system, as given in almost every book on quantum mechanics, causes problems in some situations. The operators that appear in quantum mechanics are either bounded or unbounded. Unbounded operators are not defined for all the vectors (wave functions) of the Hilbert space of the system; when applied to some states, they give a non-normalizable state. Therefore, if H is an unbounded operator, the definition in terms of the power series expansion does not make sense because it may diverge or result in a non-normalizable wave function. In this article, we explain why this is so and suggest, as an alternative, another definition used by mathematicians.

H. D. Zeh

The concept of time as used in various applications and interpretations of quantum theory is briefly reviewed.

Zbysław Horbaczewski

The article presents the stance taken by the creator of operationism P. W. Bridgman in a dispute about a possibility of interpreting deterministically the results of quantum mechanics. A natural consequence of a gnoseological view created by Bridgman and called operationism is recognition that the indeterministic Copenhagen interpretation of the results of quantum mechanics, called "orthodox" by Bridgman, is the only possible interpretation at the present state of physics. Only new empirical facts, if they are discovered, may - according to Bridgman - pave the way for deterministic description of phenomena occurring in the microworld. This thesis of Bridgman is questioned by the author who tends to share a view that it is rather the appearance of a new theoretical concept that may allow for a new deterministic interpretation of empirical facts known for a long time.

Juan Eduardo Reluz Machicote