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Physics Today

Thermodynamics constrains interpretations of quantum mechanics

Steven K. Blau

Published Dec 16, 2016• 0 citations
Publisher

Abstract

Theories that incorporate hidden variables are consistent with quantum mechanics only if the systems they describe can store unlimited information.
DOI
10.1063/pt.5.7331

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In this paper, we shall show how the theory of measurements is to be understood from the point of view of a physical interpretation of the quantum theory in terms of "hidden" variables, developed in a previous paper. We find that in principle, these "hidden" variables determine the precise results of each individual measurement process. In practice, however, in measurements that we now know how to carry out, the observing apparatus disturbs the observed system in an unpredictable and uncontrollable way, so that the uncertainty principle is obtained as a practical limitation on the possible precision of measurements. This limitation is not, however, inherent in the conceptual structure of our interpretation. We shall see, for example, that simultaneous measurements of position and momentum having unlimited precision would in principle be possible if, as suggested in the previous paper, the mathematical formulation of the quantum theory needs to be modified at very short distances in certain ways that are consistent with our interpretation but not with the usual interpretation.We give a simple explanation of the origin of quantum-mechanical correlations of distant objects in the hypothetical experiment of Einstein, Podolsky, and Rosen, which was suggested by these authors as a criticism of the usual interpretation.Finally, we show that von Neumann's proof that quantum theory is not consistent with hidden variables does not apply to our interpretation, because the hidden variables contemplated here depend both on the state of the measuring apparatus and the observed system and therefore go beyond certain of von Neumann's assumptions.In two appendixes, we treat the problem of the electromagnetic field in our interpretation and answer certain additional objections which have arisen in the attempt to give a precise description for an individual system at the quantum level.
In this paper a 'hidden variables' interpretation of the quantum world is presented. A hidden variables explanation assumes current quantum mechanical theories are imperfect in that they do not incorporate a physical reality to the quantum world. At the Solvay conference of 1927, Louis De Broglie presented a hypothesis which was to be the forerunner to hidden variables theory: at the quantum level, a 'matter wave' steered particles. Under the powerful influence of Neils Bohr, Louis De Broglie's matter wave was disregarded in favor of the 'Copenhagen Interpretation' championed by Bohr himself, and the Copenhagen interpretation became the de facto accepted theory of quantum mechanics. In 1932, John Von Neumann presented a supposed that no hidden variables theory could properly describe the quantum world. He was first shown to be wrong by Grete Hermann, but she was largely ignored do to Neumann's immense stature as a mathematician. Later in 1966, John Bell further established that the proof was flawed, and the hidden variables interpretation has since seen a renewal of interest amongst researchers. The model presented in this paper incorporates d-branes and Type I strings into a hidden variables quantum structure; this physical structure can be interpreted as both 10-dimensional and 11- dimensional, and is designated: the D-string.
Quantum information, which studies the representation of information by quantum mechanical systems and the type of information processing this makes possible, is a relatively new field. Its roots, however, go back to early discussions of the interpretation of the quantum mechanical formalism. In 1935 Einstein, Podolsky and Rosen suggested that there were interpretational issues with quantum mechanics, having to do with local realism. Einstein was puzzled by an apparent lack of locality in quantum mechanical descriptions of reality, and suggested that quantum mechanics was not a complete theory. This stimulated a subsequent series of theoretical and experimental investigations. In particular, John Bell realized that Einstein's proposal for a ‘completion’ of quantum mechanics by the addition of more variables – called ‘hidden’ variables – was not consistent with quantum predictions, and could not be carried out. While these interpretational issues set the stage for what followed, the modern field of quantum information arose in the 1980s stimulated by the ever decreasing size of the elements in information processing circuits. It was realized that at some point a threshold would be crossed and the devices would start to exhibit quantum mechanical behavior. It was first determined that, if they did, it would not present a problem, and, in addition, it could even be advantageous. This led to the idea of a quantum computer that stores information in quantum states, or ‘qubits’, rather than as binary digits, or ‘bits’, in a standard digital computer. The field took off when, in 1994, Peter Shor found an efficient quantum algorithm for finding the prime factors of an integer.