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Philosophy of Science

Is Quantum Mechanics Pointless?

Frank Arntzenius

Published Dec 1, 2003• 27 citations
Publisher

Abstract

There exist well-known conundrums, such as measure-theoretic paradoxes and problems of contact, which, within the context of classical physics, can be used to argue against the existence of points in space and space-time. I examine whether quantum mechanics provides additional reasons for supposing that there are no points in space and space-time.

DOI
10.1086/377421

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There exist well-known conundrums, such as measure-theoretic paradoxes and problems of contact, which, within the context of classical physics, can be used to argue against the existence of points in space and space-time. I examine whether quantum mechanics provides additional reasons for supposing that there are no points in space and space-time.
The formalism of quantum mechanics produces spectacular results, but its rules, its parameters are empirical, either deduced from classical physics, or from experimental results rather than from the postulates. Thus, quantum mechanics is purely phenomenological; for instance, the computation of the eigenvalues of the energy is generally a simple interpolation in the discrete space of the quantum numbers. The attempts to show that quantum electrodynamics is more precise than classical electrodynamics are based on wrong computations. The lack of paradoxes in the classical theory, the appearance of classical, true interpretations of the wave-particle duality justify the criticism of Ehrenfest and Einstein. The obscurity of the quantum concepts leads to wrong conclusions that handicap the development of physics. Just as building a laser was considered absurd before the first maser worked, the concept of photon leads to deny a type of coherent Raman scattering necessary to understand some redshifts of spectra in astrophysics, and able to destroy the two fundamental proofs to the expansion of the universe.
Gibbs paradox in the context of statistical mechanics addresses the issue of additivity of entropy of mixing gases. The usual discussion attributes the paradoxical situation to classical distinguishability of identical particles and credits quantum theory for enabling indistinguishability of identical particles to solve the problem. We argue that indistinguishability of identical particles is already a feature in classical mechanics and this is clearly brought out when the problem is treated in the language of information and associated entropy. We pinpoint the physical criteria for indistinguishability that is crucial for the treatment of the Gibbs’ problem and the consistency of its solution with conventional thermodynamics. Quantum mechanics provides a quantitative criterion, not possible in the classical picture, for the degree of indistinguishability in terms of visibility of quantum interference, or overlap of the states as pointed out by von Neumann, thereby endowing the entropy expression with mathematical continuity and physical reasonableness.
A controversy surrounding the "tunnelling time problem" stems from the seeming inability of quantum mechanics to provide, in the usual way, a definition of the duration a particle is supposed to spend in a given region of space. For this reason, the problem is often approached from an "operational" angle. Typically, one tries to mimic, in a quantum case, an experiment which yields the desired result for a classical particle. One such approach is based on the use of a Larmor clock. We show that the difficulty with applying a non-perturbing Larmor clock in order to "time" a classically forbidden transition arises from the quantum Uncertainty Principle. We also demonstrate that for this reason a Larmor time (in fact, any Larmor time) cannot be interpreted as a physical time interval. We provide a theoretical description of the quantities measured by the clock.
Classically general covariance is found from the idea that a vector is a physical quantity which exists independently of choice of coordinate system and is unchanged by a change of coordinate system. It is often assumed that there exists some form of absolute mathematical space or space-time, and that in a flat space approximation vectors can be imagined between defined points in this space-time, much as we can imagine an arrowed line drawn on a piece of paper. However, while classical vector quantities can be represented on paper, in the quantum domain physical quantities do not in general exist with precise values except in measurement; a change of apparatus, for example by rotating it, may affect the outcome of the measurement, so the condition for general covariance does not apply. The purpose of this paper is to re-examine covariance within the context of an orthodox, Dirac-Von Neumann interpretation of quantum mechanics, to replace it with a new condition, here called quantum covariance, and to show that quantum covariance is the required condition for the unification of general relativity with quantum mechanics for non-interacting particles.
Quantum mechanics (QM) has attracted a considerable amount of mysticism, in public opinion and even among academic researches, due to some of its conceptually puzzling features, such as the modification of reality by the observer and entanglement. We argue that many popular "quantum paradoxes" stem from a confusion between mathematical formalism and physics; We demonstrate this by explaining how the paradoxes go away once a different formalism, usually inconvenient to perform calculations, is used. we argue that some modern developments, well-studied in the research literature but generally overlooked by both popular science and teaching-level literature, make quantum mechanics (that is, "canonical" QM, not extensions of it) less conceptually problematic than it looks at first sight. When all this is looked at together, most "conceptual puzzles" of QM are not much different from the well-known paradoxes from probability theory. Consequently, "explanations of QM" involving physical action of consciouses or an infinity of universes are conceptually unnecessary