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International Journal of Hydrogen Energy

The nature of free electrons in superfluid helium—a test of quantum mechanics and a basis to review its foundations and make a comparison to classical theory

Randell L Mills

Published Oct 1, 2001• 69 citations
Publisher
DOI
10.1016/s0360-3199(01)00023-4

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Due to the advent of Quantum Mechanics' 100th anniversary in 2025, we wrote this review paper in order to present a discussion that addresses the foundations of this theory. And since the creation of this Mechanics and other quantum theories was guided, for instance, by correspondence principles that needed to be identified between them and other well-established physical theories, this paper will be devoted to discussing the correspondence between these quantum theories and Maxwell's theory of electromagnetism. More precisely, what we will do throughout this paper is discuss how the Maxwell's electromagnetic theory in free space and the stronger formulation of the correspondence principle already pointed, together, to the basis of a Quantum Mechanics that was only be formulated half a century later. And, in order to make this very clear, we will show that the quantum-mechanical description of a photon can already be identified, simply, by manipulating Maxwell's equations in free space with mathematical resources that, for instance, were already well known before the advent of Quantum Mechanics.
When liquid helium-4 is cooled to 2.17 K it changes from an ordinary fluid to a superfluid somewhat similar in nature to superfluid helium-3 and to the electron fluid in superconductors. Extensive investigation over the last five decades has given us a highly refined phenomenological description of how superfluid He4 behaves, even though the underlying quantum theory is only partially understood. Much of the current research on superfluid He4 is part of a continuing effort to work out the implications of this phenomenological description, in the same way as classical fluid dynamicists are still working out the implications of the Navier-Stokes equations.