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

Abstract

The Schrödinger equation was originally postulated in 1926 as having a solution of the one electron atom. It gives the principal energy levels of the hydrogen atom as eigenvalues of eigenfunction solutions of the Laguerre differential equation. But, as the principal quantum number n⪢1, the eigenfunctions become nonsensical. Despite its wide acceptance, on deeper inspection, the Schrödinger solution is plagued with many failings as well as difficulties in terms of a physical interpretation that have caused it to remain controversial since its inception. Only the one electron atom may be solved without approximations, but it fails to predict electron spin and leads to models with nonsensical consequences such as negative energy states of the vacuum, infinities, and negative kinetic energy. In addition to many predictions which simply do not agree with observations, the Schrödinger equation predicts noncausality, nonlocality, spooky actions at a distance or quantum telepathy, perpetual motion, and many internal inconsistencies where contradicting statements have to be taken true simultaneously. Recently, the behavior of free electrons in superfluid helium has again forced the issue of the meaning of the wave function. Electrons form bubbles in superfluid helium which reveal that the electron is real and that a physical interpretation of the wave function is necessary. Furthermore, when irradiated with light of energy of about a 0.5 to several electron volts (H.J. Marris, J. Low Temp. Phys. 120 (2000) 173), the electrons carry current at different rates as if they exist with different sizes. It has been proposed that the behavior of free electrons in superfluid helium can be explained in terms of the electron breaking into pieces at superfluid helium temperatures (H.J. Marris, J. Low Temp. Phys. 120 (2000) 173). Yet, the electron has proven to be indivisible even under particle accelerator collisions at 90 GeV (LEPII). The nature of the wave function must now be addressed. It is time for the physical rather than the mathematical nature of the wave function to be determined. A theory of classical quantum mechanics (CQM) was derived from first principles by Mills (The grand unified theory of classical quantum mechanics. January 2000 ed; Cranbury, NJ, 2000, Blacklight Power, Inc., (Distributed by Amazon.com; Posted at www.blacklightpower.com)) that successfully applies physical laws on all scales. Using the classical wave equation with the constraint of nonradiation based on Maxwell's equations, CQM gives closed form physical solutions for the electron in atoms, the free electron, and the free electron in superfluid helium. The prediction of fractional principal quantum energy states of the electron in liquid helium match the photoconductivity and mobility observations without requiring that the electron is divisible.