The concept of a quasi-particle and the non-probabilistic interpretation of wave mechanics

In recent works of the author [Found. Phys. 36 (2006) 1701–1717; Math. Comput. Simul. 74 (2007) 93–103], the argument has een made that Hertz’s equations of electrodynamics reflect the material invariance (indifference) of the latter. Then the principle of aterial invariance was postulated in lieu of Lorentz covariance, and the respective absolute medium was named themetacontinuum. Here, we go further to assume that the metacontinuum is a very thin but very stiff 3D hypershell in the 4D space. The equation for he deflection of the shell along the fourth dimension is the “master” nonlinear dispersive equation of wave mechanics whose linear art (Euler–Bernoulli equation) is nothing else but the Schrödinger wave equation written for the real or the imaginary part of the ave function. The wave function has a clear non-probabilistic interpretation as the actual amplitude of the flexural deformation. The “master” equation admits solitary-wave solutions/solitons that behave as quasi-particles (QPs). We stipulate that particles re our perception of the QPs (schaumkommen in Schrödinger’s own words). We show the passage from the continuous Lagrangian f the field to the discrete Lagrangian of the centers of QPs and introduce the concept of (pseudo)mass. We interpret the membrane ension as an attractive (gravitational?) force acting between the QPs. Thus, a self-consistent unification of electrodynamics, wave echanics, gravitation, and the wave-particle duality is achieved. 2009 IMACS. Published by Elsevier B.V. All rights reserved.