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Physical Science & Biophysics Journal

Regarding the Formalism of Quantum Mechanics

Spiros Koutandos

Published Jan 1, 2021• 2 citations
Publisher

Abstract

Classical physics meets the obstacle of describing a point particle because from everyday experience we know that objects occupy a certain volume.We overcome this obstacle by using the equivalence principle for electric energy and describe a curved spacetime of fluid nature.From thereon by using the notion of a point volume the rest of the thermodynamic quantities appear.We find the alpha omega formula and the time derivative of action in quantum mechanics.

DOI
10.23880/psbj-16000175

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Classical physics meets the obstacle of describing a point particle because from everyday experience we know that objects occupy a certain volume.We overcome this obstacle by using the equivalence principle for electric energy and describe a curved spacetime of fluid nature.From thereon by using the notion of a point volume the rest of the thermodynamic quantities appear.We find the alpha omega formula and the time derivative of action in quantum mechanics.
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Quantum Mechanics is a successful model to describe physical phenomena. We show that a simple set of postulates about the description of objects in Nature allows the derivation of the principles of QM, transforming this theory into a deductive approach to Physics. The main postulate is: Objects are described as energy distributions in Space–Time. 1 Quantum Mechanics from START It is universally accepted that Quantum Mechanics is a successful model to describe physical phenomena, in particular of the electronic structure of atoms, molecules and solids. As such it has been reformulated in several different forms (see for example: Nine formulations of quantum mechanics, Daniel F. Styer et al. [15]). The aim of the present paper is to show that a simple set of postulates about the description of objects in Nature allows the derivation of the principles of QM, transforming this theory into a deductive approach to Physics. In our approach the main postulate is: Objects are described as energy distributions in Space–Time. The theory is in fact a systematic mathematical analysis of this postulate and of other general considerations about action, energy–momentum and the role of the theory as a useful description of Nature. The paper also shows the fundamental and basic status of Density Functional Theory, also contained in our approach. The initial mathematical structure is a geometric (quadratic form based) union of space, time and action. In physics bundles of trajectories are used to describe the objects of nature: distribution of heights over a surface, a real object is described as a bundle of space-time trajectories, here we use a description as a bundle of action valves in space-time (energy densities in space following light-like lines). The author is fully aware that the presentation is strongly guided by the knowledge of the usual computational approach to study atoms, molecules and condensed matter electronic structure.
In continuation of some previous work published by this author in an open access journal [S. Koutandos, IOSR J. Appl. Phys. 10, 26 (2018); 10, 35 (2018); 9, 47 (2017); 11, 72 (2019)], he now derives the London equations from an expansion of the rotation of vorticity. Vorticity is a vector quantity described in fluid mechanics which characterizes the angular motion of a point particle as it moves. A small ball, for example, found in a field of vorticity would turn around itself. This is in accordance with the existence of the spin of a particle. We claim that due to the dipolar nature of the electric charge, its rotation vortex effects appear. It is found that the total time derivative of the radius possibly due to Brownian motion is different from the velocity but is used as a starting point in describing a fluid-like flow for the electron where all the quantities behave accordingly. Finally, we ascribe the relativistic radius of the electron to a curvature of spacetime from the mass energy equivalence for the electric energy. This paper may also be looked at as one more discussion about the hidden variables quest in quantum mechanics, offering some progress in understanding them.
In classical physics, the ‘state’ of a particle, at any particular time, is taken to involve a definite position in space and a definite motion; and the state of a system of particles is taken to involve a definite position in space and a definite motion for each of the particles. The situation in relation to quantum mechanics is completely different. As in classical physics, calculations can be made concerning the position and motion of a particle. However, this representation is not by means of symbols for scalar or vector quantities: it is by a more complex mathematical object. This quantum state does not indicate or represent position or motion in any direct way: what it does in substance is to enable calculation of the probability of the particle in question being found to have a position or momentum if an appropriate measurement is made.