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Compt. rend.

THE INTERPRETATION OF QUANTUM MECHANICS. THE CASE OF THE RELATIVISTIC VELOCITY OF A PARTICLE WITHOUT SPIN

A.B. Datzeff

Published Jan 1, 1960• 0 citations
OpenAlex

Abstract

In previous works on probabilistic description of the quantum motion of a micro-particle mu the non-relativistic Schroedinger equation was derived. The idea developed is now used to show that one can find this probabilistic description for mu also for relativistic velocities. (T.R.H.)

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THE INTERPRETATION OF QUANTUM MECHANICS. RELATIVISTIC CASE OF A BODY WITH SPIN

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The quantum problem of a body with spin, in the case of relativistic velocities, is treated with the aid of wellknown Dirac equations containing four wave functions. In the present work it is shown that the development of the ideas expressed previously (Compt. rend., 250: 67(1960) and Compt. rend., 254: 434(1962)) leads to the mathematical appliance of the Dirac theory, that is, the interpretation of quantum mechanics given can be transported to Dirac equations. (J.S.R.)

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CRC Press eBooks•Apr 19, 2022•0 citations

A simple means for deriving quantum mechanics

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quant-pharXiv:2602.04524•Feb 5, 2026•0 citations
It is not possible to use the Schrödinger equation to describe the motion of a particle with relativistic effects since it is not invariant relative to the Lorentz transformation. However, the attempt to generalize quantum mechanics in the relativistic domain on the basis of the one particle theory is somehow difficult. So we find the appropriate equations on the basis of the relativistic invariance. To obtain the non-relativistic equations, we take the limit as the speed of light tends to infinity. This obviously recovers the Schrödinger equation. Under this heading, we extend the non-relativistic Schrödinger equation in the description of particles with speeds comparable with that of light. This extension should be consistent with the Lorentz transformation [ 12 ]. The characteristic feature of the relativistic wave equations is the spin which provides a useful gauge in the applicability of particular equations that describe particular kinds of particles. We have two types of relativistic equations, i.e., the equation with spin-zero due to Schrödinger and spin-half due to Dirac that describes the electron.
A type of mechanics will be presented that possesses some distinctive properties. On the one hand, its physical description & rules of operation are readily comprehensible & intuitively clear. On the other, it fully satisfies all observable predictions of non-relativistic quantum mechanics. Within it, particles exist at points in space, follow continuous, piecewise differentiable paths, and their linear momentum is equal to their mass times their velocity along their path. Yet the probabilities for position and momentum, conditioned on the state of the particle's environment, follow the rules of quantum theory. Indeed, all observable consequences of quantum theory are satisfied; particles can be entangled, have intrinsic spin, this spin is not local to the particle, particle identity can effect probabilities, and so forth. All the rules of quantum mechanics are obeyed, and all arise in a straightforward fashion. After this is established, connections will be drawn out between this type of mechanics and other types of quantum worlds; those that obey Bohmian mechanics, stochastic mechanics, the many worlds interpretation, and physical collapse. In the final section, a relativistic version of the mechanics will be presented.