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Cherkasy University Bulletin: Physical and Mathematical Sciences

WAVE-PARTICLE DUALITY AND TACHYON-BRADYON SYMMETRY – STRIKING SIMILARITY IN 2D SPACE-TIME (METHODIC NOTE)

Andriy M. Gusak

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

Is this idea crazy enough to be correct? Niels Bohr Wave-particle duality can be treated (at least, formally) as a symmetry between  subluminal and superluminal reference frames.

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WAVE PARTICLE DUALITY IN GENERAL RELATIVITY.

Abstract: In this paper a one to one correspondence is established between spacetime metrics of general relativity and the wave equations of quantum mechanics. This is done by first taking the square root of the metric associated with a space and from there, passing directly to a corresponding expression in the dual space. It is shown that in the case of a massless particle, Maxwell’s equation for a photon follows while in the case of a particle with mass, Dirac’s equation results as a first approximation. Moreover, this one to one correspondence suggests a natural explanation of wave-particle duality. As a consequence, the distinction between quantum mechanics and classical relativistic mechanics is more clearly understood and the key role of initial conditions is emphasized. PACS NUMBERS: 03.65, 04.60 I

•Jan 1, 1997•0 citations
The complementary wave and particle character of quantum objects (or quantons) was pointed out by Niels Bohr. This wave-particle duality, in the context of the two-slit experiment, is here described not just as two extreme cases of wave and particle characteristics, but in terms of quantitative measures of these characteristics, known to follow a duality relation. A very simple and intuitive derivation of a closely related duality relation is presented, which should be understandable to the introductory student.
We investigate the tachyonic nature of the de Broglie matter waves associated with a free quantum object to show that granting reality to them would lend completeness to the quantum description of reality. Basing on the robustness of the well known Einstein-de Broglie reciprocal relation between the phase and the particle velocities, we extend the concept of complementarity to them and thereby propose a complementary relation between a bradyon and its corresponding tachyon (i.e. the associated matter wave) to endow the tachyons with a degree of reality, at least on par with the bradyons, within the current framework of quantum physics and extended relativity. The duality is used to argue that because of the observed localised nature of bradyons, tachyons should always be pervasive or global in character and thus, there can be no point-like tachyons. A common misconception regarding the nonrelativistic limit of the Einstein-de Broglie relation is pointed out and the consequent error of long standing is remedied.
Despite their author, de Broglie waves for ordinary (bradyonic) particles are often considered without physical signication, mainly because they are tachyonic. I revisit some of de Broglie’s original ideas and discuss the standard approach to the problem, the \wave packet overlapped to a de Broglie wave. Using Pseudotachyonic Theory, it’s easy to conclude that this tachyonic wave actually exists but may only be detected with the same velocity of its associated particle. Furthermore, in what comes to \dualities, it appears that wave and particle are not two aspects of the same thing but instead two different though intimately correlated entities. These reections concern the physical nature of de Broglie waves, including particles \internal vibration, and lead to the premises of a new general Field Theory. Including positive as well as negative
Abstract: In this paper a one to one correspondence is established between spacetime metrics of general relativity and the wave equations of quantum mechanics. This is done by first taking the square root of the metric associated with a space and from there, passing directly to a corresponding expression in the dual space. It is shown that in the case of a massless particle, Maxwell’s equation for a photon follows while in the case of a particle with mass, Dirac’s equation results as a first approximation. Moreover, this one to one correspondence suggests a natural explanation of wave-particle duality. As a consequence, the distinction between quantum mechanics and classical relativistic mechanics is more clearly understood and the key role of initial conditions is emphasized. PACS NUMBERS: 03.65, 04.60 I