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Causal interpretation of the modified Klein-Gordon equation

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Abstract

A consistent causal interpretation of the Klein-Gordon equation treated as a field equation has been developed, and leads to a model of entities described by the Klein-Gordon equation, i.e., spinless, massive bosons, as objectively existing fields. The question arises, however, as to whether a causal interpretation based on a particle ontology of the Klein-Gordon equation is also possible. Our purpose in this article will be to indicate, by making what we believe is a best possible attempt at developing a particle interpretation of the Klein-Gordon equation, that such an interpretation is untenable. To resolve the nonpositive-definite probability density difficulties with the Klein-Gordon equation, we modify this equation by the introduction of an evolution parameter. We base our subsequent considerations on this modified Klein-Gordon equation. Partly to motivate the need for a relativistic causal interpretation and partly to give emphasis to aspects of the causal interpretation often overlooked, we begin our article with a brief historical survey of the causal interpretation.

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Authors and Affiliations

  1. Department of Physics and Electronic Engineering, University of Swaziland, P/Bag 4, Kwaluseni, Swaziland, Southern Africa

    P. N. Kaloyerou

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  1. P. N. Kaloyerou
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Other work commitments prevented publication of this article in the special issue ofFoundations of Physics in honor of Prof. J. P. Vigier. I would nevertheless like to dedicate this work to Prof. Vigier in recognition of this untiring contributions to the causal interpretation in particular and to the foundations of physics in general. I take this opportunity to thank Prof. Vigier for his help during my Royal Society fellowship spent at the Institut Henri Poincaré in the academic year 1988–1989.

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Kaloyerou, P.N. Causal interpretation of the modified Klein-Gordon equation. Found Phys 25, 1413–1460 (1995). https://doi.org/10.1007/BF02057461

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