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As currently understood since its discovery, the bare Klein-Gordontheory consists of negative quantum probabilities which are considered to bephysically meaningless if not outright obsolete. Despite this annoying setback,these negative probabilities are what led the great Paul Dirac in 1928 tothe esoteric discovery of the Dirac Equation. The Dirac Equation led to one ofthe greatest advances in our understanding of the physical world. In thisreading, we ask the seemingly senseless question -Donegative probabilities exist in quantum mechanics?- In an effort toanswer this question, we arrive at the conclusion that depending on the choiceone makes of the quantum probability current, one will obtain negativeprobabilities. We thus propose a new quantum probability current of theKlein-Gordon theory. This quantum probability current leads directly topositive definite quantum probabilities. Because these negative probabilitiesare in the bare Klein-Gordon theory, intrinsically a result of negativeenergies, the fact that we here arrive at a theory with positiveprobabilities, means that negative energy particles are not to be consideredproblematic as is the case in the bare Klein-Gordon theory. From an abstract—objective stand-point; in comparison with positive energy particles,the corollary is that negative energy particles should have equal chances toexist. As to why these negative energy particles do not exist, this isanalogous to asking why is it that Dirac’s antimatter does not exist in equalproportions with matter. This problem of why negative energy particles do notexist in equal proportions with positive energy particles is a problem thatneeds to be solved by a future theory.


Klein-Gordon Equation; Schrödinger Equation; Probability; Negative Probability

Cite this paper

G. Nyambuya -Avoiding Negative Probabilities in Quantum Mechanics,- Journal of Modern Physics, Vol. 4 No. 8, 2013, pp. 1066-1074. doi: 10.4236-jmp.2013.48143.

Author: Golden Gadzirayi Nyambuya

Source: http://www.scirp.org/


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