## Deciphering and Fathoming Negative Probabilities in Quantum Mechanics?

**Authors:** Golden Gadzirayi Nyambuya

As currently understood since its discovery, the bare Klein-Gordon theory consists
of negative quantum probabilities which are considered to be physically meaningless if not
outright obsolete. Despite this annoying setback, these negative probabilities are what led
the great Paul Dirac in 1928 to the esoteric discovery of the Dirac equation. The Dirac
equation led to one of the greatest advances in our understanding of the physical World. In
this reading, we ask the seemingly senseless question, "Do negative probabilities exist in
quantum mechanics?''. In an effort to answer this question, we arrive at the conclusion that
depending on the choice one makes of the quantum probability current, one will obtain
negative probabilities. We thus propose a new quantum probability current of the
Klein-Gordon theory. This quantum probability current leads directly to positive definite quantum
probabilities. Because these negative probabilities are in the bare Klein-Gordon theory,
intrinsically a result of negative energies, the fact that we-here arrive at a theory with
positive probabilities, it means that negative energy particles are not to be considered
problematic 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 to exist. As to why these negative energy
particles do not exist, this is redolent to asking why is it that Dirac's antimatter does not
exist in equal proportions with matter. This problem of why negative energy particles not
exist in equal proportions with positive energy particles is a problem that needs to be solved
by a future theory.

**Comments:**
11 pages, no figure, no tables.

**Download:** **PDF**

### Submission history

[v1] 19 Feb 2011

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