Avoiding Negative Probabilities in Quantum Mechanics

Affiliation(s)

Department of Applied Physics, National University of Science and Technology, Bulawayo, Republic of Zimbabwe.

Department of Applied Physics, National University of Science and Technology, Bulawayo, Republic of Zimbabwe.

ABSTRACT

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, 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
analogous to asking why is it that Dirac’s antimatter does not exist in equal
proportions with matter. This problem of why negative energy particles do not
exist in equal proportions with positive energy particles is a problem that
needs to be solved by a future theory.

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.

G. Nyambuya, "Avoiding Negative Probabilities in Quantum Mechanics,"

References

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[1] P. A. M. Dirac, Proceedings of the Royal Society of London, Vol. 117, 1928, pp. 351-361.

[2] P. A. M. Dirac, Proceedings of the Royal Society of London, Vol. 118, 1928, pp. 610-612

[3] P. A. M. Dirac, Proceedings of the Royal Society of London, Vol. 180, 1942, pp. 1-39.

[4] R. P. Feynman, “Negative Probability,” In: D. Bohm, F. D. Peat and B. Hiley, Eds., Quantum Implications, Routledge & Kegan Paul Ltd., London, New York, 1987, pp. 235-248.

[5] G. Ghirardi, “Sneaking a Look at God’s Cards,” Princeton University Press, Princeton, 2005.

[6] E. Schrodinger, Physical Review, Vol. 28, 1926, pp. 1049-1070. doi:10.1103/PhysRev.28.1049

[7] M. Born. Zeitschrift für Physik, Vol. 37, 1926, pp. 863-867.

[8] D. Bohm, Physical Review, Vol. 89, 1953, pp. 458-466. doi:10.1103/PhysRev.89.458

[9] D. Bohm, Physical Review, Vol. 85, 1952, pp. 166-193. doi:10.1103/PhysRev.85.166

[10] B. R. Desai. “Quantum Mechanics with Basic Field Theory,” Cambridge University Press, Cambridge, 2010.

[11] W. Pauli and V. F. Weisskopf, Helvetica Physica Acta, Vol. 7, 1934, pp. 709-731.

[12] R. P. Feynman, “Quantum Electrodynamics: Lecture Notes,” W. A. Benjamin Inc., 1961.