The Dirac equation consistent with the principles of quantum mechanics and the special theory of relativity, introduces a set of matrices combined with the wave function of a particle in motion to give rise to the relativistic energy-momentum relation. In this paper a new hypothesis, the wave function of a particle in motion is associated with a pair of complementary waves is proposed. This hypothesis gives rise to the same relativistic energy-momentum relation and achieves results identical to those of Dirac. Additionally, both the energy-time and momentum-position uncertainty relations are derived from the complementary wave interpretation. How the complementary wave interpretation of the Dirac equation is related to the time-arrow and the four-vectors are also presented.
International Letters of Chemistry, Physics and Astronomy (Volume 14)
D.L. Bulathsinghala and K.A.I.L. Wijewardena Gamalath, "On the Complementary Wave Interpretation of the Dirac Equation", International Letters of Chemistry, Physics and Astronomy, Vol. 14, pp. 103-115, 2013