The aim of this paper is to explain the contributions of G. Lemaître to Spinor Theory. At the end of the paper, we edited also, for the first time two short manuscripts: Spineurs et Quanta and Les spineurs et la physique quantique, written by Lemaître in December 1955 and in January 1956. This edition is a way of honouring Professor Michael Heller because he was the first, with Professor Odon Godart, who discovered, classified and published unedited manuscripts of G. Lemaître.
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In this paper an ansatz that the anti-commutation rules hold only as integrated average over time intervals and not at every instant giving rise to a time-discrete form of Klein-Gordon equation is examined. This coarse-grained validation of the anti-commutation rules enables us to show that the relativistic energy-momentum relation holds only over discrete time intervals, fitting well with the timeenergy uncertainty relation. When this time-discrete scheme is applied to four vector notations in relativity, the line-element can be quantized and thereby how the physical attributes associated with time, space and matter can be quantized is sketched. This potentially enables us to discuss the Zeno’s arrow paradox within the classical limit. As the solutions of the Dirac equation can be used to construct solutions to the Klein-Gordon equation, this temporal quantization rule is applied to the Dirac equation and the solutions associated with the Dirac equation under such conditions are interpreted. Finally, the general relativistic effects are introduced to a line-element associated with a particle in relativistic motion and a time quantized line-element associated with gravity is obtained.
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.
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