The Weyl Equation — The Neutrino

Abstract

In 1930 W. Pauli postulated the existence of the neutrino in order to guarantee the energy and momentum conservation for the weak interaction, which at that time seemed to be violated in the β-decay experiments. Since the energy of the neutrino could not be determined even in the most sensitive measurements of the β decay of nuclei, the interaction of this postulated particle with matter must be extremely small. For example, it must not have electric charge, and accordingly, mass and magnetic moment must be assumed to be nearly vanishing, or even zero. The particle was named “neutrino” and abbreviated by “v”. Because of the relativistic mass—energy relation, a particle with rest mass m _v = 0 moves with the velocity of light. The experimental upper bound for the rest mass of the electronic neutrino is about a few electron volts and thus less than a thousandth of the electron’s rest mass. Therefore the assumption m _v = 0 seems to be reasonable. Further experimental observations of the angular momentum balance during β decay showed that the neutrino has spin ½. Consequently the Dirac equation for m ₀ = 0 should be the fundamental equation of motion for the neutrino.