Inconsistency of the Neutrino Theory of Light

Abstract

The neutrino theory of light proposed by Jordan¹ postulates a connexion between the quantized wave function of the light field (F) and that of the neutrino-field (). Since satisfies the commutation rules for Fermi statistics and F those of the Bose statistics, the connexion cannot be a linear one. On the other hand, we know from quantum electrodynamics that F satisfies a linear differential equation; a similar-equation of d'Alembert's type is to be expected for . Thus a contradiction arises between the linearity of the equations and the non-linearity of the connexion between F and . (This contradiction is avoided only in the case of plane waves propagating in one definite direction.) Besides, serious doubts arise as to the possibility of expressing the quantized amplitudes b() for F (Bose statistics) in terms of the-amplitudes () for (Fermi statistics), the operators b() and () being of a quite different mathematical nature.