On the quantum theory of the electromagnetic field

Abstract Existing attempts to apply the quantum theory to the electromagnetic field are open to serious objections. Above all, the time is treated differently from the space co-ordinates; the quantities defining the state (e. g., field strengths) are developed in Fourier series according to their space distribution, but the Fourier coefficients are not considered a classical functions of the time but as quantum oscillators. Also the subsequent development of these principles into formulæ, in which the field quantities are operators depending on position in space, does not affect the fundamental distinction between time and space variables. This is also shown by the fact that the relativistic invariance cannot be derived simply from the symmetry of the formulæ in the four world co-ordinates, but must be artificially imposed and demonstrated by a complicated proof. Further, it is not a self-contained theory of the elctromagntic field, but a superposition of Maxwell's electromagnetic fieldon the material field of Schrodinger or Dirac, in which the elementary particles poccur as point-charges. Thus there is no idea of the radius of the particle, and consequently no rational notion of mass, not to mention a theory of the ratio of the mass of a proton to that of an electron. In addition to these fundamental difficultiees there are others, such as that of the infinitely great "Nullpunksenergie", which is avoided by an artificial modification of the formalism.