Can atomic processes be described by non-linear wave mechanics in space-time?

Abstract

Generalizing from a classical application of the paradigm of Elementary Measurement discussed elsewhere (Leiter, 1969), we consider a non-linear, spinor wave-mechanical field theory of Elementary Measurement. In this theory, charged particles are represented by complex spinorc-number fields interacting through their associated electromagnetic fields in space-time. The paradigm of Elementary Measurement implies that the particle fields, and their associatedc-number electromagnetic fields, are interdependent degrees of freedom in an action principle associated with the measurement interaction, and are not elementary in themselves. Making the action stationary with respect to the interacting field degrees of freedom gives the equations of motion of the measurement. The application of this model theory to atomic hydrogen yields the result that the inherent ‘limit cycle solutions’ (LCS) of the non-linear measurement equations correspond to the quantum levels of conventional relativistic Dirac quantum mechanics of hydrogen, in the approximation that the nucleus has infinite mass. Superpositions of these Dirac-LCS solutions have the property of collapsing (reduction of the wave packet) into one of the LCS in the superposition,in a characteristic time which is identical to the ‘lifetime’ of the associated atomic levels as calculated from conventional quantum mechanics. Hence, in thisc-number electromagnetic theory,both spontaneous and induced transitions can be accounted for. ‘Photons’, in this theory, are not elementary particles, but instead are associated with the secondary dynamics related to the inherent nonlinear structure in the elementary measurement equations of motion. The ‘hidden variable’ characteristics of this measurement theory (as seen from the point of view of ordinary quantum mechanics), in describing a universe made up of such hydrogen atoms, is discussed. Within this context, a consistent derivation of the Planck blackbody radiation formula is given, in which the associated electromagnetic fields arec-numbers and arenot second quantized. Finally, a generalization of this prototype model theory, to a more consistent form which can account for the presence of ‘vacuum interaction processes’ and negative energy states, is suggested.