Towards a unified deterministic theory of fields and particles

A summary is given of the principal concepts of a unified deterministic theory of fields and particles that have been developed in more detail in a previous comprehensive four-part paper (Hasselmann, 1996a,b, 1997a,b). The model is based on the Einstein vacuum equations, Ricci tensor RLM = 0, in a higher-dimensional space. A space of at least eight dimensions is required to incorporate all other forces as well as gravity in Einstein’s general relativistic formalism. It is hypothesized that the equations support soliton-type solutions (”metrons”) that are localized in physical space and are periodic in extra (”harmonic”) space and time. The solitons represent waves propagating in harmonic space that are locally trapped in physical space within a wave guide produced by a distortion of the background metric. The metric distortion, in turn, is generated by nonlinear interactions (radiation stresses) of the wave field. (The mutual interaction mechanism has been demonstrated for a simplified Lagrangian in Part 1 of the previous paper). In addition to electromagnetic and gravitational fields, the metron solutions carry periodic far fields that satisfy de Broglie’s dispersion relation. These give rise to wave-like interference phenomena when particles interact with other matter, thereby resolving the wave-particle duality paradox. The metron solutions and all particle interactions on the microphysical scale (with the exception of the kaon system) satisfy strict time-reversal symmetry, an arrow of time arising only at the macrophysical level through the introduction of time-asymmetrical statistical assumptions. Thus Bell’s theorem on the non-existence of deterministic (hidden variable) theories, which depends crucially on an arrow-of-time, is not applicable. Similarly, the periodic de