The metron model: elements of a unified deterministic theory of fields and particles

In the first part of this four-part paper, the framework of a unified deterministic theory of fields and particles is presented. The model is based on a single set of field equations, Einstein’s vacuum equations for a higher-dimensional metric space. The extra space is not compactified, for example by assuming a spherical topology with very high extra-space curvature, the metric being represented as a perturbation superimposed on a flat-space background metric. It is proposed that the equations contain nonlinear soliton-type solutions, termed metrons, which are strongly localized in physical space, while carrying far fields which are independent of or periodic with respect to extra space and time. The solutions are generated through the mutual interaction between an inhomogeneous mean field (e.g. a gravitational or electromagnetic field), which acts as a wave guide, and a wave field, which is periodic in extra (harmonic) space and is trapped in the wave guide. The modetrapping mechanism is demonstrated for a simplified Lagrangian which reproduces the basic nonlinear properties of the gravitational Lagrangian while suppressing its tensor complexities. The more difficult task of computing metron solutions for the higher-dimensional gravitational system is not attempted in this paper. The model is strictly symmetrical with respect to time reversal. Thus Bell’s basic theorem on the non-existence of deterministic hidden-variable theories, which is based on the existence of an arrow of time, is not applicable. Time-reversal symmetry, Bell’s theorem and the metron interpretation of the EPR experiment are discussed in more detail in Part 3. Since the Einstein vacuum equations contain no physical constants, all particle properties (mass, charge, spin etc.) and physical constants (the gravitational constant, Planck’s constant, the electroweak and strong coupling coefficients, the parmeters of the Standard Model, etc.) are inferred from the properties of the metron solutions. The paradoxes of wave-particle duality are explained by the dual nature of the metron solutions. The localized, strongly nonlinear core regions of the solutions embody the corpuscular properties, while the metron far fields, including a periodic standing-wave de Broglie field, are responsible for the wave-like interference phenomena. The existence of discrete atomic spectra is explained by resonant interactions between the eigensolutions of the Maxwell-Dirac field equations and the orbiting electrons. Thus the metron picture of the atomic system represents an amalgam of QED (at the tree level) and Bohr’s original orbital theory. The principal properties of the Standard Model are reproduced assuming a four-or five-dimensional harmonic-space background metric. The Standard Model gauge symmetries are explained as a special case of the diffeomorphic gauge symmetries of the Einstein equations. Details are given in Parts 2 and 4.