Abstract
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 pre-
vious 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 re-
quired to incorporate all other forces as well as gravity in Einstein’s gen-
eral 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 met-
ric. 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 introduc-
tion 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 Broglie far fields of the particles do not lead to unstable radiative damping,
the time-asymmetrical outgoing radiation condition being replaced by the
time-symmetrical condition of zero net radiation.
Assuming suitable polarization properties of the metron solutions, it can
be shown that the coupled field equations of the Maxwell-Dirac-Einstein sys-
tem as well as the Lagrangian of the Standard Model can be derived to low-
est interaction order from the Einstein vacuum equations. Moreover, since
Einstein’s vacuum equations contain no physical constants (apart from the
introduction of units, namely the velocity of light and a similar scale for the
harmonic dimensions, in the definition of the flat background metric), all
physical properties of the elementary particles (mass, charge, spin) and all
universal physical constants (Planck’s constant, the gravitational constant,
and the coupling constants of the electroweak and strong forces) must fol-
low from the properties of the metron solutions. A preliminary inspection
of the structure of the solutions suggests that the extremely small ratio of
gravitational to electromagnetic forces can be explained as a higher-order
nonlinearity of the gravitational forces within the interior metron core. The
gauge symmetries of the Standard Model follow from geometrical symme-
tries of the metron solutions. Similarly, the parity violation of the weak
interactions is attributed to a reflexion asymmetry of the metron solutions
(in analogy to molecules with left- and right-rotational symmetry), rather
than to a property of the basic Lagrangian. The metron model also yields
further interaction fields not contained in the Standard Model, suggesting
that the Standard Model represents only a first-order description of elemen-
tary particle interactions.
While the Einstein vacuum equations reproduce the basic structure of
the fields and lowest-order interactions of quantum field theory, the particle
content of the metron model has no correspondence in quantum field theory.
This leads to an interesting interpretation of atomic spectra in the metron
model. The basic atomic eigenmodes of quantum electrodynamics appear in
the metron model as the scattered fields generated by the interaction of the
orbiting electron with the atomic nucleus. For certain orbits, the eigenmodes
are in resonance with the orbiting electron. In this case, the eigenmode and
orbiting electron represent a stable self-supporting configuration. For circular
orbits, the resonance condition is identical to the integer-action condition of
the Bohr orbital model. Thus the metron interpretation of atomic spectra
yields an interesting amalgam of quantum electrodynamics and the original
Bohr model. However, it remains to be investigated whether higher-order computations of the metron model are able to reproduce atomic spectra to
the same high degree of agreement with experiment as QED. On a more
fundamental level, the basic questions of the existence, structure, stability
and discreteness of the postulated metron solutions still need to be addressed.
However, it is encouraging that, already on the present exploratory level, the
basic properties of elementary particles and fields, including the origins of
particle properties and the physical constants, can be explained within a
unified classical picture based on a straightforward Kaluza-Klein extension
to a higher dimensional space of the simplest vacuum form of Einstein’s
gravitational equations.
