Substratum Approach to a Unified Theory of Elementary Particles
Authors: Winterberg F. 
Published: February 2015

If special relativity is a dynamic symmetry caused by true physical deformations of bodies in absolute motion through a substratum or ether, the question if all interactions and elementary particles arc excitations of this ether must be raised. The ether being the cause of all the observed relativistic effects should then obey an exactly nonrelativistic law of motion, and which permits it to consist of positive and negative masses. The fundamental constants of nature, which according to Planck are 1) Newton's constant (G), 2) the velocity of light (c) and 3) Planck’s constant (ћ), suggest that the ether is made up of densely packed positive and negative Planck masses (Planckions), each with a diameter equaling the Planck length. Symmetry demands that the number of positive and negative Planck masses should be equal, making the cosmological constant equal to zero. Because the Planckions are nonrelativistic spin-zero bosons, the ether would therefore consist of two super­fluids, one for the positive mass Planckions, and the other one for the negative mass Planckions. By spontaneous symmetry breaking this superfluid ether can in its ground state form a lattice of small vortex rings, with the vortex core radius equaling the Planck length. Force fields of massless vector gauge bosons can be interpreted as quantized transverse vortex waves propagating through this lattice. Because the smallest wave length would be about equal the ring radius of the circular vortices, the ring radius would assume the role of a unification scale. The ring radius is estimated to be about 103 times the Planck length, in fairly good agreement with the empirical evidence for the value of the grand unification scale of the standard model.
Charge is explained by the zero point fluctuations of the Planckions attached to the vortex rings, wrhich thereby become the source of virtual phonons. Charge quantization is explained as the result of circulation quantization. Spinors result from bound states of the positive and negative masses of the substratum, and special relativity as a dynamic symmetry would be valid for all those objects. Quantum electrodynamics is derived as a low energy approximation
If spinors are made up from the positive and negative masses of the vortex ring resonance energy, whereby the spinors would assume the character of excitons, the spinor mass can be computed in terms of the Planck mass. Vice versa, with the lowest quark mass m given, a value for the gravitation­al constant in terms of m, ћ, and c can be obtained. The existence of different particle families can be understood by internal excitations of the spinors, and parity violation may find its explanation in a small nonzero vorticity of the ether. Bacause of its simple fundamental symmetry the theory is unique, it is always finite and has no anomalies.
In the proposed theory all fields and interactions are explained in a completely mechanistic way by the Planck masses and their contact interactions. With special relativity as a derived dynamic symmetry and space remaining euclidean, the proposed approach can be seen as an alternative to Einstein’s program to explain all fields and their interactions by symmetries and singularities of a noneuclidean spacetime manifold.
In Part I, the fundamental equation for the substratum, which has the form of a nonrelativistic nonlinear Heisenberg equation, is formulated. It is shown how it leads to a Maxwell-type set of equations for the gauge bosons. In Part II, Dirac-type spinors and quantum electrodynamics are derived. These results are then applied to obtain the lowest quark mass in terms of the Planck mass.