We reproduce the dynamics of quantum mechanics with a four-dimensional spacetime manifold that is branched and embedded in a six-dimensional Minkowski space. Elementary fermions are represented by knots in the manifold, and these knots have the properties of the familiar particles. We derive a continuous model that approximates the behavior of the manifold's discrete branches. The model produces dynamics on the manifold that corresponds to the gravitational, strong, and electroweak interactions.

INTRODUCTION

Physics possesses two fundamental theories, general relativity and the Standard Model, both strongly tested and verified in their respective domains. A naive combination of these theories results in unresolvable infinities. Theorists have produced quantum theories of gravity with varying degrees of success. String theory (or M-theory) makes few assumptions and has few parameters, and it produces a quantum theory of gravity along with producing familiar particles. Unfortunately, string theory does not specify a particular choice for the way the vacuum's small dimensions should curl up, and most or all predictions depend on this configuration of the Calabi-Yau space. Loop quantum gravity makes few assumptions and has few parameters, and it produces a quantum theory of gravity and explains a few astrophysical phenomena. Unfortunately, its predictions and explanatory power are quite limited.

Like string theory, the theory presented here makes few assumptions and has few free parameters, and it also produces a quantum theory of gravity, as well as the familiar forces and particles. By contrast, however, it has greater explanatory power and the power to predict observations at energies achievable with current technology. In particular, we use this theory to calculate the fine structure constant from first principles.

The theory is fully geometric. We assume that the spacetime manifold can be knotted. From knot theory we know that a piecewise linear n-manifold can be knotted only if it is embedded in an n+2-dimensional space. Therefore we assume the 4-dimensional spacetime manifold is embedded in a 6-dimensional Minkowski space. We assume that the manifold is branched so that paths along the manifold may separate and recombine. In this way we introduce interference and thus a probabilistic theory.

In this short presentation we provide an informal description of the theory. This theory begins from very different assumptions than the Standard Model, and this video provides useful conceptual background.

SHORT PRESENTATION A 15 minute, informal introduction to the theory.

THE AUTHORS

CLIFF ELLGEN graduated Caltech in 1999 with a degree in mathematics. He has been contemplating this theory for more than fifteen years. Since August of 2014, he has been collaborating with Garrett Biehle to refine the theory.

GARRETT BIEHLE received his Ph.D. from Caltech in astrophysics under advisors Kip Thorne and Roger Blandford. He worked out the structure and observational signature of stars with neutron-degenerate cores.