Elementary Particles and the Causet Approach to Discrete Quantum Gravity

Abstract

In a previous paper, the author introduced a covariant causet ($c$-causet) approach to discrete quantum gravity. A $c$-causet is a finite partially ordered set that is invariant under labeling. The invariant labeling of a $c$-causet $x$ enables us to uniquely specify $x$ by a sequence $\brac{s_j(x)}$, $j=0,1,2,\ldots$, of positive integers called a shell sequence of $x$. A $c$-causet $x$ describes the microscopic structure of a possible universe at a particular time step. In general, $x$ represents one of many universes in a multiverse and $x$ grows by a single element at each time step. Since early stages of a universe were probably composed of elementary particles, we propose that elementary particles can be described by simple $c$-causets. Although we do not have a rigorous theory for such a description, we present our guess as to how it might appear. The shell sequence can be applied to find theoretical masses of particles and these seem to approximately agree with known masses. We point out that the causal order provides a unification of the strong and weak forces for elementary particles and also determines the geometry of $c$-causets which describes gravity. Moreover, it appears that some particles correspond to dark matter-energy.