Dr. Peter Rowlands

Abstract:

Physics at its most fundamental is codified into a single operator. In the first instance this appears as a component of the Dirac equation, the relativistic quantum mechanical equation that describes the most fundamental physical state, the fermion or fundamental particle. At first sight, this equation contains mathematical objects which are not otherwise seen in physics, and most people who use the equation use them in a form close to that given by Dirac in his discovery paper of 1928. In this form they give the impression of being the result of a guess or reverse engineering which happen to give the correct results when applied to physical situations. However, Dirac’s 4 × 4 matrices disguise a more fundamental algebraic structure, whose form derives from the nature of the most fundamental quantities in physics and which has been derived from first principles of computation using a universal rewrite structure. When we apply this algebra in its most efficient form, we see that the Dirac equation is not sui generis but can be derived by a standard quantization procedure from classical relativistic energy-momentum conservation, with the operator alone, once specified, determining everything that follows. We also see immediate explanations of many previously unexplained physical facts without further assumptions.