A Causal Net Approach to Relativistic Quantum Mechanics

In this paper we discuss a causal network approach to describing relativistic quantum mechanics. Each vertex on the causal net represents a possible point event or particle observation. By constructing the simplest causal net based on Reichenbach-like conjunctive forks in proper time we can exactly derive the 1+1 dimension Dirac equation for a relativistic fermion and correctly model quantum mechanical statistics. Symmetries of the net provide various quantum mechanical effects such as quantum uncertainty and wavefunction, phase, spin, negative energy states and the effect of a potential. The causal net can be embedded in 3+1 dimensions and is consistent with the conventional Dirac equation. In the low velocity limit the causal net approximates to the Schrödinger equation and Pauli equation for an electromagnetic field. Extending to different momentum states the net is compatible with the Feynman path integral approach to quantum mechanics that allows calculation of well known quantum phenomena such as diffraction.

Biography

Dr. Richard Bateson is Honorary Senior Research Associate at the London Centre of Nanotechnology (LCN), University College London (UCL). He worked at the European Synchrotron Radiation Facility (ESRF), Institut Laue Langevin (ILL) and CERN. He has a double first M.A. (Hons) in Theoretical Physics and a PhD from Cambridge University. Richard was also previously Managing Director of the Royal Bank of Canada (RBC) and CEO of an investment management company affiliated with Man Group, the world’s largest alternative asset manager. He is the recent author of ‘Financial Derivative Investments’ (Imperial College Press, July 2011) and ‘Causal Space-Time’ (Cassini, Dec 2010).