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This is a wiki for me to explore discrete models of fundamental physics, especially models of relativistic quantum mechanics as described by the Dirac equation and spinors.

Why discrete physics models?

  • The concept of a continuum seems rather complicated to build up out of discrete elements, requiring methods like the Dedekind cut or Cauchy sequences.
  • Many physics theories have ultraviolet divergences that might be solved if there is a small distance cutoff
  • The Planck length would be a natural candidate for something like a minimum length because it can be built entirely from fundamental constants like {$G$}, {$\hbar$}, and {$c$}.
  • Discrete models could describe a wealth of phenomena, so that a continuum may not be needed
  • Even if discrete models don't properly describe physics on a fundamental level it could be a useful exercise to explore ideas that COULD be applicable in continuous settings as well

Why start with relativistic quantum theory?

  • It's possible that understanding QM from a discrete standpoint can only be done in a relativistic model. Relativity requires spin and helicity. Those may needed

These pages will be divided between self-education and exploration of my own toy models. The goal is that by looking at an overview of the ideas I've played around with I might gain some general insights.


Education:


My own models I've been learning from


My general guiding philosophy


Other discrete approaches to physics


The Strangest Man, a biography of Paul Adrian Maurice Dirac by Graham Farmelo