International Journal of Theoretical Physics

, Volume 32, Issue 10, pp 1801-1813

First online:

Quantum relativity

  • David FinkelsteinAffiliated withGeorgia Institute of Technology, School of Physics
  • , J. Michael GibbsAffiliated withGeorgia Institute of Technology, School of Physics

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


We propose a unified description of the known forces. We formulate a quantum relativistic spacetime as a (directed) graph of causal arrows with indefinite Hilbert metric, whose physical meaning is given. The simplest graph whose quantum relativity supports conservation of energy-momentum also supports a semidirect product of the cyclic groups2 and3 and the four-group2 2. We call these lattice degrees of freedom (permutational) twain, trine, and spin. Quantized2 2 becomes LorentzSpin(4). Gauged, the energy-momentum and spin groups lead to gravity and torsion, and twain and trine lead toSU 2 andSU 3. We infer that color is actually trine, and thez component of isospin is twain.