Derivation of the Dirac Equation from Principles of Information Processing
arXiv:1306.1934 · doi:10.1103/PhysRevA.90.062106
Abstract
We show how the Dirac equation in three space-dimensions emerges from the large-scale dynamics of the minimal nontrivial quantum cellular automaton satisfying unitariety, locality, homogeneity, and discrete isotropy, without using the relativity principle. The Dirac equation is recovered for small wave-vector and inertial mass, whereas Lorentz covariance is distorted in the ultra-relativistic limit. The automaton can thus be regarded as a theory unifying scales from Planck to Fermi. A simple asymptotic approach leads to a dispersive Schroedinger equation describing the evolution of narrow-band states at all scales.
20 pages, 9 figures, revtex4, revised version
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