The Principles of Quantum Information Theory, Dirac’s Equation, and Locality Beyond Relativity

Arkady Plotnitsky

Arkady Plotnitsky

Giacomo Mauro D’Ariano, Paolo Perinotti

Without using the relativity principle, we show how the Dirac equation in three space dimensions emerges from the large-scale dynamics of the minimal nontrivial quantum cellular automaton satisfying unitarity, locality, homogeneity, and discrete isotropy. The Dirac equation is recovered for small wave vector and inertial mass, whereas Lorentz covariance is distorted in the ultrarelativistic limit. The automaton can thus be regarded as a theory unifying scales from Planck to Fermi. A simple asymptotic approach leads to a dispersive Schr\"odinger equation describing the evolution of narrowband states at all scales.

Daniel R. Terno

Cláus Lämmerzahl

A new test theory for describing tests of fundamental principles of Special and General Relativity is presented. Using a generalised Pauli equation which may be based on a generalised Dirac equation, possible violations of local Lorentz invariance and local position invariance on the quantum level are described. On the quantum level there are more possibilities to violate these principles than on the classical level. The corresponding terms can be tested by Hughes–Drever type experiments or by atom interferometry. It is proposed that an atom interferometric test of Local Position Invariance will give a three order improvement of existing estimates. 1

Igor Vasil'evich Volovich