Doubly-Special Relativity from Quantum Cellular Automata

Abstract

It is shown how a Doubly-Special Relativity model can emerge from a quantum cellular automaton description of the evolution of countably many interacting quantum systems. We consider a one-dimensional automaton that spawns the Dirac evolution in the relativistic limit of small wave-vectors and masses (in Planck units). The assumption of invariance of dispersion relations for boosted observers leads to a non-linear representation of the Lorentz group on the $(\omega ,k)$ space, with an additional invariant given by the wave-vector $k=\pi /2$. The space-time reconstructed from the $(\omega ,k)$ space is intrinsically quantum, and exhibits the phenomenon of relative locality.

5 pages, 5 figures

References in corpus (3)

• Derivation of the Dirac Equation from Principles of Information Processing
• Constraining the energy-momentum dispersion relation with Planck-scale sensitivity using cold atoms
• The Dirac Quantum Cellular Automaton in one dimension: Zitterbewegung and scattering from potential

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• Quantum State Transfer through Noisy Quantum Cellular Automata
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