Special Relativity induced by Granular Space

Abstract

We show that the special relativistic dynamics when combined with quantum mechanics and the concept of superstatistics can be interpreted as arising from two interlocked non-relativistic stochastic processes that operate at different energy scales. This interpretation leads to Feynman amplitudes that are in the Euclidean regime identical to transition probability of a Brownian particle propagating through a granular space. Some kind of spacetime granularity could be held responsible for the emergence at larger scales of various symmetries. For illustration we consider also the dynamics and the propagator of a spinless relativistic particle. Implications for doubly special relativity, quantum field theory, quantum gravity and cosmology are discussed.

6 pages, RevTeX4. Some revisions in DSR section and in Conclusions. References added

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• On the possible distributions of temperature in nonequilibrium steady states
• Extreme Value Laws for Superstatistics
• The gravitational baryogenesis and a new higher-order extended uncertainty principle with parameter adaptability for the minimum length
• Michelson-Morley Experiments: at the crossroads of Relativity, Cosmology and Quantum Physics
• Quantum Non-Locality and the CMB: what Experiments say
• The vacuum as a form of turbulent fluid: motivations, experiments, implications