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.
Highlights
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
The concept of “emergence” plays an important role in quantum field theory (QFT) and, in particular, in condensed matter and particle physics, since it embodies the essential feature of systems with several interlocked time scales
To evade the no-interaction theorem it is necessary to have an infinite number of degrees of freedom to describe interaction. The latter is typically achieved via local quantum field theories (QFTs)
Summary
The concept of “emergence” plays an important role in quantum field theory (QFT) and, in particular, in condensed matter and particle physics, since it embodies the essential feature of systems with several interlocked time scales. In these systems the observed macroscopic-scale dynamics and related degrees of freedom differ drastically from the actual underlying microscopic-scale physics [1,2,3]. 3 we display how the superstatistics paradigm can be used to analyse single-particle relativistic quantum dynamics in terms of two interlocked stochastic processes that operate at two separate spatio-temporal scales. The interested reader can find the related bibliography, and proofs of the relevant statements and formulas in the accompanying paper [19]
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