Stochastic Causality Is Inconsistent with the Lorentz Group

According to modern physics, all physical processes are described by quantum theory. In particular, due to quantum fluctuations, even in the empty space, the causal relation is, in general, slightly different from the usual Minkowski one. Since quantum effects are probabilistic, to properly represent the corresponding stochastic causality, we need to describe, for every two events e and e′, the probability p(e, e′) that e can causally influence e′. Surprisingly, it turns out that such a probability functions cannot be Lorentz-invariant. In other words, once we take into account quantum effects in causality, Lorentzinvariance is violated – similarly to the fact that it is violated if we take into account the presence of matter and start considering cosmological solutions.