Locality and probability in relativistic quantum theories and hidden variables quantum theories

We define criteria for a hidden variables theory to be Lorentz invariant and prove that it implies no signaling. As a result, we show that a Lorentz invariant and contextual theory (e.g., quantum field theory) must be genuinely stochastic, i.e., it cannot have a deterministic (strong or weak) hidden variables model. This proof is an improved version of a theorem we proved previously, and it has a wider scope. Finally, we show that Bell's definition of locality is equivalent to non contextuality (or strong determinism). We propose an alternative definition of locality for contextual and relativistic theories according to which quantum field theory is local.