Locality and Probability in Relativistic Quantum Theories and Hidden Variables Quantum Theories

We use the framework of Empirical Models (EM) and Hidden Variables Models (HVM) to analyze the locality and stochasticity properties of relativistic quantum theories, such as Quantum Field Theory (QFT). First, we present the standard definition of properties such as determinism, no signaling, locality, and contextuality for HVM and for EM and their relations. Then, we show that if no other conditions are added, there are only two types of EM: An EM is either classical, by which we mean that it is strongly deterministic, local, and non-contextual; Or else an EM is non-classical, in which case it is weakly deterministic, non-local and contextual. Consequently, we define criteria for an HVM to be Lorentz invariant and prove that Lorentz invariance implies parameter independence. As a result, we show that a Lorentz invariant and contextual model (e.g., relativistic quantum theory) must be genuinely stochastic i.e., it cannot have a deterministic (strong or weak) HVM. This proof is an improved version of a theorem we proved previously, and it has a wider scope. Finally, we discuss Bell’s definition of locality and show that it is equivalent to non-contextuality. We argue that Bell’s justification for this definition tacitly assumes non-contextuality (which is equivalent to strong determinism). We propose an alternative definition of locality for contextual and relativistic theories that accounts for correlations that result from common history and renders QFT a local theory.