Why a Relativistic Quantum Mechanical World Must Be Indeterministic

We present the framework of Empirical Models and Hidden Variables Models in the foundations of Quantum Mechanics and its relation to Special Relativity. In this framework we discuss the definitions of properties such as non-signaling, strong and weak determinism, locality and, especially contextuality and show that (under mild assumptions) contextuality is equivalent to non-locality and to weak determinism, and non-contextuality is equivalent to locality and strong determinism. The central derivation of this paper is that a contextual Empirical Model cannot be accounted for by a Lorentz invariant (in the broad sense; see Sect. 19.1) and deterministic (strong or weak) theory. Hence, a relativistic theory which yields the empirical predictions of quantum mechanics must be genuinely stochastic (i.e., cannot be deterministic at its fundamental level). Finally, we discuss certain debates about the existence of relativistic versions of Bohm’s and the GRW interpretations of quantum mechanics.