In 1976, John Bell proved that any locally causal theory can't account for certain observed correlations, he formulated the local causality hypotesis in terms of "local beables".
In particular, he argued that this was necessary to distinguish between theories that are relativistic and theories that aren't. For instance, in the Coulomb gauge of Electromagnetism, the scalar potential instantaneously changes depending on the location of all charges in the universe, but the theory is considered locally causal because the physically relevant quantities are the EM fields.
In quantum mechanics, the wave function (like the scalar potential) also depends on the configuration space of all particles, and therefore can't be considered physically relevant. On the other hand, if you don't introduce any relevant quantity in the theory, it seems to be impossible to impose/discuss a relativistic extension of it, because Bell's notion would be meaningless.
- Can the notion of local causality be relaxed so that it doesn't depend on local beables?
- Would this new notion of local causality allow us to decide if a theory is relativistic or not? If it doesn't contain local beables, in which sense would EM be relativistic according to this notion?