I discuss various formulations of stochastic Einstein locality (SEL), which is a version of the idea of relativistic causality, i.e. the idea that influences propagate at most as fast as light. SEL is similar to Reichenbach’s Principle of the Common Cause (PCC), and Bell’s Local Causality. My main aim is to discuss formulations of SEL for a fixed background spacetime. I previously argued that SEL is violated by the outcome dependence shown by Bell correlations, both in quantum mechanics and in quantum field theory. Here I re-assess those verdicts in the light of some recent literature which argues that outcome dependence does not violate the PCC. I argue that the verdicts about SEL still stand. Finally, I briefly discuss how to formulate relativistic causality if there is no

The analyzability of the universe into subsystems requires a concept of the "independence" of the subsystems, of which the relativistic quantum world supports many distinct notions which either coincide or are trivial in the classical setting. The multitude of such notions and the complex relations between them will only be adumbrated here. The emphasis of the discussion is placed upon the warrant for and the consequences of a particular notion of subsystem independence, which, it is proposed, should be viewed as primary and, it is argued, provides a reasonable framework within which to sensibly speak of relativistic quantum subsystems.

An overview is given of what mathematical physics can currently say about the vacuum state for relativistic quantum field theories on Minkowski space. Along with a review of classical results such as the Reeh–Schlieder Theorem and its immediate and controversial consequences, more recent results are discussed. These include the nature of vacuum correlations and the degree of entanglement of the vacuum, as well as the striking fact that the modular objects determined by the vacuum state and algebras of observables localized in certain regions of Minkowski space encode a remarkable range of physical information, from the dynamics and scattering behavior of the theory to the external symmetries and even the space–time itself. In addition, an intrinsic characterization of the vacuum state provided by modular objects is discussed. 1

It is shown that the correlations predicted by relativistic quantum eld theory in locally normal states between projections in local von Neumann algebras A(V 1 ); A(V 2 ) associated with spacelike separated spacetime regions V 1 ; V 2 have a (Reichenbachian) common cause located in the union of the backward light cones of V 1 and V 2 . Further comments on causality and independence in quantum eld theory are made.

Open problems and recent results on causal completeness of probabilistic theories – p. 1/2 Open problems and recent results on causal completeness of probabilistic theories

Forthcoming (after an Appendectomy) in