An intrinsic causality principle in histories-based quantum theory: a proposal

Abstract

Relativistic causality (RC) is the principle that no cause can act outside its future lightcone, but any attempt to formulate this principle more precisely will depend on the foundational framework that one adopts for quantum theory. Adopting a histories-based (or "path integral") framework, we relate RC to a condition we term "Persistence of Zero" (PoZ), according to which an event $E$ of measure zero remains forbidden if one forms its conjunction with any other event associated to a spacetime region that is later than or spacelike to that of $E$. We also relate PoZ to the Bell inequalities by showing that, in combination with a second, more technical condition it leads to the quantal counterpart of Fine's patching theorem in much the same way as Bell's condition of Local Causality leads to Fine's original theorem. We then argue that RC per se has very little to say on the matter of which correlations can occur in nature and which cannot. From the point of view we arrive at, histories-based quantum theories are nonlocal in spacetime, and fully in compliance with relativistic causality.