 It is known however that quantum field theory is causally complete in the weaker sense of containing common causes localized in the union (as opposed to the intersection) of the backward light cones of the spacelike separated spacetime regions \(V_1\) and \(V_2\) that contain the correlated observables (Rédei &amp; Summers 2002, 2007b; Hofer-Szabó et al. 2013). It also is possible logically that the status of the Common Cause Principle in relativistic quantum field theory cannot be decided: The quantum field theory in which the abundance of correlations between spacelike separated observables has been proven is defined by axioms (Haag-Kastler axiomatization). The axioms might just be too weak to give an answer to the question whether all correlations between spacelike separated observables have properly localized common causes. Proving such an independence result would be very interesting. Given how difficult it is to create any model of the Haag-Kastler axioms, attempting such a proof also appears to be extremely difficult because it requires displaying two models, one in which the Common Cause Principle holds (with properly localized common causes), one in which it does not.