  In the paper it will be shown that Reichenbach's Weak Common Cause Principle
is not valid in algebraic quantum field theory with locally finite degrees of
freedom in general. Namely, for any pair of projections A and B supported in
spacelike separated double cones O(a) and O(b), respectively, a correlating
state can be given for which there is no nontrivial common cause (system)
located in the union of the backward light cones of O(a) and O(b) and commuting
with the both A and B. Since noncommuting common cause solutions are presented
in these states the abandonment of commutativity can modulate this result:
noncommutative Common Cause Principles might survive in these models.
