#### rubi

Science Advisor

- 847

- 348

If ##P(\lambda|\vec a,\vec b)## depends on ##\vec a## and ##\vec b##, it just means that it is possible that ##\vec a## and ##\vec b## depend on ##\lambda##. Let's say ##\lambda## is in the intersection of the past light cones. A local theory can perfectly well violate ##P(\lambda|\vec a,\vec b)=P(\lambda)##. You prepare two particles in the non-entangled state ##\left|\vec a\right>\otimes\left|\vec b\right>## and before you send the particles to Alice and Bob, you send Alice to order to align her detector along ##\vec a## and you do the same with Bob. This introduces a perfectly local dependence of ##\vec a## and ##\vec b## on the prepared state. So obviously, the condition can easily be violated in a local theory. Hence, it is not required by a local theory to satisfy the condition.I disagree; it's the combination of no-superdeterminism and locality that prevents [itex]\lambda[/itex] from depending on [itex]\vec{a}[/itex] and [itex]\vec{b}[/itex]. If the choice of [itex]\lambda[/itex] is only made after Alice and Bob make their choices, then it doesn't imply superdeterminism, but it does imply nonlocality, since Alice's choice influences the [itex]\lambda[/itex] that in turn influences Bob's result.