A philosophical archive for the constructive study of substance dualism: www.newdualism.org.
Quantum Physics & Dualism:
Is Orthodox Quantum Physics consonant with a Plausible Dualism?
Quantum Physics may be indeterministic about the detailed choices between differerent outcomes for some classes of microscopic events, namely decoherent measurements, but it is not completely arbitary. Rather, it makes very precise predictions for the probabilities of those outcomes, and, furthermore, the evolution of these probability distributions is completely deterministic.
Either dualist input influences the choice of when decohering measurements occur (as Stapp suggests), or it changes the probabiliities of different outcomes (as Saunders et al also consider). In the first case, the range of influence is extremely limited, and hardly plausible in a dualist theory. In the second case, the dualist input change the probability rules of quantum physics, in just the same way as dualist input would have to change Newton's laws of motion if it were to influence classical systems.
We conclude therefore, with Saunders and Brecha, that it is very doubtful that any dualist or divine input into the operation of the natural world proceeds by exploiting the small residual indeterminism of quantum physics. Dualist control in quantum physics is no easier than in classical physics. That is, any influence of a dual degree must affect those properties of objects that are also measured by physics.
The challenge, therefore, is to find a coherent theory which explains what, how, when and why those physical properties are changed.