I have suspected that modern quantum theory contains the seeds of a new theory of causality. I did a search on Google scholar looking for more papers. I thought this one, by mathematical physicist V.P. Belavkin, was interesting, and I offer the briefest of summaries below. As usual, I was limited in my ability to follow the formalism, and therefore will “bleg” anyone with expertise in this area to comment or offer references which help explain this in layman’s terms.
Belavkin says that “the latest developments in quantum probability, stochastics, and in quantum information theory” make it possible to bypass the paradoxes of the measurement problem in the traditional quantum theory. The original theory divides the world into an external observer and a closed quantum system to be observed, which results in the problem.
It goes something like this: Belavkin analyzes open quantum systems using a dynamical approach which gives the output statistics of continuous quantum measurements which result from the solution of a stochastic differential equation. He then applies a special filtering method or superselection rule – which he calls a causality principle – which imposes a past-future boundary. The past consists of classical particle trajectories, the future are the quantum probabilities compatible with these trajectories. The statistical results obtained are consistent with experiment, just as in the traditional formulation.
Now it seems we haven’t gotten “something for nothing” here. In exchange for getting rid of the seemingly subjective observer problem in the original theory and making things more objective, he had to insert “by hand” a boundary defining the arrow of time. Still, it is appealing to think that time and causality are in an objective way intimately bound up with the transformation of quantum potentials into classical realities, as is the case with this proposal.