where an appropriate manipulation of the density matrix corresponding to this system ought to give us the Bell system above. In classical probability we can do this. In other words, in classical probability the notion of “probabilistic dependence” is abstracted away from notions like time and space.
Yes, but the notion of Bayesian inference, where you start with a prior and build a sequence of posteriors, updating as evidence accumulates, has an intrinsic notion of time. I wonder if that’s enough for Quantum Bayesianism (I haven’t read the original works, so I don’t really know much about it).
The temporal order for sequential computation of posteriors is just our interpretation, it is not a part of the formalism. If we get pieces of evidence e1, e2, …, ek in temporal order, we could do Bayesian updating in the temporal order, or the reverse of the temporal order, and the formalism still works (that is our overall posterior will be the same, because all the updates commute). And that’s because Bayes theorem says nothing about time anywhere.
Yes, but the notion of Bayesian inference, where you start with a prior and build a sequence of posteriors, updating as evidence accumulates, has an intrinsic notion of time. I wonder if that’s enough for Quantum Bayesianism (I haven’t read the original works, so I don’t really know much about it).
The temporal order for sequential computation of posteriors is just our interpretation, it is not a part of the formalism. If we get pieces of evidence e1, e2, …, ek in temporal order, we could do Bayesian updating in the temporal order, or the reverse of the temporal order, and the formalism still works (that is our overall posterior will be the same, because all the updates commute). And that’s because Bayes theorem says nothing about time anywhere.