Hm, if you just consider unitary time evolution, I think it is compatible with quantum mechanics. "Psi(t) = U(t-t_0) Psi(t_0) for all real values for t" and all that.
And, if you want to suppose objective collapse, I think you can still consider a probability distribution over histories, where each history could be considered as like, something like the described above Psi(t), except that if at time t_i some measurement is made with the outcome of the measurement being described with the projection P, then like, for t > t_i , Psi(t) = U(t-t_i) P U(t_i-t_0) Psi(t_0) = U(t-t_0) (U(t_i-t_0)^* P U(t_i - t_0)) Psi(t_0) = (U(t-t_i) P U(t-t_i)^*) U(t-t_0) Psi(t_0) ,
except add in a projection for each objective-collapse event.
I guess you might also want to add in normalization factors.
Also, I guess maybe one might want to make the collapse be a thing that is happening constantly to some extent or another? I think I saw something about the quantum zeno effect arguing that time evolution could be described in terms of constantly applying continuously varying projection operators.
Now, in these cases, you wouldn't have the future deterministically determining the past, but you also don't have the past deterministically determining the future, so..
I think this seems like it could be considered a "slab model" or "block universe" in a reasonable sense? Though perhaps not in the sense you have in mind, but I don't know what about it fails to satisfy what you have in mind.
And, if you want to suppose objective collapse, I think you can still consider a probability distribution over histories, where each history could be considered as like, something like the described above Psi(t), except that if at time t_i some measurement is made with the outcome of the measurement being described with the projection P, then like, for t > t_i , Psi(t) = U(t-t_i) P U(t_i-t_0) Psi(t_0) = U(t-t_0) (U(t_i-t_0)^* P U(t_i - t_0)) Psi(t_0) = (U(t-t_i) P U(t-t_i)^*) U(t-t_0) Psi(t_0) ,
except add in a projection for each objective-collapse event.
I guess you might also want to add in normalization factors.
Also, I guess maybe one might want to make the collapse be a thing that is happening constantly to some extent or another? I think I saw something about the quantum zeno effect arguing that time evolution could be described in terms of constantly applying continuously varying projection operators.
Now, in these cases, you wouldn't have the future deterministically determining the past, but you also don't have the past deterministically determining the future, so..
I think this seems like it could be considered a "slab model" or "block universe" in a reasonable sense? Though perhaps not in the sense you have in mind, but I don't know what about it fails to satisfy what you have in mind.