In arrow of time discussions quantum theory is on the level that does not prefer one direction.For example on a electron the future question would be “where is the electron going (at a future time in which position there is an electron)?” and the past question would be “where did the electron come from (at a past time in which position there was an electron)?”. That the electron is here and an electron happened is going to stay fixed.
“uncollapsing” is probably mathematically sensible. Take the past superposition then forget where we found the electron and project forward paths from each of the past positions up to present. Those are the electron positions which are past-compatible with our found electron. Analysis of choice erasure experiments probably runs the same maths. If you do not know the source there is probably no other consistent position than the actual one (because deterministic theory). If you have a reason to know the electron came from a particular source point then the destination is going to fan out.
It seems to me that if you sum up the spreads from knowing the source was in each position that is a different spread than not knowing at all, the spread of one point. So a true superposition behaves differently than being uncertain of a non-superposition source. In this deduction I am losing a complex phase in treating “where the electron could have been from this source” as a real field out of which I sum up a new real field. Would keeping the phases end up agreeing that only the detected position was possible? Without being able to run the complex math in my head, indirect argument that it does: deterministic outcome evolving to a stochastic outcome T-symmetry reversed means there is a process that turns a stochastic state into a deterministic state. Which means it can’t really be that stochastic at all if it can be unscrambled. So any interpretation that insists that there is a single classical underlying reality and the rest is just all epistemics is going to run into bookkeeping trouble explaining these “merger” processes. So the complex valuedness is connected to the fact that it is not dice playing at all.
In arrow of time discussions quantum theory is on the level that does not prefer one direction.For example on a electron the future question would be “where is the electron going (at a future time in which position there is an electron)?” and the past question would be “where did the electron come from (at a past time in which position there was an electron)?”. That the electron is here and an electron happened is going to stay fixed.
“uncollapsing” is probably mathematically sensible. Take the past superposition then forget where we found the electron and project forward paths from each of the past positions up to present. Those are the electron positions which are past-compatible with our found electron. Analysis of choice erasure experiments probably runs the same maths. If you do not know the source there is probably no other consistent position than the actual one (because deterministic theory). If you have a reason to know the electron came from a particular source point then the destination is going to fan out.
It seems to me that if you sum up the spreads from knowing the source was in each position that is a different spread than not knowing at all, the spread of one point. So a true superposition behaves differently than being uncertain of a non-superposition source. In this deduction I am losing a complex phase in treating “where the electron could have been from this source” as a real field out of which I sum up a new real field. Would keeping the phases end up agreeing that only the detected position was possible? Without being able to run the complex math in my head, indirect argument that it does: deterministic outcome evolving to a stochastic outcome T-symmetry reversed means there is a process that turns a stochastic state into a deterministic state. Which means it can’t really be that stochastic at all if it can be unscrambled. So any interpretation that insists that there is a single classical underlying reality and the rest is just all epistemics is going to run into bookkeeping trouble explaining these “merger” processes. So the complex valuedness is connected to the fact that it is not dice playing at all.