This isn't correct. Photons are said to go through both slits because they travel like waves and actually go through both slits. How would your interpretation account for the fact that a single photon at a time fired through a double slit still produces an interference pattern?
not really. See mentioned below Hitachi electron double slit experiment.
> How would your interpretation account for the fact that a single photon at a time fired through a double slit still produces an interference pattern?
Because position is quantized, ie the position probability has that wave form, and thus position probability of hitting the screen has that interference looking pattern. There is no real physical interference though between any real waves here. It is just a position probability pattern formed as direct sum of 2 other patterns - the 2 cutouts made by the slits from the original wave pattern of quantized position probability.
The Hitachi electron double slit experiment (https://www.youtube.com/watch?v=PanqoHa_B6c) is much more illustrative because electron position quantization is different from the electron's DeBrogile - unlike photons. In Hitachi you can see that each electron hits the screen as a singular point and only the statistical aggregation of these hits - such aggregation naturally visualizes the position probability density - forms the "interference" pattern.
I really don't know what you're disagreeing with.
Thing is, an interpretation cannot account for anything, it is a theory that does...
Can't we just agree that "brain" has no place in objective science (unless it's the brain science, of course).
No, one could easily imagine fundamental laws of physics which map multiple states at one time step to the same state at the next. Indeed, the emergent laws of thermodynamics, which govern the accessible physical quantities of macroscopic systems, have this feature. It turns out in our universe that this apparent irreversibility is due to a special initial state and information being dumped into inaccessible microscopic degrees of freedom, so that statistical mechanics and atomic theory can be used to derive the appearance of thermodynamics. But there's nothing internally inconsistent about a fundamentally irreversible theory.
You asserted that there was something wrong in principle with many-to-one dynamics. I pointed out that we have consistent irreversible theories that are considered in-principle acceptable theories, and in particular are strictly preferred over one-to-one theories in their respective domains.
> You can conjecture that our current reality could have been arrived at from two different paths. What you cannot do is assert the truth of a theory which selects one path in favor of the other, because the existence of any information which would make that determination would contradict that these both histories led to the same present.
Just because two different pasts would have led to identical presents does not mean we don't have criteria (such as simplicity) to favor one past over another. Indeed, all of science is based on this. Ultimately all we can use to check our theories are our observations, and the actual microscopic state of the universe is vastly under-determined from these observations alone. Assumptions about simplicity and regularity must be deployed.
As an extreme example: it's logically possible a cheesecake materialized in the center of the sun 1 second ago. (You can either think of this as a thermodynamic fluke, or as a new proposed fundamental theory where the standard model of physics is temporarily suspended 13.8 billion years after the big bang and exactly 1 cheesecake appears in the center of each star.) The cheesecake would be instantly destroyed, and it would not influence my observations, and thus there are two possible pasts (cheesecake vs. no cheesecake) which give the same present state and observations and we cannot categorically rule one out. Nevertheless, we assign astronomically low probability to the cheesecake past.
What you suppose is logically inconsistent with that fact, and the whole idea is going to be unfalsifiable. The human brains' ability to distinguish possibilities is contingent upon the presence of information.
>Do photons have their probability distributions with interference patterns on screens to resolve a some sort of preferential history information storage? Like there is not enough bits available to say which screen the photons went through so they must say both?
Yes, photons are said to go through both slits because there does not exist any information which would distinguish the paths. As soon as you arrange an experiment which provides such information, the chosen path becomes clear.