

The Harvard physicist Jacob Barandes proved that quantum mechanics is mathematically equivalent to a statistical theory with history dependence in his paper here. There is thus always a rather simple and intuitive explanation for most quantum mechanical phenomena without resorting to things like multiverses or collapsing wavefunctions, but that it is just a statistical theory + history dependence.
I will use this simulator to illustrate: https://ophysics.com/l3.html
Rotating only the first 90 degrees blocks the light.

Rotating only the second 90 degrees blocks the light.

Rotating both 90 individually blocks the light.

Rotating the first at 45 degrees and the second at 90 degrees allows light to pass through.

Rotating the first at 90 degrees and the second at 45 degrees does NOT allow light to pass through.

To say that there is history dependence means the behavior of the particles is a function over its history, and so the behavior of the particle during an interaction can change if its history is different. If not all the light is blocked by the time it reaches the second one, then the behavior of the photon at the second one can be different if, in its history, it had interacted with the first one rotated at 45 degrees, and thus the second one may not block all the light as we would normally expect it to because you have changed the history of the particle.
In classical statistics, you can represent the statistical outcome of an interaction according to p(t)=f(U(t),p(t-1)) whereby U is the definition of the operator describing the interaction and p is the probability distribution. Mathematically, you can decompose the quantum state into two real-valued vectors according to its two degrees of freedom where one is a probability vector, common in classical statistics, and the other is the phase, and the way the probability vector evolves with an interaction can be defined by p(t)=f(U(t),p(t-1),h(t-1)) where h is the phase.
The phase can be interpreted as a sufficient statistic over the system’s historical trajectory, because you can get rid of the phase entirely by expanding out h(t-1) over its whole history such that you get:
p(t)=f(U(t),p(t-1),g(U(t-1),p(t-2),g(U(t-2),p(t-3),…)))
This extension would stop at a base case. It is quite trivial to prove that a degenerate distribution would be a base case, and so if there is a point in the system’s history where you know its value with certainty, then you can stop the expansion there, and thus the phase disappears from the evolution rule. Of course, that doesn’t mean you shouldn’t use the phase mathematically, you just don’t interpret it as a physical entity, but as a sufficient statistic over the system’s statistical history.
You can think of each physical interaction like a black box the particle enters, the box alters its state, and then it leaves the black box. The black box is described by a function, which takes the particle’s pre-interaction state as an input, and then outputs its post-interaction state. You can conceive of quantum mechanics as just a form of statistical mechanics whereby the statistical behavior of the particle is a function not just of the particle’s statistical state right now and the current operator, but of all its previous statistical states and previous operators.
Each black box is, in a sense, “aware” of the whole history of the particle which enters it. The second polarizer “knows” that the particle had just interacted with the previous one at a 45 degree angle, so it changes its behavior accordingly. If we express it like this:
p(t)=f(U(t),p(t-1),g(U(t-1),p(t-2)))
Then the behavior of the second polarizer given by this function can change if U(t-1), the previous polarizer’s orientation, is changed.



Questions like these stem from the cancer that was the abandonment of “materialism” for “physicalism.” Physicalism has rotted people’s brains to believe that every law of nature needs an underlying “explanation” whereby the explanation is always some invisible entity that is impossible to observe under any possible circumstances but, like the hand of God, pilots the objects we can perceive in order to “explain” why they behave in that way, according to that law.
No, we do not need such an “explanation.” It is perfectly logically consistent to just treat is as nomological. It is a law of nature that tells you how the particles behave. The law is itself the “explanation.” There need not be any underlying invisible entities piloting the objects we perceive to “explain” why their behavior operates according to those natural laws. It is simply in their nature to do so.
The natural laws simply are a function of the historical state of the system. The explanation is the law. There is no deeper, invisible mechanism.