True, this is a phenomenon we do not understand, but it could provide an opening for non-deterministic influence in nature. That is, if our scientific picture of the world were that there are only four forces of nature and all of them are deterministic, then it would be hard to explain free choice, because we could not explain it with any force of nature. But if our scientific picture of the world suddenly reveals a phenomenon that is not explained by any force of nature, that means there is something beyond the four deterministic forces of nature, and that already opens the door to non-deterministic influences in reality.

As for hidden variables, this is what I got from GPT:
The thesis of local hidden variables was rejected by most of the physics community בעקבות empirical experiments, mainly Bell tests, which showed that the correlation between the measurement outcomes of entangled particles violates Bell’s inequality, something that should not happen if local hidden variables exist.
Nonlocal hidden variables (such as in Bohmian mechanics) have still not been empirically disproven. They accept spooky action as real and assume instantaneous action at a distance.

As for information transfer, I know that you cannot transfer information this way faster than light, but there is still a physical effect here that happens faster than light (even though no information can be carried by it).

That is exactly the point. Nonlocal hidden variables describe a deterministic influence, only not a local one. Beyond that, free will is also not compatible with quantum theory, even though it is non-deterministic. And finally, if you cannot transmit information this way, then it has no ability to explain phenomena that do involve information.

Okay, so either the phenomenon is explained by hidden variables that are nonlocal, or it is explained without hidden variables, but even on that possibility locality is violated. Since the four laws of nature we know operate locally, do you think this means there is some kind of fifth law of nature here that operates nonlocally?

It is not another law of nature. The quantum version of those laws is nonlocal.

Regarding what you said above:
“Free will is also not compatible with quantum theory, even though it is non-deterministic.”

I wanted to suggest a mechanism by which quantum theory could explain free choice, but in a different way from what you presented in your book The Science of Freedom:

In your book you said that because the statistical distribution of the wave function is random and cannot be controlled, you really cannot insert free choice here, only random “choice.” But what can be controlled is the very choice of whether or not to collapse the wave function. For example, suppose that inside my brain there were some mechanism resembling the double-slit experiment, in which there is a stream of electrons passing through two slits, and the spirit decides whether to perform a measurement on the electrons before they enter the slits (or not to perform one). The decision made in the brain would depend on the interference pattern that appears on the screen. If the spirit decided to measure, then the interference pattern would be of particles and not of waves, and therefore the brain would make decision A; and if the spirit decided not to measure, then a wave interference pattern would arise, and the brain would accordingly make decision B. You could ask how this is different from the spirit directly affecting the electrons, and my answer is that collapse of the wave function is not exactly a physical process, unlike moving an electron. That is, if the spirit decides to collapse the wave function of a certain electron, it does not need to use any force to do so (for, as we saw above, one can collapse the wave function of a quantum-entangled particle nonlocally). What do you think of this possibility?

I did not understand. The result of the collapse is dictated by the quantum distribution. If you want to intervene in that, then that is exactly what I was talking about.

Indeed, the result of the collapse is dictated, but I do not care about the result of the collapse; I care about the very fact of whether there was a collapse or not. That question has physical implications for reality, as demonstrated in the double-slit experiment, and so one can encode decision-information in it.

You are assuming choice, not proving it. If I can choose whether to measure or not, then one can plant the choice in the physics. I also do not understand what locality has to do with it. Nonlocality too is deterministic.

I am not trying to prove that there is choice, but to raise the possibility of a physical mechanism that could allow it without violating the determinism of the four known laws of nature. That is, to suggest a plausible place and mechanism for contact between physics and metaphysics (or spirit and matter). On your view, at the beginning of the event-chain of choice, there is some electron that moves without any force acting on it. What I am trying to suggest is that at the beginning of the event-chain of choice there is a collapse of a wave function. For example: if some electron in my brain collapses, I will perform action A, and if it does not collapse, I will perform action B. Note that it does not matter what the result of the collapse is, only whether a collapse happened or not. The advantage of such a mechanism is that there is no electron here moving without a force acting on it (that is, no violation of the laws of nature).

But the question of whether a collapse will happen or not depends on my decision to measure. Beyond that, even if the collapse happens randomly (and it does not), then that is randomness and not choice. I do not understand what you gain.

The nonlocality of quantum mechanics only serves as an indication (not a necessary one, of course) that the act of measurement or the collapse of the wave function is a nonphysical process, because physical processes are usually local. There is another indication of this from the double-slit experiment in a case where a detector is placed at the entrance to only one slit (say, the left one), and the particle passes through the right slit, meaning it does not undergo any physical interaction with the detector, and still its wave function collapses, and the interference pattern on the screen changes accordingly.

It is true that the collapse will happen only if I decide to collapse it, just as the electron will move only if I decide to move it in your model. The collapse does not happen randomly; it happens if I decide to collapse it, just as in your model the electron will move only if I decide to move it.

As for your question about what I gain:
The advantage of a mechanism like the one I am proposing is that it does not contain an electron moving without a force acting on it (that is, a violation of the laws of nature).

Of course it does. You decide to collapse it. Is that decision itself also the result of a prior decision to collapse? As for locality, I already wrote above that this is not a different force.

And we have not even talked yet about the fact that a quantum movement of an electron gets washed out at large scales and at our temperatures.

Wait, let’s put things in order. Both according to your view and according to my proposal, every chain of events that begins with choice starts in the mental or spiritual dimension, and then unfolds into the physical dimension. According to your view, there is no need for quantum mechanics, and one can locate the interface between the spiritual and physical dimensions in the movement of an electron that is influenced by the spirit in a nonphysical way (an electron moves without a physical force acting on it). According to my proposal, I replace the movement of the electron without a force acting on it with the collapse of an electron’s wave function. The very collapse of the electron’s wave function can cause a macroscopic physical change in reality, as seen in the double-slit experiment. Statistically, there is a difference between a stream of collapsed and uncollapsed electrons passing through two slits because of each electron’s interference with itself. Does that description sound reasonable to you?

You did not put things in order for me. I repeat that I do not understand what you are saying. How does the story begin? With the person’s decision to measure? Then how will you explain that? There too there is a collapse without human action, so you are back to my explanation. I do not see any gain.

The difference between my explanation and yours is that in mine there is no violation of the laws of nature. A collapse without human action does not contradict the laws of nature, whereas movement of an electron without a force does contradict them.

A collapse without human action does contradict them. Collapse is the result of measurement.

Ah, now we are getting to the core of the discussion. Now, if we go back to entangled quantum particles, there you can see that when one particle is measured, the particle entangled with it also collapses immediately, even though it is very far away. Also in the double-slit experiment you can see that the wave function collapses even in a case where a detector is placed at the entrance to one of the slits (say, the left one), and the particle passed through the right slit, meaning that even though there was no act of measurement by the detector, the particle’s wave function still collapsed. From both of these one can see that collapse of the wave function is a nonphysical process, and therefore a collapse of the wave function “out of nowhere” does not violate any law of nature.

I apologize, but this “core” of the discussion has already been discussed here for quite some time. I simply cannot understand what the argument is about. It seems to me that I explained well why this proposal says nothing different and adds nothing to the discussion. I’m stopping because I do not understand what we are talking about.