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I've been reading a lot on determinism from a quantum mechanics perspective in order to reach a conclusion about freewill and determinism. So far, it seems that quantum interpretations (Copenhagen, Bohmian, Everett, etc) are simply interpretations, not testable. The question to whether our world is blurry/indeterminate/probabilistic or concrete/casually deterministic depends on which interpretation you like.

But the problem of freewill makes no sense whichever way you look, and I know I am stretching the theories now, but let's assume that quantum interpretations do have impacts on human behavior:

I use 'free' to mean an element of an action that is independent of all causes. But whether our actions are probabilistic or deterministic, neither are truly ‘free’, they are merely statistical probabilities, not arising out of free choice, but out of causal events. This is true whichever quantum interpretation you go with, it simply means your choice is either fixed or a probability.

The only answer I can come up with is this:

There are many causes to your actions, maybe some deterministic, some probabilistic, but there is an element that arises independently from anything before it, like the Big Bang, and only you have control over it arising. It cannot arise spontaneously, that is not freewill either, that is just chaos. It must arise out of a will. It has a 'cause' in the sense that a thought triggers a set of particles or atoms inside your brain to do something, and it leads to (the conditions for) the spontaneous creation of a particle or a spontaneous action, which has just come into existence without a prior physical cause, and begins to affect the things around you. It just appears, like the Big Bang. Some of its characteristics might be determined when it comes into being.

That would be my only explanation. Didn't Hawkings write that atoms can just pop into existence and out again? What about energy conservation? Could this atom (or set of atoms, or set of atom-activities) pop into existence through an intangible, non-physical force? I know this sounds like telekinesis magic, but quantum entanglement is pretty weird too. I've run out of options. I would like to know if this idea is theoretically possible. Physics or philosophically.

  • Actions can not be statistical probabilities, and one can equally say that "probabilistic causes" are not truly causes. If actions are subject to statistical probabilities only then they are, in the end, "truly free". If all the "causes" can do is determine probabilities of the result, but not the result itself, the final choice is "uncaused" or "free", as in electron "choosing" between two slits. Energy conservation is moot as either choice is consistent with it. Probabilities leave outcomes undetermined and wide open to "free choice". – Conifold Apr 25 at 22:29
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Anything is theoretically possible. The question that makes sense is "can we show that this is the case ?"

With this in mind, we can can subdivide this question in sub problems:

  • what exactly is a "will" ?

  • how does it command to seemingly chaotic quantum phenomenons?

  • why does it do such only through a brain, what is more only through one specific brain?

  • when/how/why does it get associated with this specific brain ?

  • where did it get such a fine grained knowledge of physics and neural biology, that it can purposefully create specific thoughts in a brain by popping atoms in existence ?

  • how would come, although our will has this fine grained, instinctual knowledge of our brain, that we as individual don't have it ?

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  • For your last two points, I don’t think these are necessary. It’s like the fact that a dog’s brain does calculus when it’s figuring out when to jump to catch a frisbee. The dog doesn’t actually have any knowledge of calculus, it’s performing this calculation in a different manner. I don’t think knowledge is necessarily part of the mechanism of will-brain interaction, all it needs is a certain capability to make the neural events happen. – Era Jul 19 at 19:25
  • The two points are still valid in my opinion. We have a very fine knowledge of how animals learn to move by training. So fine that we can apply it to robots to teach them how to reach and grab things like babies learn to, by trial and error. We have absolutely no idea of how an immaterial mind would gain a similar practical knowledge of quantum mechanics. – armand Jul 20 at 6:04
  • As for the second point, animals who know how to move just happen to, well, know how to move. Yet, our soul would know how to pop matter into existence and interfere with chemical process, but we wouldn't ? – armand Jul 20 at 6:36
  • I’m not saying that these points are invalid, just not necessary. My point is that the quantum stuff is just a mechanism, it doesn’t necessarily require any conscious understanding to use. It could be what is often called procedural knowledge or tacit knowledge. I’m also not sure about the distinction between the self and the “soul” here. – Era Jul 22 at 1:55
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It cannot arise spontaneously, that is not freewill either, that is just chaos. It must arise out of a will. It has a 'cause' in the sense that a thought triggers a set of particles or atoms inside your brain to do something, and it leads to (the conditions for) the spontaneous creation of a particle or a spontaneous action, which has just come into existence without a prior physical cause, and begins to affect the things around you.

In this situation, the particles or atoms inside your brain doing something is a cause of the spontaneous creation of the particle; it's setting up the conditions. You're not going to get an un-caused cause out of this. (And such un-caused cause would just be chaos, as you say.)

The prior physical cause, in this situation, would be the thought (or, at least, the physics “implementing” the thought). As a rule of thumb, you're not going to get free will out of some exotic physics. (What happens when we understand that physics? You'll need new exotic physics.)

There are two kinds of "particles popping out of nowhere" I can think of, off the top of my head:

  • Virtual particles, where a matter / antimatter pair spontaneously forms, then annihilates. Energy is conserved, because there's no net energy change from such an event. (This is responsible for Hawking radiation and the Casimir effect.)
  • Pair production, where a high density region of (non-mass, non-kinetic) potential energy forms some matter, but that matter has enough energy to not immediately cease to be.

Neither of them meet your stated requirements; virtual particle formation is unpredictable (not, technically speaking, what a physicist would call chaotic, but it's what you're calling chaos), and pair production requires energies significantly higher than (are known to) exist in our brains.

TL;DR: No.

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Your text suggests that the world is a mix of probabilistic and deterministic behaviors, but that is like saying that nature is made of objects and things. Each behavior belong to a specific domain. And that could shed some light for your answer.

A mathematical formula like v=x/t expresses a fact with 100% of probability (=determinism). The only problem is that such formula is valid only in the universe of our experience; it is false in the structural (let's call it "real") nature. The macroscopic world, the world of our interpretation, is deterministic. The real nature (the scale of qm phenomena) seems to be probabilistic. Most of mathematics is FALSE in such realm. The more we focus our lens on such nature, the more we end up observing ourselves. As the standard rule, it seems that the object is always defined by the subject, meaning that the world is so because of our subjective features.

That, on one hand, is a strong argument against determinism. On the other hand, we would need to know if there's only one future (which would make a deterministic nature) or there are multiple (that would be a probabilistic nature). But that is impossible. Or at least, we have come to know that the only way to express the future is in a probabilistic manner.

Anyway, the problem of free will is an arbitrary mix of ideas. But also in such case, the free will option seems to prevail: If our decisions are determined by few qm events, then we have free will. If our decisions are determined by massive qm events, then, there is no free will. But ask yourself, how qm-massive an event should be in order to be considered deterministic? You will probably conclude, as I did, that v=x/y carries not a probability of 100%, which is true (do the experience without excluding the results that raise from exceptional situations! The more precise you are with the measurement of the speed of a body, the more you will get convinced that the speed is a probability in a range[1]). Determinism is in consequence just an ideal.

So, you don't need of spontaneous particles creation to address the problem; that's why it is not necessary to enter in such precise issue to answer the question, since the result will be the same: if you consider qm, determinism is just an ideal mechanism that reason uses to create an interpretation of nature. As soon as qm is considered, determinism comes to be a feature introduced by the epistemic mechanism of the observer.

[1] Stating that the speed of a body is 15.329 km/h implies a probabilistic reification: depending on the rounding method introduced by the measuring device, the speed is most probably in the range 15.3285000...<speed<15.3294999... (there's no possible device that measures physical values with absolute precision, meaning that the speed is far from being exactly 15.329000000...)

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https://www.ams.org/notices/200902/rtx090200226p.pdf goes to "The Strong Free Will Theorem" which addresses the very subject of your question rather nicely.

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  • From reading the summary here, it seems their result has to do with a loophole in Bell's inequality sometimes called "super-determinism", which I mentioned in the "violation of freedom" section of this answer I wrote up summarizing Bell's inquality. The summary seems to to say that if you say the experimenters at different locations are "free" in a sense that rules out super-determinism, with an axiom saying their choices are statistically independent of one another, – Hypnosifl Apr 25 at 20:55
  • (cont.) then the behaviors of the particles at each location must also be free in the same sense (statistically independent of one another, not explainable by their common past). So I don't think their reasons for calling it "free will" had to do with specifically wanting to rule out the idea that choices were simply random (which would itself imply statistical independence), but just to say that particles and experimenters' choices must be "free" in the same sense, which could just mean both are random. – Hypnosifl Apr 25 at 20:55
  • Unfortunately, the Conway-Kochen theorem does not address the subject in its title at all, it is a typical no go result packaged into sensational buzzwords, see Is Conway-Kochen's “free will” theorem about quantum measurements an argument for panpsychism? – Conifold Apr 25 at 22:22

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