Could free will exist as spontaneous particle creations?

Free will has nothing to do with physics. Free will is our ability to make decisions.

Decisions are not physical events, they cannot be caused, but they do cause voluntary muscle actions. Basically decisions are just information, knowledge about what the decider is about to do.

Decision-making is a mental process, not a physical one. It cannot be described in terms of physics, the laws of physics don't apply.

If the 'element' you speak of 'arises independently from anything before it', it cannot simultaneously 'arise out of a will'. You actually specify a cause; the 'thought [which] triggers a set of particles or atoms inside your brain'.

When you state, "It just appears, like the Big Bang. Some of its characteristics might be determined when it comes into being", it is important to remember that we have no reason to think that the big bang was uncaused, and that any characteristics which "come into being" after such an event are either caused or somehow random, in which case you remain without the kind of agency that free will requires.

I stand to be corrected, but I don't imagine that if Hawking wrote that "atoms can just pop into existence and out again", that he necessarily subscribed to the idea that such events were uncaused. It would seem more reasonable to presume - given our understanding of physics to date - that the causes for now remain unobservable to us.

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...)

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.

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 ?

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.