The key that I feel a LOT of the discussion on this topic could use more mention of is that free will seems to be an intuition, not a precise logical claim. So falsifying some version like "if we rewound time, could you have picked chocolate instead of vanilla" may not be the most meaningful thing, because for one thing, that we have a sense of choice is intimately tied to there being a sense of a difference between the future and the past (even if the equations of physics may be reversible).
The fact is that the equations of physics only show how quantities relate -- there are some brute facts from the outset that we may have to accept, such as that our universe had initial conditions which would force time-flow to "essentially" be unidirectional. I think this is the leading idea or one of them.
I personally think that people should consider what freedom would really mean (i.e. instead of falsifying free will of some peculiar variety, try to find out what the intuition IS and what it isn't, what it can and can't be): if you really were spontaneous, you would not have a well-defined nature, i.e. a sense of identity. Spontaneity aka randomness is not what people want -- they want an identity (meaning some predetermination from genes as a starting point from which you can shape yourself)...but also an element of choice. This is achieved by the divide between a conscious and unconscious brain -- your brain certainly determines all your actions, but part of that iswhat you feel is your ego, i.e. the center of your conscious identity.
Most free will doubters essentially ant to say that the conscious vs unconscious distinction is less fundamental than the laws of physics, as the distinction is a property of biology. That is, once particles assemble in a certain position, they will become conscious. As everything just obeys these mechanistic laws, our ego and sense of choice is secondary (although compatibalists suggest that on a higher biological level we as good as have choice, even if on the fundamental level, choice is not part of the theory)
I think the real answer to this question requires a full understanding of consciousness and how the way we see the laws of physics relates to it. If we can truly say the laws of physics in some sense are a higher truth than our consciousness, rather than being emergent properties of it, then sure. However, amidst the many woolly claims of quantum mysticism, one can't overlook that our ability to perceive sense data is HEAVILY influenced by our consciousness -- why would there be such a divide between our conscious intuitions of physical reality and quantum laws otherwise?
In my view, perhaps instead of trying to explain consciousness using quantum physics, we should be putting effort at least somwhat into understanding why conscious systems in our sense are unable to "directly intuit" quantum physics.
A conscious entity like ourselves seems unable even in principle to operate with the view that our future is determined just as surely as our past (both free will and causality come under fire under certain views of physics, not just free will, since we infer all our physics -- even stuff that is abstract like the quantum wavefunction -- from experiment). That is, one must be detached from a system in order to predict its behavior, and the very definition of consciousness (although we hardly have a scientifically rigorous one) would seem to include some sense of involvement/participation in the time-evolution of the body/brain system. The same issue as in quantum physics, namely we can't measure the system withotu disturbing it, is in a way present here.
What this does is "enable" our intuition from above, namely that we have a certain nature (given by our brain structure), but that we're "directing" the outcomes of that nature -- the conscious/unconscious divide seems essential to this sensation, as well as to the sensation that we simply must choose, not just "let things happen as they are predetermined."
Yet we also know that all seems to be a product of physics in the end. That is, physicalism seems preferable to dualism.
I consider all this mysterious, but if I had to bet, the answer might have to do somewhat with the link between consciousness and the concept of something "participating in time." After all, that is what prevents our prediction of our future -- that our involvement in our own past-present-future continuum prevents us from making a detached prediction, as the very act of trying to predict modifies the future.
My view is a blend of believing there are ways we can understand this stuff much better, but I see there being an element of uncertainty remaining.I'm far from an expert on these topics, but I've thought/worried about tehm before.
Suffice it to say for most of society's needs, naive physicalism and compatibilism seems a fine combo so you can just go on with your life.
But more conceptually, I personally don't know if physicalism suffices. It's certainly better than naive dualism, and for all practical purposes probably the best theory we have...but I'm feeling like we can't escape some metaphysical nonsense when free will and consciousness are concerned.
My goal in all these things is to present what I find is the most reasonable view, I find rigid logicality doesn't work because it refuses to acknowledge the fuzzier domains. I think ethics, metaphysics, consciousness, free will are very very fundamentally hard to subsume in a physicalist view. At the very least, we might come to the conclusion that physicailsm is a full theory of the universe, but it fulfills only our truth-needs and not our pragmatic needs---a distinction between pragmatic reasoning and truth might persist nonetheless.