Physicalists have always had a hard time believing in free will! Real choice seemed excluded by conditioning and the perspective that all things and beings, including humans, are nothing but machines with predictable responses has held sway.
Quantum mechanics and the many-worlds theory of Hugh Everett seem to be able to reconcile possible free will with the physicalist viewpoint, however. As explained in my book, the many-worlds theory operates on the assumption that the state of superposition that precedes every alternative route, every choice, leads to one observable reality for one actor, but equally to the alternative reality for a doublet actor spawned by the state of superposition. In other words, every alternative, every choice, gives rise to a parallel universe where another version of you will live your discarded choice. The you that is you will only experience one version of reality, but parallel yous will live all possible permutations of your choice. In this theory, every possible variation of reality will play out in its own parallel universe, and the number of parallel universes will be almost infinite.
To digest this is obviously a tall order, but the many-worlds idea is, nevertheless, a respectable theory in theoretical physics. Relative to free will the interesting thing is that it may break the stranglehold of the mechanistic perspective without discarding it. Physicalists assume that every alternative can have only one logical outcome, but in the many-worlds theory every alternative will be a reality in some parallel universe, and every alternative will have come into being according to its own impeccable logic. In the past physicalists assumed that if you are faced with the choice between a red and a blue shirt you will choose the colour based on your conditioning. You choose blue – with the consequence that your buying the red one will end up on the garbage heap of discarded possibilities. Mechanistic logic meant that only blue was possible.
In the many-worlds theory the resolution of the superposition (red and blue co-exist) means that two universes will be the result. One in which you will have chosen blue and one in which you will have chosen red. And the reality and logic of either universe is unassailable on its own premises!
Does this mean that you have free will to choose which universe to occupy? Not necessarily!
Even if every choice you make will give rise to a parallel you who lives your discarded choice, you as a unique single being, will live only one existence, of course. This is so even if all your parallel yous will live the alternative existences of your discarded choices. The thread of existence perceived by you embodies a unique logic which is the only one you will live. The fascinating question is, however, whether the many-worlds theory means that every time superposition is achieved and new universes are born, you may be able to choose freely which one you will occupy! The many-worlds theory means that you have been conditioned to be able to choose all alternatives! Will the choice of where the specific you will live be random or will you as you be able to decide in which universe your consciousness will reside?