Free will and determinism: a physicist's perspective

This is an amusing topic I've discussed with many people over the years. My opinion: if our current understanding of physical laws is correct, humans have only the illusion of free will.

What do I mean by free will? Well, that is hard to define. But the absence of free will or deterministic behavior is not hard to define. In classical physics the future evolution of a system is completely determined by the state of the system (including time derivatives) at any instant. For example, suppose that at some instant t I know all of the positions and momenta of every molecule or atom in the universe. Then, in a classical universe, I could in principle predict with certainty its future evolution. Another universe prepared in the identical state would evolve identically. So, in a classical universe everything that has happened since the big bang could (again, in principle) have been predicted at that moment. Such a universe is deterministic, and no subcomponent of that universe (i.e., a dog, a human, a robot, or a martian) can have free will.

Note that chaos does not help. Suppose the classical evolution is nonlinear, and exhibits chaos. Then initial states which are very similar may, after only a short time, have evolved into radically different configurations. This makes the job of predicting the future behavior of some initial data very hard, but nevertheless possible in principle.

Does quantum mechanics help? Well, a quantum universe is not deterministic. (In the many-worlds description, the evolution of the wavefunction describing all possible universes is deterministic, but only a single branch of the wavefunction is perceived by any macroscopic observer, and the path followed by a particular observer at each branching is not predictable.) However, it seems that the functioning of our brains is almost entirely classical. The number of atoms involved in the firing of a synapse, or other chemical reactions in brain functioning, is quite large, and there is little quantum coherence. As far as we know, our brains are readily simulated by purely classical processes.

Still, the inputs received by our brains may be non-deterministic in a quantum world. For example, the clicks of a geiger counter (which detects the photons from individual radioactive decays) are intrinsically random according to quantum theory. But, it is hard to see how introducing occasional random inputs amounts to granting free will to an otherwise deterministic machine. A classical robot which is fed occasionally random data does not seem to me to have free will. If prepared in an identical state and fed the same inputs, it would behave the same way every time.

If the previous discussion is correct, all we really have left is the illusion of free will. It seems like I chose what to have for lunch today. The conscious part of my brain didn't know what the answer was until going through what seemed to be a decision process. But, given that there are lots of lower-level brain processes that my consciousness has only a vague awareness of, it seems quite plausible to me that the "decision" was made in a deterministic way without my knowledge.