Does free will violate the laws of physics?

The title of this six-minute video is "Does free will violate the laws of physics?" But it could also be called "Is free will an illusion?"

Physicist Sean Carroll says people who believe in free will (non-determinists) are usually contrasted with those who think human behavior is determined solely by the cause-and-effect of physics. But Carroll thinks assuming a relationship between determinism vs. non-determinism and free will vs. non-free will is a mistake.

"'Libertarian free will,'" he says, is the belief that the "ability to make choices and do things in the world that cannot even, in principle, in any way, be explained by stuff obeying the laws of physics." The idea of "compatibilist free will," to which Carroll subscribes, "says that we can still talk about human beings as agents making choices, while also agreeing that we don't violate the laws of physics." How can that be so?

Compatibilists think it possible to be both a physical system subject to the laws of nature and an agent making choices, as long as one is talking about different levels of description. "What it's saying is that you can both be a law-abiding thing in the universe, a physical system subject to the laws of nature, and it makes sense to talk about you as an agent making choices because you're talking about a different level of description — a higher-level, emerging kind of phenomenon."