How much free will do we have?

Quantum mechanics is inherently statistical in that it can tell you the probability of something like a nucleus emitting an alpha particle in a given time, but it can’t tell you exactly when or how. In the early days of quantum mechanics this caused great consternation for many scientists, including Einstein whose dislike of this apparent randomness prompted him to protest “God does not play dice!”

Einstein and others proposed what’s now known as hidden variable theory, to get some causality back into the quantum world. In essence this says that there are mechanisms within the nucleus that lead to the emission of the alpha particle in a deterministic way, but we can’t see them so they appear random to us. However in 1964, the physicist John Bell published a famous paper in which he argued that no hidden variable theory can reproduce all of the observed quantum phenomena.