Quantum theory is one of the most important and least understood advances in physics over the last 150 years. Beginning with Max Planck’s supposition in a paper published in 1900 that energy could only be emitted in quantized form, it eventually led to the realization that, particularly at the atomic and sub-atomic level, it was more accurate to represent objects and their interactions, mathematically at least, in terms of wave functions and probability distributions than in terms of the deterministic prescriptions of classical physics. There has been a great deal of speculation regarding the implication of these discoveries touching the matter of free will (see, for example, here, here, and here, and Google will turn up many more examples). As often happens in such philosophical speculations (and as some of the authors of the linked articles themselves point out), the various hypotheses occasionally go considerably further than is warranted by what we actually know.
One can’t really say anything positive about free will unless one understands what it is, and to understand what it is, one must understand consciousness. Unfortunately, we don’t. We can be more confident in speaking about what free will is not. For example, let us assume for the sake of argument that insects are not self-aware or conscious, and they only react to their environment via instinct. They may seem to make decisions such as whether to fight or flee, admit another insect into the hive or nest or not, etc., but free will is not involved. Machines could be programmed to react in exactly the same ways. Proponents of free will believe that, somehow, the human mind can consicously override such programming, and deliberately make choices that are not pre-ordained by physical law or instinct. These choices, in turn, can alter the outcome of events. Again, without resorting to supernatural arguments, we cannot state positively that free will exists because we lack sufficient understanding of what goes on in the human mind to do so. We literally don’t understand what we’re talking about. We can, however, discuss whether it is even possible for it to exist to begin with.
In that limited sense, the implications of quantum physics are profound. If everything in the universe obeyed the laws of classical physics, there would be no room for free will. Given a certain initial state of the universe, everything in the future would be pre-ordained by physical law, or so, at least, it has seemed to many great thinkers in the past. In principle, we could create mathematical models that would predict the future with absolute certainty, although, at least at the current state of the art, the complexity of the universe is so great as to put such models completely out of the question. We would just be along for the ride, and free will would be just an illusion. In a quantum universe, at least we have some wiggle room.
True, we still don’t know at a fundamental level what all this stuff in the universe around us really is, or why it exists to begin with. However, we can demonstrate with repeatable experiments that it conforms to mathematical models in which probability plays a significant role. Now if, once again, we are given a certain initial state of the universe, the claim that the future outcome of events is pre-ordained by the laws of physics is not as plausible in such a probabilistic universe. The mathematical models may be misleading us about the true nature of things, but, in principle, an infinity of possible outcomes becomes possible. In such a universe, it is at least possible for free will to exist, although it is hardly certain, and the manner in which it exists, if it does, must remain a mystery to us until we learn a great deal more about the nature of our own minds.
That is the implication of quantum physics regarding free will. From a classical universe whose eventual fate was written in stone depending on its state at some point in the past, we have proceeded to one in which many outcomes are possible, and free will is, therefore, not completely excluded. It seems a rather limited implication on the face of it. However, it’s comforting that a universe in which what we think or do actually matters is, at least, not out of the question.