Laplace's Deamon: a hypothetical omniscient being that knows the location, mass, speed, and direction of every particle of matter and every energy field in the universe.
Like many of his colleagues in the early 19th century, the French natural scientist P.S. Laplace believed that the universe could be exhaustively explained by a set of simple mechanical laws of force:
"I have endeavored to prove that all natural phenomena can be eventually reduced to interactions between molecules from a distance and that the theory of these interactions must be the basis of a mathematical theory of phenomena in nature. "*
With this knowledge of the laws governing interactions between molecules plus the current total state of the universe, Laplace's demon is able to predict the future in every detail. Thus, the future of the world is fully predetermined. Free will (at least as traditionally understood)** is an illusion, and the soul nothing but a myth.
Since the development of quantum theory in the 20th century, however, we know that due to the ►uncertainty principle a complete description of the state of the universe is not possible at any given time. Moreover, at least at the level of microphysics, our universe is indeterministic; that is to say, even with complete knowledge of the state of the universe and of the laws of nature, one could not in principle predict the next state of the universe (or any part of it) with certainty and precision. Put crudely, at the level of microphysics, certain things "just happen" one way rather than another, but given the previous state of the universe and the laws of nature, they could just as well have happened the other way. In other words, their happening the way they did was not causally determined by previous events/states and could not have been predicted even by a hypothetical omniscient observer.
So, is free will (again, as traditionally understood) saved? Not so fast! Even supposing that indeterminacies at the level of microphysics make their way up to the macro-level of human action, the most we could conclude is that some of the things we do are not determined to happen by anything preceding them. But as many philosophers have pointed out, an action that was like this would be a far cry from what we mean by "acting of your own free will"; it would be more like having your arm suddenly just shoot up all on its own without your having decided to raise it. In "freely willed" action, rather, something is supposed to be in control of, and the cause of, the action — namely, you; your deliberations, your choices, your decisions. But action that is not determined by anything, obviously, is not determined by you, and therefore is not at all what people generally have in mind when they speak of the actions of a free will.
The basic point is that the operations of a free will, traditionally understood, are not undetermined occurrences, but occurrences determined by a special kind of cause: an agent, person, soul, or will, that is self-determining (which also is quite different from being indeterministic). Thus, the indeterminism allowed for by quantum theory is no more congenial to the traditional conception of free will than Laplace's determinism — which does seem to put defenders of that conception between a rock and a hard place.
* P.S. Laplace, Sur les mouvements de la lumière, Mem. Inst. France 10, 1810
**Many philosophers have defended conceptions of "free will" according to which having freedom of will is fully compatible with being causally determined. This view is known, unsurprisingly, as compatibilism. Immanuel Kant, whose own views on the subject are (as usual) too complex to be summarized here, memorably dismissed compatibilism as a "wretched subterfuge".