Does free will contradict the laws of physics?

People often say that free will contradicts the laws of physics because free will implies a 'garden of forking paths' where you can do A or B. But the laws of physics imply that either history was fixed at the time of the Big Bang or that where chance exists it is merely randomness and probability. Where does that leave free will?

An interesting way of imagining how free will can be compatible with the laws of physics comes from quantum mechanics. The 'Schroedinger's cat' idea gives a good account of it (from Wikipedia):

Schrödinger's Cat: A cat, along with a flask containing a poison and a radioactive source, is placed in a sealed box shielded against environmentally induced quantum decoherence. If an internal Geiger counter detects radiation, the flask is shattered, releasing the poison that kills the cat. The Copenhagen interpretation of quantum mechanics implies that after a while, the cat is simultaneously alive and dead. Yet, when we look in the box, we see the cat either alive or dead, not both alive and dead.

This article explains a bit more about why the cat is both alive and dead:

The principle of superposition states that if the world can be in any configuration, any possible arrangement of particles or fields, and if the world could also be in another configuration, then the world can also be in a state which is a superposition of the two, where the amount of each configuration that is in the superposition is specified by a complex number.

There is superposition with regard to the Geiger counter detecting radiation, because it's a subatomic phenomena. Therefore, after a while an atom has in some sense both decayed and not decayed, releasing and not releasing radiation. Thus, after a while the cat is both dead and alive.

In the Copenhagen interpretation of quantum mechanics, a system stops being a superposition of states and becomes either one or the other when an observation takes place. This experiment makes apparent the fact that the nature of measurement, or observation, is not well-defined in this interpretation. The experiment can be interpreted to mean that while the box is closed, the system simultaneously exists in a superposition of the states "decayed nucleus/dead cat" and "undecayed nucleus/living cat", and that only when the box is opened and an observation performed does the wave function collapse into one of the two states.

Schroedinger's cat illustrates how quantum mechanics seems, at least superficially, to allow for something that sounds like a 'garden of forking paths'. The cat is both alive and dead, two contradictory possibilities exist, and our conscious observation forces reality to 'choose' one. Perhaps our brain has many possible configurations and our consciousness/the soul can make out of them one reality?

But does quantum mechanics apply to the workings of the brain? Some scientists have come up with theories of how it could (link).

So with free will, imagine that until our consciousness/soul affirms a value, e.g., 'I think it's important to be truthful', then the neurons in our brain are simultaneously affirming a 'truthful' brain state and a 'not truthful' brain state. But after the conscious decision is made then the 'truthful' brain state 'resolves' into being - just like the cat is alive or dead only when the scientist looks into the cage and 'forces' an answer.

This type of analysis doesn't explain what free will is, it just indicates how the soul or consciousness might be able to change the brain using free will. (Libertarian) free will's workings would still be beyond our understanding.

I apologise in advance for my scientific ignorance if this idea is fundamentally flawed, but, as others have said, it seems that a genuine free will can be compatible in theory with the laws of physics.

(Edited 5 April 11).