Abstract: the existence of free will is denied by classical physics but it is compatible with quantum physics.
Are the natural sciences compatible with the existence of free will?
The laws of Nature state natural necessities. They say that what is cannot be otherwise. They claim that as soon as certain conditions are met certain effects will occur. Events always have previous causes. If everything is determined by previous causes then everything is written in advance. But free will supposes that the future is not written in advance, that what will be could have been otherwise.
Laws are deterministic when they impose that the instantaneous state of a system determines all its future states. The future is completely determined by the present or the past.
If the Universe obeys deterministic laws, all the destinies of all the beings it contains are as if written in advance. If there is a creator, he created the Universe, its past, its present and its future in a single decision, at a single stroke. Everything happens as if the future has already been created even if it has not yet happened.
It seems that a deterministic Universe leaves no room for freedom. If everything is written in advance, no one is free to choose their destiny, freedom is only an illusion, we believe that we make our decisions freely but it was written in advance, even before our birth, that we would make them .
Sometimes our actions are thoughtless. It is a source of embarrassment because we have to take responsibility for things we did not really want. We want to say like children that we didn't do it on purpose.
Sometimes decisions seem to impose themselves. The question is not even asked. No room for doubt, no need to think.
When we take the time to reflect, to anticipate the consequences of a decision, to weigh the pros and cons, to doubt, to hesitate, each stage of this journey has previous causes. Nothing prevents us from assuming that all the thinking that led to the decision was written in advance.
If everything is written in advance, a deliberation which precedes a decision resembles a mock trial. The sentence was pronounced before the trial began.
Are the laws of Nature deterministic? There is no simple answer.
Classical physics (from Newton to Einstein) is frankly deterministic. Fundamental laws are differential equations that completely determine the evolution of a system from its initial state.
Quantum physics is both deterministic and probabilistic at the same time. Like classical physics, it determines the evolution of a system from its initial state with a differential equation, the Schrödinger equation. It is therefore deterministic. But Born's rule interprets quantum states (calculated with Schrödinger's equation) with probabilities of observed outcomes. From this point of view quantum physics is probabilistic. There is no contradiction because Schrödinger's equation determines the probabilities calculated with Born's rule.
When quantum physics describes the evolution of an observer, it assigns him a tree of possible destinies. From an initial state, the observer has before him an incalculable number of possible destinies, all of which have a non-zero probability of being realized.
If I am free to make my decisions, it is me who decides, not chance. It therefore seems that even fundamentally probabilistic laws, such as quantum laws, do not solve the problem of free will. That the laws of Nature determine the probabilities of evolution rather than evolution itself does not seem to leave more room for freedom.
A probabilistic theory of our destinies is however compatible with the main axioms of free will:
Decisions are not written in advance. A decision is not completely determined by previous causes.
The power of decision gives a power of control over the future, because a decision has consequences.
It makes sense to think before deciding, because even random thinking gives chances of finding good reasons for deciding, while the absence of thinking leaves no chance of finding such reasons.
Quantum physics is therefore compatible with the existence of free will.