What is Free Will

One blog article asked : What the Hell is "Free Will?"

"nobody ever seems to give me a straight definition".

I do have a straight definition of free will, maybe not containing its full nature (which I don't think can ever be formulated), but at least a negative definition already sufficient to make it rigorously clear that it differs from the case it had no real meaning:

Precise formulation of free will

Free will is the combination of determination and indetermination that is the very expression of the time order, that is : the actual outcome cannot be predicted in advance because "correct prediction" would require the full underlying stuff (the individual mind with all past experience in memory...) to be correctly produced in the way it is produced: by that real mind actually coming to really exist into that circumstance, all that stuff which can only come to exist and produce that behavior at the time and place where it indeed comes to produce that behavior in reality. That is the same situation as what has been demonstrated to be the fact of how things go in the universe of pure mathematics itself (so that such a seemingly paradoxical statement of “combination of determination and indetermination” cannot be dismissed as illogical nonsense): except that the actual content is moreover very different from these "random" contents of the facts of pure mathematics (as explored by Gregory Chaitin), by the fact that the mind with its free will (unpredictable behavior), is not only non-algorithmic (as Penrose considered) but not mathematical.

Short, logical positivist formulation

Precisely, this concept of non-algorithmicity, that conscious behavior cannot be well approximated by any algorithmically expressible probabilistic law, can be expressed by the following statement, clearly very meaningful for logical positivism (experimentally falsifiable)

Artificial intelligence cannot pass the Turing test

More remarks

About time (unpredictability) and about the non-algorithmicity of the mind: Gödelian arguments against mechanism : what was wrong and how to do instead, namely justify that ZF is consistent.
For more comments on the mathematical details of around this concept in terms of information entropy, please refer to my pdf presentation of the mind/mathematics duality.
More comments on the experimental testing of free will

Reply to his "challenge":

"Across from you are what appear to be two identical twins.  They look the same, they act the same, and in all physical respects, they are as alike as two people can possibly be. However, there is one key distinction that exists between them: one of them has free will, while the other one does not. (...) Your only job is to tell me which is which. Which one has free will and which one does not?"

My answer is simple : if they are physically identical, and one has free will but the one hasn't (is a zombie), then they do not act in the same "human way". They can be distinguished by their behavior (as soon as they are put in such difference circumstances that prevent you from solving the problem of "programming the zombie" by the simple answer "let us program the zombie's behavior by the simple instruction of copying the behavior observed from the real person" in which case "observing the zombie" would be a mere indirect way of observing the real person). The zombie's behavior is best described as obeying the probability law given by quantum mechanics (something usually not observed; still I guess it sometimes happens and is then qualified as a sort of coma); the one with free will is visibly departing from this law.

Does Free Will violate any physical law (Born's rule) ?

In the article Is Quantum Indeterminism Relevant to Free Will? by Michael Esfeld (2000)
it is stated that the idea of free will is physically unacceptable as it would be a violation of one of the laws of physics : Born's probability rule.
It is compared to some ancient speculations (by Descartes) on how a non-physical mind would act on matter by a "non-physical force" that would violate the conservation laws of classical mechanics:

"Indeterminism in physics in the described sense opens up the possibility of an interactionism which does not have to assume a force over and above those force that are acknowledged in physics. It thereby reduces the ontological burden of interactionism.
(...) instead of having to endorse an additional force for metaphysical reasons, we have to endorse a change to the probabilities that a physical theory indicates for metaphysical reasons.
Within the framework of the positions considered in this paper, the conclusion is as follows: taking everything into account and given the current state of the art, quantum physics does not reduce the price which one has to pay for interactionism."

Visibly, he contradicts himself on the question whether the "burden" or "price" is reduced or not by taking quantum randomness as the place of operation of free will. In his mind, the diverse "laws of physics" seem to be assumed as being all at "the same level" of necessity.
These are quite naive and far from any kind of well-assessed comparisons "given the current state of the art", I would say. By the way, whose "state of the art" is he referring to ? Probably, the one of science philosophers trained with their usual bullshit kind of "reasoning", who pretend to discuss science without having any decent understanding of the needed concepts and theories.

Actually, Born's rule is very far from having a status of "physical law" with a necessity for things to obey it, that can stand any comparison of strength with the the conservation laws of mechanics. These conservation laws (of energy, momentum...) are not mere "postulates" like arbitrary assumptions, axioms or speculations, but come as theorems in either framework of General Relativity and QM. Thus, there is absolutely no way, even for any God, to violate them, as this would contradict a mathematical theorem. It is absolutely impossible, logically unconceivable (the only "conceivable" process that would look like this would be a transformation of ordinary matter into dark matter, but that is still so unlikely....).

On the other hand, the "strict respect of Born's rule" is not really a law of physics, because:

Is quantum randomness "at the right place" to be able to control behavior ?

This objection appears in diverse articles on the subject : "The kinds of indeterminacies discoverable at the quantum level may not correspond in any useful way to our ordinary idea of mental causes."
The answer is that quantum randomness is much more pervasive in reality than many people naively imagine when thinking that many phenomena, such as classical chaos and the randomness of statistical mechanics, can be understood without reference to quantum physics. I mean that while, admittedly, the place of not-yet-decohered forms of quantum superposition, that require the quantum mechanical concepts to be understood, seems limited to molecular scales irrelevant for consciousness, quantum randomness is anyway the real source of a large flow of effectively random data (classically probabilistic superpositions produced by decoherence), where free will has a wide margin for possible intervention. More comments on this fact in the text on Bohmian mechanics.

Quora questions

Is there any relationship between quantum mechanics and free will?

Related pages

A call to clarify the debate on the links between quantum physics and consciousness
Specifications for a Mind Makes Collapse interpretation of quantum physics
A mind/mathematics dualistic foundation of physical reality
Introduction to quantum physics (notions of states and measurements)
Main page of arguments on quantum physics interpretations
On materialism and its pathological pseudo-arguments far from science
my reply on quantum idealism and science