Indeterminism of quantum mechanics is considered as an immediate corollary from the theorems about absence of hidden variables in it, and first of all, the Kochen – Specker theorem. The base postulate of quantum mechanics formulated by Niels Bohr that it studies the system of an investigated microscopic quantum entity and the macroscopic apparatus described by the smooth equations of classical mechanics by the readings of the latter implies as a necessary condition of quantum mechanics the absence of hidden variables, and thus, quantum indeterminism. Consequently, the objectivity of quantum mechanics and even its possibility and ability to study its objects as they are by themselves imply quantum indeterminism. The so-called free-will theorems in quantum mechanics elucidate that the “valuable commodity” of free will is not a privilege of the experimenters and human beings, but it is shared by anything in the physical universe once the experimenter is granted to possess free will. The analogical idea, that e.g. an electron might possess free will to “decide” what to do, scandalized Einstein forced him to exclaim (in a letter to Max Born in 2016) that he would be а shoemaker or croupier rather than a physicist if this was true. Anyway, many experiments confirmed the absence of hidden variables and thus quantum indeterminism in virtue of the objectivity and completeness of quantum mechanics. Once quantum mechanics is complete and thus an objective science, one can ask what this would mean in relation to classical physics and its objectivity. In fact, it divides disjunctively what possesses free will from what does not. Properly, all physical objects belong to the latter area according to it, and their “behavior” is necessary and deterministic. All possible decisions, on the contrary, are concentrated in the experimenters (or human beings at all), i.e. in the former domain not intersecting the latter. One may say that the cost of the determinism and unambiguous laws of classical physics, is the indeterminism and free will of the experimenters and researchers (human beings) therefore necessarily being out of the scope and objectivity of classical physics. This is meant as the “deterministic subjectivity of classical physics” opposed to the “indeterminist objectivity of quantum mechanics”.
Indeterminism of quantum mechanics is considered as an immediate corollary from the theorems about absence of hidden variables in it, and first of all, the Kochen – Specker theorem. The base postulate of quantum mechanics formulated by Niels Bohr that it studies the system of an investigated microscopic quantum entity and the macroscopic apparatus described by the smooth equations of classical mechanics by the readings of the latter implies as a necessary condition of quantum mechanics the absence of hidden variables, and thus, quantum indeterminism. Consequently, the objectivity of quantum mechanics and even its possibility and ability to study its objects as they are by themselves imply quantum indeterminism. The so-called free-will theorems in quantum mechanics elucidate that the “valuable commodity” of free will is not a privilege of the experimenters and human beings, but it is shared by anything in the physical universe once the experimenter is granted to possess free will. The analogical idea, that e.g. an electron might possess free will to “decide” what to do, scandalized Einstein forced him to exclaim (in a letter to Max Born in 2016) that he would be а shoemaker or croupier rather than a physicist if this was true. Anyway, many experiments confirmed the absence of hidden variables and thus quantum indeterminism in virtue of the objectivity and completeness of quantum mechanics. Once quantum mechanics is complete and thus an objective science, one can ask what this would mean in relation to classical physics and its objectivity. In fact, it divides disjunctively what possesses free will from what does not. Properly, all physical objects belong to the latter area according to it, and their “behavior” is necessary and deterministic. All possible decisions, on the contrary, are concentrated in the experimenters (or human beings at all), i.e. in the former domain not intersecting the latter. One may say that the cost of the determinism and unambiguous laws of classical physics, is the indeterminism and free will of the experimenters and researchers (human beings) therefore necessarily being out of the scope and objectivity of classical physics. This is meant as the “deterministic subjectivity of classical physics” opposed to the “indeterminist objectivity of quantum mechanics”.
According to the widely accepted opinion, classical (statistical) physics does not support objective indeterminism, since the statistical laws of classical physics allow a deterministic hidden background, while --- as Arthur Fine writes polemizing with Grünbaum --- "{\sl the antilibertarian position finds little room to breathe in a statistical world if we take laws of the quantum theory as exemplars of the statistical laws in such a world. So, it appears that, contrary to what Grünbaum claims, the libertarians' 'could have done otherwise' does indeed find support from indeterminism if we take the indeterministic laws to be of the sort found in the quantum theory.}" In this paper I will show that, quite the contrary, quantum mechanics does not save free will. For instance, the EPR experiments are compatible with a deterministic world. They admit a deterministic local hidden parameter description if the deterministic model is 'allowed' to describe not only the measurement outcomes, but also the outcomes of the 'decisions' whether this or that measurement will be performed. So, the derivation of the freedom of the will from quantum mechanics is a tautology: from the assumption that the world is indeterministic it is derived that the world cannot be deterministic.
If the concept of “free will” is reduced to that of “choice” all physical world share the latter quality. Anyway the “free will” can be distinguished from the “choice”: The “free will” involves implicitly a certain goal, and the choice is only the mean, by which the aim can be achieved or not by the one who determines the target. Thus, for example, an electron has always a choice but not free will unlike a human possessing both. Consequently, and paradoxically, the determinism of classical physics is more subjective and more anthropomorphic than the indeterminism of quantum mechanics for the former presupposes certain deterministic goal implicitly following the model of human freewill behavior. Quantum mechanics introduces the choice in the fundament of physical world involving a generalized case of choice, which can be called “subjectless”: There is certain choice, which originates from the transition of the future into the past. Thus that kind of choice is shared of all existing and does not need any subject: It can be considered as a low of nature. There are a few theorems in quantum mechanics directly relevant to the topic: two of them are called “free will theorems” by their authors (Conway and Kochen 2006; 2009). Any quantum system either a human or an electron or whatever else has always a choice: Its behavior is not predetermined by its past. This is a physical law. It implies that a form of information, the quantum information underlies all existing for the unit of the quantity of information is an elementary choice: either a bit or a quantum bit (qubit).
The problem of indeterminism in quantum mechanics usually being considered as a generalization determinism of classical mechanics and physics for the case of discrete (quantum) changes is interpreted as an only mathematical problem referring to the relation of a set of independent choices to a well-ordered series therefore regulated by the equivalence of the axiom of choice and the well-ordering “theorem”. The former corresponds to quantum indeterminism, and the latter, to classical determinism. No other premises (besides the above only mathematical equivalence) are necessary to explain how the probabilistic causation of quantum mechanics refers to the unambiguous determinism of classical physics. The same equivalence underlies the mathematical formalism of quantum mechanics. It merged the well-ordered components of the vectors of Heisenberg’s matrix mechanics and the non-ordered members of the wave functions of Schrödinger’s undulatory mechanics. The mathematical condition of that merging is just the equivalence of the axiom of choice and the well-ordering theorem implying in turn Max Born’s probabilistic interpretation of quantum mechanics. Particularly, energy conservation is justified differently than classical physics. It is due to the equivalence at issue rather than to the principle of least action. One may involve two forms of energy conservation corresponding whether to the smooth changes of classical physics or to the discrete changes of quantum mechanics. Further both kinds of changes can be equated to each other under the unified energy conservation as well as the conditions for the violation of energy conservation to be investigated therefore directing to a certain generalization of energy conservation.
Since quantum mechanics (QM) was formulated, many voices have claimed this to be the basis of free will in the human beings. Basically, they argue that free will is possible because there is an ontological indeterminism in the natural laws, and that the mind is responsible for the wave function collapse of matter, which leads to a choice among the different possibilities for the body. However, I defend the opposite thesis, that free will cannot be defended in terms of QM. First, because indeterminism does not imply free will, it is merely a necessary condition but not enough to defend it. Second, because all considerations about an autonomous mind sending orders to the body is against our scientific knowledge about human beings; in particular, neither neurological nor evolutionary theory can admit dualism. The quantum theory of measurement can be interpreted without the intervention of human minds, but other fields of science cannot contemplate the mentalist scenario, so it is concluded that QM has nothing to say about the mind or free will, and its scientific explanation is more related to biology than to physics. A fatalistic or materialist view, which denies the possibility of a free will, makes much more sense in scientific terms.
If the concept of “free will” is reduced to that of “choice” all physical world share the latter quality. Anyway the “free will” can be distinguished from the “choice”: The “free will” involves implicitly certain preliminary goal, and the choice is only the mean, by which it can be achieved or not by the one who determines the goal. Thus, for example, an electron has always a choice but not free will unlike a human possessing both. Consequently, and paradoxically, the determinism of classical physics is more subjective and more anthropomorphic than the indeterminism of quantum mechanics for the former presupposes certain deterministic goal implicitly following the model of human freewill behavior.The choice is usually linked to very complicated systems such as human brain or society and even often associated with consciousness. In its background, the material world is deterministic and absolutely devoid of choice. However, quantum mechanics introduces the choice in the fundament of physical world, in the only way, in which it can exist: All exists in the “phase transition” of the present between the uncertain future and the well-ordered past. Thus the present is forced to choose in order to be able to transform the coherent state of future into the well-ordering of past. The concept of choice as if suggests that there is one who chooses. However quantum mechanics involves a generalized case of choice, which can be called “subjectless”: There is certain choice, which originates from the transition of the future into the past. Thus that kind of choice is shared of all existing and does not need any subject: It can be considered as a low of nature.There are a few theorems in quantum mechanics directly relevant to the topic: two of them are called “free will theorems” by their authors, Conway and Kochen, and according to them: “Do we really have free will, or, as a few determined folk maintain, is it all an illusion? We don’t know, but will prove in this paper that if indeed there exist any experimenters with a modicum of free will, then elementary particles must have their own share of this valuable commodity” “The import of the free will theorem is that it is not only current quantum theory, but the world itself that is non-deterministic, so that no future theory can return us to a clockwork universe”.Those theorems can be considered as a continuation of the so-called theorems about the absence of “hidden variables” in quantum mechanics.
The concept of 'super-indeterminism' captures the notion that the free choice assumption of orthodox quantum mechanics necessitates only the following requirement: an agent's free-choice performance in the selection of measurement settings must not represent an exception to the rule of irreducible quantum indeterminism in the physical universe (i.e, "universal indeterminism"). Any additional metaphysical speculation, such as to whether quantum indeterminism, i.e., intrinsic randomness, implicates the reality of experimenter "freedom", "free will", or "free choice", is redundant in relation to the predictive success of orthodox quantum mechanics. Accordingly, super-indeterminism views as redundant also, from a technical standpoint, whether an affirmative or a negative answer is claimed in reference to universal indeterminism as a necessary precondition for experimenter freedom. Super-indeterminism accounts, for example, for the circular reasoning which is implicit in the free will theorem by Conway and Kochen [1,2]. The concept of super-indeterminism is of great assistance in clarifying the often misunderstood meaning of the concept of "free variables" as used by John Bell [3]. The present work argues that Bell sought an operational, effective free will theorem , one based upon the notion of "determinism without predetermination", i.e., one wherein "free variables" represent universally uncomputable variables. In conclusion, the standard interpretation of quantum theory does not answer, and does not need to answer in order to ensure the predictive success of orthodox theory, the question of whether either incompatibilism or compatibilism is valid in relation to free-will metaphysics and to the free-will phenomenology of experimenter agents in quantum mechanics.