As for quantum mechanics, I don't see a lot of relevance for neurological phenomena: the scales of size are just too different. QM tends not to have a big role in anything above the size of molecules.
I largely agree with this (I would say emphatically agree but for the caveats below). I think it extremely unlikely that quantum theory is necessary in any non-trivial way to explain the neurophysiology or neurobiology underlying cognitive processes. But quantum theory is still relevant to discussions on consciousness and free will, even if largely indirectly.
Firstly, quantum theory shows us that classicality is an emergent phenomenon. It is not agreed upon what exactly it is that classical physics emerges from (i.e., what quantum theory is supposed to be or describe, assuming that it is fundamental), but certain results such as the various so-called Bell theorems hold for any and all possible theories regardless.
Secondly, and related to the Bell theorems and similar no-go theorems (CHSH, Kochen–Specker, etc.), have—alongside quantum foundations more generally—forced us to take quite seriously even on an operational level questions which not long ago would have been thought relevant only to philosophers. The ability to make free choices is a prerequisite for the entirety of scientific inquiry. But it was not until the introduction of superdeterminism and choices between other loopholes of Bell inequality violations that we were forced not only to seriously consider the ways in which the capacity to make free rather than somehow predetermined choices became a serious, theoretical and operational issue in fundamental physics. It is possible to deny the validity of any theorem applied to physics or others sciences such as the Bell inequality by denying the capacity of experimentalists to determine experimental or observational conditions. Even those who strongly dislike the implications of violations of Bell’s inequality, however, do not go for this option as an out. It is now much clearer how,and has been made formally more explicit that, if experimenters are not capable of free choices than empirical inquiry is logically baseless and empirical science fruitless:
“The condition that the choice of the experimenters is taken to be a free one means that the experimentalist must be thought to be able to choose them at will, without being unconsciously forced to one or the other choice by some hidden determinism. This condition has an important role in the proof of the theorem. It is often left implicit because of its apparent obviousness. Here it is explicitly stated. But let it be observed that, when all is said and done, it appears as constituting the very condition of the possibility of any empirical science.” (p. 64)
B. d’Espagnat (2006).
On Physics and Philosophy. Princeton University Press.
“the existence of such curves would seem to lead to the possibility of logical paradoxes…Of course there is a contradiction only if one assumes a simple notion of free will; but this is not something which can be dropped lightly since the whole of our philosophy of science is based on the assumption that one is free to perform any experiment” (p. 189)
S.W. Hawking & G. F. R. Ellis (1973).
The Large Scale Structure of Space-Time (
Cambridge Monographs on Mathematical Physics). Cambridge University Press.
“Sometimes it is claimed that such a freedom is illusory. Yet, without this freedom all experimental science would be pointless:
To deny the freedom of action of an experimenter
is to deny the meaningfulness of experimental science.” (p. 175; italics in original)
H. Primas (2009). Complementarity of Mind and Matter. In H. Atmanspacher & H. Primas (Eds.)
Recasting Reality: Wolfgang Pauli's Philosophical Ideas and Contemporary Science (pp. 171-209). Springer.
Thirdly, and again relatedly, quantum theory forced us to once again consider our role as observers in physical theory. In classical physics, notions of measurement and observation are external to theory due to the determinate, realist, and objective nature of descriptions of physical systems. This is not so in quantum theory. As a result, we were forced to recognize how far afield we had taken certain assumptions in classical physics and how erroneous were certain extrapolations regarding the relevance of physical laws which hold strictly only for closed, isolated systems to the universe:
“The scientist subconsciously, almost inadvertently, simplifies his problem of understanding Nature by disregarding or cutting out of the picture to be constructed, himself, his own personality, the subject of cognizance.
Inadvertently the thinker steps back into the role of an external observer. This facilitates the task very much. But it leaves gaps, enormous lacunae, leads to paradoxes and antinomies whenever, unaware of this initial renunciation, one tries to find oneself in the picture or to put oneself, one's own thinking and sensing mind, back into the picture.”
Schrödinger, E. (1954). Nature and the Greeks. In E. Schrödinger
'Nature and the Greeks' and 'Science and Humanism' (pp. 1-99). Cambridge University Press.
“The freedom of experimentation, presupposed in classical physics, is of course retained and corresponds to the free choice of experimental arrangement for which the mathematical structure of the quantum mechanical formalism offers the appropriate latitude.”
Bohr, N. (1958).
Atomic Physics and Human Knowledge. John Wiley & Sons.
Other relevancies could be raised, but this post is long enough as is.