RustSilverfish
Nicely written essay, thanks for the good read! Your thesis, AFAIU it, is summarised by acknowledging current quantum chemical applications in biology (magnetoreception etc.) and their potential for demonstrating "generalized quantum advantage", and then asking the deeper question:
does such quantitative quantum advantage exhaust the explanatory novelty of quantum mechanics as applied to life, or can we go beyond it to genuine qualitative novelty?
I'm very much on the side of your qualitative quantum novelty thesis, especially given what I've found to be, as a nonspecialist in the quantum biology field, the surprisingly evidentially underdetermined state of the "1. Schrodingerian level". I wouldn't go so far as to say Tegmark et al. think quantum biology is "impossible" but I do agree with the @SepiaBeetle thesis that if you want to seriously argue for quantum effects operating in "large, warm and wet" biological systems, then there's a several orders of magnitude gap to bridge. Pretty much every quantitative essay I've read in this competition fails to bridge the spatial and temporal gap between quantum chemical effects and biological process, relying on speculative explananda that are largely empirically unsubstantiated. I'm most surprised at just how aspirational the 'quantum advantage in biology' discourse appears. So I appreciate, and entirely agree with, your turn to qualitative explanatory potential:
Most current applications of quantum mechanics to biology are of this form: classically inefficient or infeasible
processes are enhanced by quantum mechanical effects, thus providing a boost to biological systems making
use of them. But quantum theory’s explanatory potential does not end here.
Indeed, and my own submission to this competition avoided the quantitative field entirely and went straight to foundational Everettian considerations in a psycho-physical model linking phenomenal consciousness with the correlation structure of the universal wave function. And like you, I’m very much sympathetic to the idea that the deeper explanatory resources of quantum theory might lie not in coherence‑enhanced biological processes but in how quantum theory reshapes the conceptual space of explanation itself. That said, I'm not sure how your levels 2-3 might be specifically related to biology.
Your "2. The Feynmannian level" invokes the QM explanations for the stability, extension and least-action behaviour of matter, which is all fine, but these are just universal properties of matter. They characterise a rock just as well as an organism, and so are necessary conditions for biology but not specifically explanatory of biological phenomena as such.
Similarly with "3. The Bohrian level". I understand that much of our logical/cognitive processing is non-commutative, but this is entirely classical and these mathematical effects occur in any complex classical dynamical system. Yes, the quantum formalism can model it, but what's the physical tie-in with quantum biology apart from the classical/quantum mathematical analogy?
I understand you're just pointing towards possible application of these quantum explananda to biology, but the specifics rather than generality of that application are just not evident to me. Some concrete biological examples might have helped.
Now "4. The Paulian level" is much closer to my philosophical interests! His dalliance with Jung and 'psycho-physical complementarity' demonstrates, for me, both a fascinating episode in 20th C intellectual history, and a general tendency of that group of Bohr's disciples towards what I call 'Copenhagen mysticism' (Heisenberg wandered into similar territory). For Pauli's speculative dualism, mind and matter are two deeply irreducible and thus 'complementary' aspects of our experiential reality. My problem with this characterisation of the mind–matter dualism is that it's again rather philosophically aspirational, leaning heavily on conceptual analogy, with no demonstration how mental states might actually physically instantiate non-commutativity or complementarity in Bohr’s technical sense. Without a psycho-physical bridge to model just how mental states are linked to the quantum formalism (à la Everett), then I think you're making more of an aspirational metaphysical gesture rather than positing an explanation – and most especially where the "Hard Problem" is concerned.
So while I completely agree with you that quantum theory’s explanatory potential in biology goes well beyond the quantitative frontier, I'm not sure you've demonstrated just how quantum theory might offer qualitative explanations of biological phenomena.
