I see quantum physics as the only thing I can think of to cast reasonable doubt on hard determinism.
So do most (Mathias Frisch being a notable exception). For me, it's a bit like the goal for a complete, consistent, and formalized mathematics if no Gödel ever came along and instead Russell & Whitehead's
PM was replaced by several different systems. In other words, Hilbert's goal was squashed by proof (I mean real proof of the type only possible in mathematics/logic, not "proof" as used colloquially). For classical mechanics, it was more that we just found it wasn't a description of reality in that it failed at both the micro- and macro-scales. It was assumed (for a long time rather unconsciously) that because physics (as it had developed since before Newton up through Laplace) was deterministic and physics described how things worked, things must work in a deterministic way. The fact that statistical mechanics wasn't deterministic but was classical was treated as irrelevant because it was deemed an epistemic barrier and the successes of classical physics elsewhere continually reinforced the notion that the universe was deterministic. But at no time was the physics we now deem classical considered to be complete.
I don't mean complete in the sense that we know everything. Quantum mechanics doesn't explain everything (and in a very real sense doesn't actually "explain" anything), but is generally considered complete because there are no internal inconsistencies or problems from an experimental, practical, or mechanistic viewpoint. Before "classical mechanics" became "classical" (and was just "mechanics" or a theory explaining motion), there remained significant unknowns. Planck's constant was conjured up somewhat out of thin air (or at least luck). Classical electromagnetism couldn't explain black-body radiation or the photo-electric effect, the gravitation of classical mechanics was, theoretically, a nonlocal force but didn't act non-locally and perhaps
the central component of classical mechanics was internally inconsistent and empirically flawed, etc.
In truth, determinism was a byproduct of success and 19th century positivism. There is no real evidence that, without quantum indeterminacy everything operates deterministically. There's just the various successes of a deterministic physics that failed (as a theory, not as a tool; as a tool it is unbelievably useful). It's likewise true that there is no real evidence that there is (ontological) indeterminacy without quantum physics. There's an important but often overlooked aspect of the history of modern physics regarding the effects of the development of quantum mechanics (its counterintuitive nature, how completely it took physicists by surprise, how loathe physicists were to accept it and having done so how quickly it was banished to Bohr's netherworld of mathematical entities whose relation to the physical world was meaningless, etc.). Namely, how much the work by Poincare, Lorenz, and other founders of "chaos" theory went underappreciated and relatively unnoticed. The discovery that extremely simple systems were vastly more complex than we could have imaged was, apparently, nothing when compared to systems that seemed not so much complicated as paradoxical.
The delay in our appreciation for complex systems is largely ended, and alongside buzzwords like "superposition", "non-locality", "quantum gravity", or "entanglement" we find "emergence", "downward causation", "self-organization", etc. Systems biology (and to a lesser extent systems sciences) has developed in part by throwing reductionism out the window as a viable framework, its "founder" (Rosen and his "relational biology") sparked the ongoing debate as to whether living systems are closed to efficient causation, and mathematical biologists and systems scientists like Alwyn C. Scott have argued that reductionism is dead in the water from a
classical standpoint because it fails rather completely to capture the dynamics of living ("open") systems. I'm not saying they're right, just that the idea our options are "determinism or QM" isn't really built on much. While classical and then quantum physics advanced our knowledge of the non-living systems in nearly unimaginable ways, we still can't really model single cells. Our ability to control quantum systems has progressed enough to actually build the first quantum computers, we can manipulate atomic and subatomic "matter" to create massive explosions or medical imaging, yet our models for neurons haven't progressed qualitatively since the 40s.
Our brains may not be capable of that freedom but the freedom must be possible at some levels.
It depends upon how you define freedom. Conway and Kochen developed their "Free will theorem", which holds that everything basically has free will by simultaneously reducing free will to something rather meaningless.
Aside from that we need to find out where our biology might harness what it can do at the micro levels.
Quite true. Nanotechnology is already close if not sometimes touching quantum physics and quantum dots have for years been used in medical and biological sciences.
