Well, quantum mechanics describes the universe as a wave function which describes a probability distribution. Most physicists who work on quantum mechanics seem to believe that wave function collapse is a truly nondeterministic process; the only real alternative, from what I understand, is hidden variable theories, which we know imply nonlocality thanks to Bell's theorem.
There's the caveat of Everettian quantum mechanics, where the universe is described exclusively through the wave function which evolves completely deterministically. However, this still causes the observer to experience a measurement outcome as truly nondeterministic; there's just one version of the observer for each measurement outcome.
EDIT: Though while this topic is fascinating, I don't think it's extremely relevant to my own thoughts on free will or whatever. I'm perfectly happy to discuss a hypothetical brain which is truly deterministic, and I don't think I would consider a consciousness simulated on a deterministic computer to have any less "free will". The consciousness in the computer would _be_ the circuitry and program. Of course it couldn't make different choices twice given the exact same state and input; it wanted to make the choice it did because of its state and inputs. I don't understand how the choice is any less free just because it's deterministic.
The quantum substrate being non-deterministic doesn't mean that free-will exists/doesn't exist. It has to be shown as such.
What is happening at the quantum level, to the extent that we can understand it, isn't directly translatable into a non-deterministic world at the higher macro level. And so, we do expect and observe a certain level of determinism in our macro scale world. For e.g. A topic relevant to this community - Computing. For the vast vast majority of cases when thousands of people execute the same program on the same or similar hardware at different times in different regions we do expect, and observe the same deterministic result. The outliers to this are primarily due to damage to the processor/equipment, software bugs, or other known factors (including alpha particles/radiation, etc).
Ah, I see what you're saying. I interpreted what you said to mean that current philosophical thinking is that the universe is deterministic, but you're saying that even though the universe is nondeterministic, the processes in the brain are completely deterministic. This feels like a purely empirical question rather than a philosophical one; I don't know whether there are processes in the brain which depend on quantum measurement outcomes. Though I would be kind of surprised if there's nothing at all; something as simple as putting a polarization filter in front of your eyes would make which exact photons are hitting your retina determined by the outcomes of quantum measurements, which seems to mean you'd be introducing truly nondeterministic noise into the system. But I'm also completely open to the idea that in general, quantum measurements don't affect the processing of the brain or sensory inputs in any way which affects decision-making, if that's what empirical investigation of the matter shows. Whether the brain is deterministic or nondeterministic doesn't really have any impact on the way I think about the concept of free will.
I think Everettian interpretations are secretly quite popular among physicists because the Copenhagen interpretation doesn't really get you that far. In Everettian QM, the evolution of the entire system remains deterministic.
There's the caveat of Everettian quantum mechanics, where the universe is described exclusively through the wave function which evolves completely deterministically. However, this still causes the observer to experience a measurement outcome as truly nondeterministic; there's just one version of the observer for each measurement outcome.
Here's the Wikipedia article on quantum indeterminacy, which I'm sure you can use as a jumping-off point for further reading: https://en.m.wikipedia.org/wiki/Quantum_indeterminacy
EDIT: Though while this topic is fascinating, I don't think it's extremely relevant to my own thoughts on free will or whatever. I'm perfectly happy to discuss a hypothetical brain which is truly deterministic, and I don't think I would consider a consciousness simulated on a deterministic computer to have any less "free will". The consciousness in the computer would _be_ the circuitry and program. Of course it couldn't make different choices twice given the exact same state and input; it wanted to make the choice it did because of its state and inputs. I don't understand how the choice is any less free just because it's deterministic.