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What is the mechanism that makes subjectivity exist?
Oh boy... This question is the exact reason I went into the field. I have no idea, but I hope we get the answer before I die.
At this point we are still just poking around in a vast mess of goo hoping to find some neural correlates of perception or motor planning or consciousness. Giving a mechanistic explanation for how these activity patterns produce subjective experience is going to take massive efforts, and maybe a leap of 'faith'. Probably the most progress will be made in areas of sensory perception or motor control, where we can be precisely quantitative about either the sensory input or motor output. Then we can record activity within various areas of the circuits responsible for a given modality, do high resolution reconstruction of the structure and connections between cells in that circuit, and then perturb the circuit, buy selectively silencing or activating functional groups of neurons on a trial by trial basis to probe how changing the circuit modifies the perception. Add to this the challenge of having to 'read-out' these effects via the behavior of an animal, rather than what a human can describe (who wants to volunteer to have channelrhodopsin virus injected into their head and a fiberoptic laser guide installed through their skull??). I don't think I'll work myself out of a job any time soon.
It really boils down to the question, does 1 electron make a difference? Maybe, but probably not.
Quantum mechanics tends to break down on the scale of single proteins, and I'm not sure that it is fair to call the thermal noise of opening and closing ion channels a true 'quantum' effect... But lets say that a 'quantum' thermal noise event or some electron wiggle drives a single voltage-gated ion channel to open or close at a given time. And the neuron that the channel resides is in, this single channel out of 10s or 100s of thousands in the neuron, is so close to firing threshold that the channel contributes enough current to drive the single neuron to add an action potential. What impact does that extra action potential have on the network and on the brain? Is it washed out in a sea of billions of spikes per second? Or does that perturbation magnify and drive the brain into a different state (thought). Is this where the unpredictability of human action, and our apparent free will comes from? Maybe... But more likely is that the precise variation of massive and specific sensory inputs into the brain overwhelm any of this quantum/thermal noise.
Quantum theory isn't needed to explain chaos, and I think brain dynamics most closely resemble a semi-chaotic system, with many possible attractor states (correlates of conscious and unconscious thoughts) that one can switch between. We don't yet really know how we can seem to volitionally switch between them, but neither I nor most professional neuroscientists I've met (including many many physicists) think the answer lies with quantum mechanics. Rather, its is something that will hopefully be uncovered with a combination of dense electrical and optical recordings of brain activity during awake behavior that are used to constrain mathematical models of network dynamics.
Here is an example of a cool paper on what a single spike can do... BUT, its just a small step towards understanding that issue http://www.ncbi.nlm.nih.gov/pubmed/20596024
There is no reason to think that quantum physics has anything to do with the nature of conciousness. It is not useful to explain free will, or the illusion of free will, of the qualia of objects, or the steadyness of perception on a background of constantly varying spike rates in the brain.
Perhaps the best, short, free, relatively recent summary of the field was written by Christof Koch and Francis Crick, A Framework for Conciousness, and is available here : http://papers.klab.caltech.edu/29/1/438.pdf
I also have a little essay on the nature of free will on my blog here, if interested. http://brainwindows.wordpress.com/philosophy/philosophy-the-science-of-free-will/