The question of free-will in a quantum uncertain universe led several of the early researchers of quantum physics to propose that the brain may be in some way utilizing the uncertainty of individual quanta that appears to violate causality at the foundation of physics , to give rise to a quantum uncertain brain state consistent with free-will. Eddington , for example, noted that the uncertainty of position of a synaptic vesicle was large enough to be comparable with the width of the membrane, making synaptic release potentially subject to quantum uncertainty. Walker  noted quantum tunneling in synaptic transmission and Eccles  noted the relation between mental events, neural events and quantum probability fields.
To mount an effective solution to the hard problem requires making a connection between subjective consciousness and the physical world, which has mutual explanatory power. The functionally closest phenomena to subjective consciousness we know of are global electrochemical brain processes that appear to be "holographically" distributed, chaotic, and potentially relate to the binding problem of the central theater of conscious attention through phase coherence. The most promising avenue, given what we have discovered about the quantum world is to look for a bridge between global phase coherences and those we associate with quantum entanglement and transactions. This raises the enticing possibility of linking the paradox of conscious will with the paradox of reduction of the superposition of quantum states to a physical history, thus providing a complementary view of the mystery the hard problem presents both from physical unpredictability and from subjective intentional decision making.
The fractal dynamics model proposes that the conscious state corresponds to phase-coherent, temporally edge-of-chaos, excitations of coupled regions of the cortex and thalamus, capable of entering a critically poised unstable state if faced with conflicting stimuli that cannot be resolved from learned experience. This would in turn enable quantum fluctuations at the molecular level to become an unstable "watershed" that tips the global state towards a resolution. The fractal model uses the molecular processes of synaptic vesicles and ion channels currently believed to be pivotal in supporting active conscious states. Such a model enables instability at the quantum level to become amplified when the global brain state is critically poised, in a way that could be possible even though the corresponding excitations are distributed across the cortex. The situation could in principle enable global excitations to be considered as "inflated" quanta - either simple harmonic excitations or solitons, and phase coherence of global brain states to thus be interpreted as coherent quantum states.
The model of Hameroff and Penrose seeks a more specific mechanism in the microtubules of the neuron. In particular, they have noted that tubu-lin exists in two forms and could thus enter a quantum superposition of states. They thus envisage tubulin acting as a quantum cellular automation, interleaving between classical and quantum computational states. However, microtubules are extensively involved in transport of essential molecules and whole organelles, as well as cytoskeletal architecture and synaptic growth and it is unclear wether they have a direct role in the fast forms of excitation of the electrochemical states we associate with conscious awareness. Generally, when a single cellular system serves two critical, yet differing functions, evolution by gene duplication is likely to occur, so that both characteristics can be selected for independently. It is hard to see how the microtubules can be both involved in active transport and at the same time performing quantum calculations essential to the organism without potential conflicts of interest. These considerations do not apply to membrane excitation and synaptic transduction, which are already directly connected to excitability.
In the OOR model, consciousness is a passive result of a quantum computation that occurs in the pre-conscious state and is resolved objectively by a self-energy splitting of the gravitational centers of mass of the superimposed states in "objective reduction" and conscious awareness emerges only subsequently, based on the outcome. Effective quantum computation of even simple problems, such as Shor's algorithm  for factoring a number, involve complex boundary constraints, including the capacity to Fourier transform one part of a quantum "register" to represent periodicities in the superimposed states of the other part (see p. 431). It is unclear whether the microtubular automation can be configured to do this at the same time as serving the active transport of molecules and organelles. The Penrose and Hameroff model suggests the neuron can very rapidly alternate quantum computing with normal function by temporarily isolating the microtubules from the membrane through disassociating the linking MAP proteins (to avoid quantum deco-herence effects). This means the quantum computation is isolated from the global brain state during the quantum computation cycle. The quantum computation phase would thus be fragmented at the cellular level and could not correspond to the subjectively conscious state.
Quantum computing is subject to decoherence because any quantum interaction with the outside world except the measurement itself disrupts the superposition of states by interacting with it. By contrast, transactional su-percausality incorporates contingent interaction foci, in developing the complexity of the subquantum system, and would thus be robust to decoherence.
The fractal model envisages chaotic and unstable processes penetrating the quantum level in a way that minimizes decoherence because of the self-coupling of the brain state to a restricted class of global excitations. A variety of closed quantum systems that correspond to classical chaos, including nuclear dynamics, the quantum stadium and magnetically perturbed high-energy orbitals display inhibition of quantum chaos in phenomena such as scarring of the wave function, in which periodic repelling orbits "reclaim" the probability distribution. However, quantum-kinetic interactions in an open molecular system  do appear to retain the attributes of chaotic instability. Unlike the OOR model the transactional model we investigate next envisages subjectively conscious decision making associated with a global dynamical criticality as capable of participating in "anticipatory" collapse of the wave function and thus actively changing subsequent brain dynamics.
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