Fringe hypothesis
The quantum mind or quantum consciousness is a group of hypotheses proposing that local physical laws and interactions from classical mechanics or connections between neurons alone cannot explain consciousness, positing instead that quantum-mechanical phenomena, such as entanglement and superposition that cause nonlocalized quantum effects, interacting in smaller features of the brain than cells, may play an important part in the brain's function and could explain critical aspects of consciousness. These scientific hypotheses are as yet unvalidated, and they can overlap with quantum mysticism.
History.
Eugene Wigner developed the idea that quantum mechanics has something to do with the workings of the mind. He proposed that the wave function collapses due to its interaction with consciousness. Freeman Dyson argued that "mind, as manifested by the capacity to make choices, is to some extent inherent in every electron".
Other contemporary physicists and philosophers considered these arguments unconvincing. Victor Stenger characterized quantum consciousness as a "myth" having "no scientific basis" that "should take its place along with gods, unicorns and dragons".
David Chalmers argues against quantum consciousness. He instead discusses how quantum mechanics may relate to dualistic consciousness. Chalmers is skeptical that any new physics can resolve the hard problem of consciousness. He argues that quantum theories of consciousness suffer from the same weakness as more conventional theories. Just as he argues that there is no particular reason why particular macroscopic physical features in the brain should give rise to consciousness, he also thinks that there is no particular reason why a particular quantum feature, such as the EM field in the brain, should give rise to consciousness either.
Approaches.
Bohm.
David Bohm viewed quantum theory and relativity as contradictory, which implied a more fundamental level in the universe. He claimed that both quantum theory and relativity pointed to this deeper theory, a quantum field theory. This more fundamental level was proposed to represent an undivided wholeness and an implicate order, from which arises the explicate order of the universe as we experience it.
Bohm's proposed order applies both to matter and consciousness. He suggested that it could explain the relationship between them. He saw mind and matter as projections into our explicate order from the underlying implicate order. Bohm claimed that when we look at matter, we see nothing that helps us to understand consciousness.
Bohm never proposed a specific means by which his proposal could be falsified, nor a neural mechanism through which his "implicate order" could emerge in a way relevant to consciousness. He later collaborated on Karl Pribram's holonomic brain theory as a model of quantum consciousness.
David Bohm also collaborated with Basil Hiley on work that claimed mind and matter both emerge from an "implicate order". Hiley in turn worked with philosopher Paavo Pylkkänen. According to Pylkkänen, Bohm's suggestion "leads naturally to the assumption that the physical correlate of the logical thinking process is at the classically describable level of the brain, while the basic thinking process is at the quantum-theoretically describable level".
Penrose and Hameroff.
Theoretical physicist Roger Penrose and anaesthesiologist Stuart Hameroff collaborated to produce the theory known as "orchestrated objective reduction" (Orch-OR). Penrose and Hameroff initially developed their ideas separately and later collaborated to produce Orch-OR in the early 1990s. They reviewed and updated their theory in 2013.
Penrose's argument stemmed from Gödel's incompleteness theorems. In his first book on consciousness, "The Emperor's New Mind" (1989), he argued that while a formal system cannot prove its own consistency, Gödel's unprovable results are provable by human mathematicians. Penrose took this to mean that human mathematicians are not formal proof systems and not running a computable algorithm. According to Bringsjord and Xiao, this line of reasoning is based on fallacious equivocation on the meaning of computation. In the same book, Penrose wrote: "One might speculate, however, that somewhere deep in the brain, cells are to be found of single quantum sensitivity. If this proves to be the case, then quantum mechanics will be significantly involved in brain activity."
Penrose determined that wave function collapse was the only possible physical basis for a non-computable process. Dissatisfied with its randomness, he proposed a new form of wave function collapse that occurs in isolation and called it "objective reduction". He suggested each quantum superposition has its own piece of spacetime curvature and that when these become separated by more than one Planck length, they become unstable and collapse. Penrose suggested that "objective reduction" represents neither randomness nor algorithmic processing but instead a non-computable influence in spacetime geometry from which mathematical understanding and, by later extension, consciousness derives.
Hameroff provided a hypothesis that microtubules would be suitable hosts for quantum behavior. Microtubules are composed of tubulin protein dimer subunits. The dimers each have hydrophobic pockets that are 8 nm apart and may contain delocalized π electrons. Tubulins have other smaller non-polar regions that contain π-electron-rich indole rings separated by about 2 nm. Hameroff proposed that these electrons are close enough to become entangled. He originally suggested that the tubulin-subunit electrons would form a Bose–Einstein condensate, but this was discredited. He then proposed a Frohlich condensate, a hypothetical coherent oscillation of dipolar molecules, but this too was experimentally discredited.
In other words, there is a missing link between physics and neuroscience. For instance, the proposed predominance of A-lattice microtubules, more suitable for information processing, was falsified by Kikkawa "et al.", who showed that all in vivo microtubules have a B lattice and a seam. The proposed existence of gap junctions between neurons and glial cells was also falsified. Orch-OR predicted that microtubule coherence reaches the synapses through dendritic lamellar bodies (DLBs), but De Zeeuw "et al." proved this impossible by showing that DLBs are micrometers away from gap junctions.
In 2014, Hameroff and Penrose claimed that the discovery of quantum vibrations in microtubules by Anirban Bandyopadhyay of the National Institute for Materials Science in Japan in March 2013 corroborates Orch-OR theory. Experiments that showed that anaesthetic drugs reduce how long microtubules can sustain suspected quantum excitations appear to support the quantum theory of consciousness.
In April 2022, the results of two related experiments at the University of Alberta and Princeton University were announced at The Science of Consciousness conference, providing further evidence to support quantum processes operating within microtubules. In a study Stuart Hameroff was part of, Jack Tuszyński of the University of Alberta demonstrated that anesthetics hasten the duration of a process called delayed luminescence, in which microtubules and tubulins re-emit trapped light. Tuszyński suspects that the phenomenon has a quantum origin, with superradiance being investigated as one possibility. In the second experiment, Gregory D. Scholes and Aarat Kalra of Princeton University used lasers to excite molecules within tubulins, causing a prolonged excitation to diffuse through microtubules further than expected, which did not occur when repeated under anesthesia. However, diffusion results have to be interpreted carefully, since even classical diffusion can be very complex due to the wide range of length scales in the fluid filled extracellular space. Nevertheless, University of Oxford quantum physicist Vlatko Vedral told that this connection with consciousness is a really long shot.
Also in 2022, a group of Italian physicists conducted several experiments that failed to provide evidence in support of a gravity-related quantum collapse model of consciousness, weakening the possibility of a quantum explanation for consciousness.
Although these theories are stated in a scientific framework, it is difficult to separate them from scientists' personal opinions. The opinions are often based on intuition or subjective ideas about the nature of consciousness. For example, Penrose wrote:
[M]y own point of view asserts that you can't even simulate conscious activity. What's going on in conscious thinking is something you couldn't properly imitate at all by computer... If something behaves as though it's conscious, do you say it is conscious? People argue endlessly about that. Some people would say, "Well, you've got to take the operational viewpoint; we don't know what consciousness is. How do you judge whether a person is conscious or not? Only by the way they act. You apply the same criterion to a computer or a computer-controlled robot." Other people would say, "No, you can't say it feels something merely because it behaves as though it feels something." My view is different from both those views. The robot wouldn't even behave convincingly as though it was conscious unless it really was—which I say it couldn't be, if it's entirely computationally controlled.
Penrose continues:
A lot of what the brain does you could do on a computer. I'm not saying that all the brain's action is completely different from what you do on a computer. I am claiming that the actions of consciousness are something different. I'm not saying that consciousness is beyond physics, either—although I'm saying that it's beyond the physics we know now... My claim is that there has to be something in physics that we don't yet understand, which is very important, and which is of a noncomputational character. It's not specific to our brains; it's out there, in the physical world. But it usually plays a totally insignificant role. It would have to be in the bridge between quantum and classical levels of behavior—that is, where quantum measurement comes in.
Umezawa, Vitiello, Freeman.
Hiroomi Umezawa and collaborators proposed a quantum field theory of memory storage. Giuseppe Vitiello and Walter Freeman proposed a dialog model of the mind. This dialog takes place between the classical and the quantum parts of the brain. Their quantum field theory models of brain dynamics are fundamentally different from the Penrose–Hameroff theory.
Quantum brain dynamics.
As described by Harald Atmanspacher, "Since quantum theory is the most fundamental theory of matter that is currently available, it is a legitimate question to ask whether quantum theory can help us to understand consciousness."
The original motivation in the early 20th century for relating quantum theory to consciousness was essentially philosophical. It is fairly plausible that conscious free decisions (“free will”) are problematic in a perfectly deterministic world, so quantum randomness might indeed open up novel possibilities for free will. (On the other hand, randomness is problematic for goal-directed volition!)
Ricciardi and Umezawa proposed in 1967 a general theory of quanta of long-range coherent waves within and between brain cells, and showed a possible mechanism of memory storage and retrieval in terms of Nambu–Goldstone bosons. 
Mari Jibu and Kunio Yasue later popularized these results under the name "quantum brain dynamics" (QBD) as the hypothesis to explain the function of the brain within the framework of quantum field theory with implications on consciousness.
Pribram.
Karl Pribram's holonomic brain theory (quantum holography) invoked quantum mechanics to explain higher-order processing by the mind. He argued that his holonomic model solved the binding problem. Pribram collaborated with Bohm in his work on quantum approaches to mind and he provided evidence on how much of the processing in the brain was done in wholes. He proposed that ordered water at dendritic membrane surfaces might operate by structuring Bose–Einstein condensation supporting quantum dynamics.
Stapp.
Henry Stapp proposed that quantum waves are reduced only when they interact with consciousness. He argues from the that the quantum state collapses when the observer selects one among the alternative quantum possibilities as a basis for future action. The collapse, therefore, takes place in the expectation that the observer associated with the state. Stapp's work drew criticism from scientists such as David Bourget and Danko Georgiev.
Catecholaminergic Neuron Electron Transport (CNET).
CNET is a hypothesized neural signaling mechanism in catecholaminergic neurons that would use quantum mechanical electron transport. The hypothesis is based in part on the observation by many independent researchers that electron tunneling occurs in ferritin, an iron storage protein that is prevalent in those neurons, at room temperature and ambient conditions. The hypothesized function of this mechanism is to assist in action selection, but the mechanism itself would be capable of integrating millions of cognitive and sensory neural signals using a physical mechanism associated with strong electron-electron interactions. Each tunneling event would involve a collapse of an electron wave function, but the collapse would be incidental to the physical effect created by strong electron-electron interactions.
CNET predicted a number of physical properties of these neurons that have been subsequently observed experimentally, such as electron tunneling in substantia nigra pars compacta (SNc) tissue and the presence of disordered arrays of ferritin in SNc tissue. The hypothesis also predicted that disordered ferritin arrays like those found in SNc tissue should be capable of supporting long-range electron transport and providing a switching or routing function, both of which have also been