Orchestrated objective reduction
Orchestrated objective reduction (Orch-OR) is a theory of consciousness, which is the joint work of theoretical physicist, Sir Roger Penrose, and anesthesiologist Stuart Hameroff. Mainstream theories assume that consciousness emerges from the brain, and focus particularly on complex computation at synapses that allow communication between neurons. Orch-OR combines approaches to the problem of consciousness from the radically different angles of mathematics, physics and anesthesia.
Penrose and Hameroff initially developed their ideas quite separately from one another, and it was only in the 1990s that they cooperated to produce the Orch-OR theory. Penrose came to the problem from the view point of mathematics and in particular Gödel's theorem, while Hameroff approached it from a career in cancer research and anesthesia that gave him an interest in brain structures.
The Penrose–Lucas argument 
In 1931, mathematician and logician Kurt Gödel proved that any effectively generated theory capable of proving basic arithmetic cannot be both consistent and complete. Furthermore, he showed that any such theory also including a statement of its own consistency is inconsistent. A key element of the proof is the use of Gödel numbering to construct a "Gödel sentence" for the theory, which encodes a statement of its own incompleteness, e.g. "This theory can't assert the truth of this statement." This statement is either true but unprovable (incompleteness) or false and provable (inconsistency). An analogous statement has been used to show that humans are subject to the same limits as machines.
However, in his first book on consciousness, The Emperor's New Mind (1989), Penrose made Gödel's theorem the basis of what quickly became an intensely controversial claim. He argued that while a formal proof system cannot prove its own inconsistency, Gödel-unprovable results are provable by human mathematicians. He takes this disparity to mean that human mathematicians are not describable as formal proof systems, and are not therefore running an computable algorithm. Similar claims about the implications of Gödel's theorem were originally espoused by the philosopher John Lucas of Merton College, Oxford.
The inescapable conclusion seems to be: Mathematicians are not using a knowably sound calculation procedure in order to ascertain mathematical truth. We deduce that mathematical understanding - the means whereby mathematicians arrive at their conclusions with respect to mathematical truth - cannot be reduced to blind calculation!—Roger Penrose
Criticism of the Penrose-Lucas argument 
The Penrose-Lucas argument about the implications of Gödel's incompleteness theorem for computational theories of human intelligence has been widely criticized by mathematicians, computer scientists and philosophers, and the consensus among experts in these fields is that the argument fails, with different authors choosing different aspects of the argument to attack.
Geoffery LaForte points out that in order to know the truth of an unprovable Gödel sentence, one must already know the formal system is consistent. Referencing Benacerraf, he then demonstrates that humans cannot prove that they are consistent, and in all likelihood human brains are inconsistent. He comically points to contradictions from within Penrose's own writings as evidence. Similarly, Marvin Minsky argues that because humans can construe false ideas to be factual, human mathematical understanding need not be consistent, and consciousness may easily have a deterministic basis.
Solomon Feferman, a professor of mathematics, logic and philosophy has made criticisms of Penrose's argument. He faults detailed points in Penrose's second book, Shadows of the Mind, but says that he does not think that they undermine the main thrust of his argument. As a mathematician, he argues that mathematicians do not progress by computer-like or mechanistic search through proofs, but by trial-and-error reasoning, insight and inspiration, and that machines cannot share this approach with humans. However, he thinks that Penrose goes too far in his arguments. Feferman points out that everyday mathematics, as used in science, can in practice be formalized. He also rejects Penrose's Platonism.
John Searle criticizes Penrose's appeal to Gödel as resting on the fallacy that all computational algorithms must be capable of mathematical description. As a counter-example, Searle cites the assignment of license plate numbers to specific vehicle identification numbers, in order to register a vehicle. According to Searle, no mathematical function can be used to connect a known VIN with its LPN, but the process of assignment is quite simple—namely, "first come, first served"—and can be performed entirely by a computer.
Another critic, Charles Seife, has said, "Penrose, the Oxford mathematician famous for his work on tiling the plane with various shapes, is one of a handful of scientists who believe that the ephemeral nature of consciousness suggests a quantum process."
Objective reduction 
If correct, the Penrose–Lucas argument creates a need to understand the physical basis of non-computational behaviour in the brain. Most physical laws are computable, and thus algorithmic. However, Penrose determined that wave function collapse was a prime candidate for a non-computable process.
In quantum mechanics, particles are treated differently from the macroscopic objects of classical mechanics. Particles are described not by position vectors, but by wave functions, which evolve according to the Schrödinger equation. Non-stationary wave functions are linear combinations of the eigenstates of the system, a phenomenon described by the superposition principle. When a quantum system interacts with a classical system (i.e. when an observable is measured), the system appears to collapse to an random eigenstate of the observable from a classical vantage point.
If collapse is truly random, then there is no process or algorithm that can deterministically predict its outcome. This provided Penrose with a candidate for the physical basis of the non-computable process that he hypothesized to exist in the brain. However, he disliked the random nature of the phenomenon, as randomness was not a promising basis for mathematical understanding. Penrose proposed that while traditional wave function collapse occurs when quantum systems are measured, systems that remain isolated from their environment may still undergo different form of collapse.
In this area, Penrose draws on both general relativity and on his own ideas about the possible structure of spacetime. Penrose, in seeking to reconcile relativity and quantum theory, suggested that at the Planck scale curved spacetime is not continuous, but discretized. Penrose postulates that each separated quantum superposition has its own piece of spacetime curvature, constituting a blister in spacetime. Penrose suggests that gravity exerts a force on these spacetime blisters, which become unstable above the Planck scale of and collapse to just one of the possible states of the particle. Penrose calls this event objective reduction (OR).
The threshold for Penrose OR is given by the indeterminacy principle E = ħ/t, where E is the gravitational self-energy or the degree of spacetime separation given by the superpositioned mass, ħ is the reduced Planck constant, and t is the time until OR occurs. Importantly, this time is a function of the mass/energy of the object undergoing collapse. Thus the greater the superposition, the faster it will undergo OR, and vice versa. Atomic-level superpositions would require 10 million years to reach OR threshold, while an isolated 1 kilogram object would reach OR threshold in only 10−37s. However objects somewhere between these two scales could collapse on a timescale relevant to neural processing.
An essential feature of Penrose's theory is that the choice of states when objective reduction occurs is selected neither randomly, as are choices following wave function collapse, nor completely algorithmically. Rather, states are selected by a "non-computable" influence embedded in the Planck scale of spacetime geometry. Penrose claims that such information is Platonic, representing pure mathematical truth, aesthetic, and ethical values at the Planck scale. This relates to Penrose's ideas concerning the three worlds: physical, mental, and the Platonic mathematical world. In his theory, the Platonic world corresponds to the geometry of fundamental spacetime that is claimed to support non-computational thinking.
There is no evidence for Penrose's objective reduction, but the theory is considered testable, and plans exist to carry out a relevant experiment.
The creation of the Orch-OR model 
When he wrote his first consciousness book, The Emperor's New Mind in 1989, Penrose lacked a detailed proposal for how such quantum processes could be implemented in the brain. Subsequently, Hameroff read The Emperor's New Mind and suggested to Penrose that certain structures within brain cells (neurons) were suitable candidate sites for quantum processing and ultimately for consciousness. The Orch-OR theory arose from the cooperation of these two scientists, and was developed in Penrose's second consciousness book Shadows of the Mind (1994).
Hameroff's contribution to the theory derived from studying brain cells (neurons). His interest centered on the cytoskeleton, which provides an internal supportive structure for neurons, and particularly on the microtubules, which are the most important component of the cytoskeleton. As neuroscience has progressed, the role of the cytoskeleton and microtubules has assumed greater importance. In addition to providing a supportive structure for the cell, the known functions of the microtubules include transport of molecules including neurotransmitter molecules bound for the synapses, and control of the cell's movement, growth and shape.
Hameroff proposed that microtubules were suitable candidates to support quantum processing. Microtubules are made up of tubulin protein subunits. The tubulin protein dimers of the microtubules have hydrophobic pockets which might contain delocalized π electrons. Tubulin has other smaller non-polar regions, for example 8 tryptophans per tubulin, which contain π electron-rich indole rings distributed throughout tubulin with separations of roughly 2 nm. Hameroff claims that this is close enough for the tubulin π electrons to become quantum entangled. Quantum entanglement is a state in which quantum particles can alter one another's quantum-mechanical state instantaneously and at any distance, in a way which would not be possible if they were macroscopic objects obeying the laws of classical physics.
In the case of the electrons in the tubulin subunits of the microtubules, Hameroff has recently suggested that these are part of a Frohlich condensate, which is a coherent oscillation of dipolar molecules. This oscillation was originally proposed to be a Bose-Einstein condensate, but in the most recent version of the theory Hameroff favours a synchronous oscillation of the electrons. Hameroff suggests that through a feature of this kind, quantum activity, which is usually at a very tiny scale, could be boosted to be a large scale influence in the brain.
Hameroff has proposed that condensates in microtubules in one neuron can link with microtubule condensates in other neurons and glial cells via gap junctions. In addition to the synaptic connections between brain cells, gap junctions are a different category of connections, where the gap between the cells is sufficiently small for quantum objects to cross it by means of a process known as quantum tunneling. Hameroff proposes that this tunneling allows a quantum object to extend across a large area of the brain as a single quantum object.
He further postulates that the action of this large-scale quantum feature is the source of the gamma synchronization observed in the brain, and viewed as a neural correlate of consciousness. In support of the much less controversial theory that gap junctions are related to the gamma oscillation, Hameroff quotes a number of studies from recent years.
The Orch-OR theory combines Penrose's hypothesis with respect to the Gödel theorem with Hameroff's hypothesis with respect to microtubules. Together, Penrose and Hameroff have proposed that when condensates in the brain undergo an objective reduction of their wave function, that collapse connects to non-computational decision taking/experience embedded in the geometry of fundamental spacetime.
The theory further proposes that the microtubules both influence and are influenced by the conventional activity at the synapses between neurons. The Orch in Orch-OR stands for orchestrated to give the full name of the theory Orchestrated Objective Reduction. Orchestration refers to the hypothetical process by which connective proteins, known as microtubule-associated proteins (MAPs) influence or orchestrate the quantum processing of the microtubules.
Further to this, in 1998, Hameroff made 20 testable predictions related to his proposal. However, most of these proposals have been falsified. The proposed predominance of 'A' lattice microtubules, more suitable for information processing, has been falsified by Kikkawa et al., who showed that all in vivo microtubules have a 'B' lattice and a seam. The suggestion of coherent photons has been falsified, as has the existence of gap junctions between neurons and glial cells, and the proposal that photons do not decohere in the retina.
The main objection to the Hameroff side of the theory is that any quantum feature in the environment of the brain would undergo wave function collapse (reduction), as a result of interaction with the environment, far too quickly for it to have any influence on neural processes. The wave or superposition form of the quanta is referred to as being quantum coherent. Interaction with the environment results in decoherence otherwise known as wave function collapse. It has been questioned as to how such quantum coherence could avoid rapid decoherence in the conditions of the brain. With reference to this question, a paper by the physicist, Max Tegmark, refuting the Orch-OR model and published in the journal, Physical Review E is widely quoted. Tegmark developed a model for time to decoherence, and from this calculated that microtubule quantum states could exist, but would be sustained for only a femtoseconds (fs) timescale at brain temperatures, far too brief to be relevant to neural processing. A recent paper by Engel et al. in Nature does indicate quantum coherent electrons as being functional in energy transfer within photosynthetic organisms, but the quantum coherence described lasts for 660 fs rather than the 25 milliseconds required by Orch-OR, and this is compatible with Tegmark's calculations. More recent papers involving Guerreshi, G., Cia, J., Popescu, S. and Briegel, H. are looking to improve their model of entanglement in protein, a test which could falsify theories of non-trivial coherence or entanglement in protein.
In their reply to Tegmark's paper, also published in Physical Review E, the physicists Scott Hagan, Jack Tuszynski and Hameroff claimed that Tegmark did not address the Orch-OR model, but instead a model of his own construction. This involved superpositions of quanta separated by 24 nm rather than the much smaller separations stipulated for Orch-OR. As a result, Hameroff's group claimed a decoherence time seven orders of magnitude greater than Tegmark's, but still well short of the 25 ms required if the quantum processing in the theory was to be linked to the 40 Hz gamma synchrony, as Orch-OR suggested. To bridge this gap, the group made a series of proposals. It was supposed that the interiors of neurons could alternate between liquid and gel states. In the gel state, it was further hypothesized that the water electrical dipoles are oriented in the same direction, along the outer edge of the microtubule tubulin subunits. Hameroff et al. proposed that this ordered water could screen any quantum coherence within the tubulin of the microtubules from the environment of the rest of the brain.
Each tubulin also has a tail extending out from the microtubules, which is negatively charged, and therefore attracts positively charged ions. It is suggested that this could provide further screening. Further to this, there was a suggestion that the microtubules could be pumped into a coherent state by biochemical energy. Finally, it is suggested that the configuration of the microtubule lattice might be suitable for quantum error correction, a means of holding together quantum coherence in the face of environmental interaction. In the last decade, some researchers who are sympathetic to Penrose's ideas have proposed an alternative scheme for quantum processing in microtubules based on the interaction of tubulin tails with microtubule-associated proteins, motor proteins and presynaptic scaffold proteins. These proposed alternative processes have the advantage of taking place within Tegmark's time to decoherence.
A number of other criticisms have come to the fore over the years. Papers by Georgiev, D. point to a number of problems with Hameroff's proposals, including a lack of explanation for the probabilistic firing of axonal synapses, an error in the calculated number of the tubulin dimers per cortical neuron, and mismodelling of dendritic lamellar bodies (DLBs) discovered by De Zeeuw et al., which showed that the DLBs are located micrometers away from gap junctions. Further Hameroff's hypothesis that cortical dendrites would be shown to contain mainly 'A' lattice microtubules was experimentally disproved by, which showed that all in vivo microtubules have a 'B' lattice and a seam.
Recently the debate has focused round papers by Reimers et al.  and McKemmish et al.  and Hameroff's replies to these, which is not regarded as being independently reviewed. The Reimers paper claimed that microtubules could only support 'weak' 8 MHz coherence, but that the Orch-OR proposals required a higher rate of coherence. Hameroff, however, claims that 8 MHz coherence is sufficient to support the Orch-OR proposal. McKemmish et al. makes two claims; firstly that aromatic molecules cannot switch states because they are delocalised. Hameroff, however, claims that he is referring to the behaviour of two or more electron clouds; secondly McKemmish shows that changes in tubulin conformation driven by GTP conversion would result in a prohibitive energy requirement. Against this, Hameroff claims that all that is required is switching in electron cloud dipole states produced by London forces.
See also 
- Electromagnetic theories of consciousness
- Holonomic brain theory
- Many-minds interpretation
- Penrose interpretation
- Quantum Aspects of Life (book)
- Quantum mind
- LaForte, Geoffrey, Patrick J. Hayes, and Kenneth M. Ford 1998.Why Gödel's Theorem Cannot Refute Computationalism. Artificial Intelligence, 104:265-286.
- Feferman, Solomon (1996). "Penrose's Gödelian argument". PSYCHE 2: 21–32. CiteSeerX: 10.1.1.130.7027.
- Krajewski, Stanislaw 2007. On Gödel's Theorem and Mechanism: Inconsistency or Unsoundness is Unavoidable in any Attempt to 'Out-Gödel' the Mechanist. Fundamenta Informaticae 81, 173-181. Reprinted in in Logic, Philosophy and Foundations of Mathematics and Computer Science:In Recognition of Professor Andrzej Grzegorczyk (2008), p. 173
- Boolos, George, et al. 1990. An Open Peer Commentary on The Emperor's New Mind. Behavioral and Brain Sciences 13 (4) 655.
- Davis, Martin 1993. How subtle is Gödel's theorem? More on Roger Penrose. Behavioral and Brain Sciences, 16, 611-612. Online version at Davis' faculty page at http://cs.nyu.edu/cs/faculty/davism/
- Lewis, David K. 1969.Lucas against mechanism. Philosophy 44 231-233.
- Putnam, Hilary 1995. Review of Shadows of the Mind. In Bulletin of the American Mathematical Society 32, 370-373 (also see Putnam's less technical criticisms in his New York Times review)
- Tegmark, Max (April 2000). "Importance of quantum decoherence in brain processes". Phys. Rev. E 61 (4): 4194. doi:10.1103/PhysRevE.61.4194. Retrieved 18 November 2012.
- Kikkawa, M., Ishikawa, T., Nakata, T., Wakabayashi, T., Hirokawa, N. (1994). "Direct visualization of the microtubule lattice seam both in vitro and in vivo". Journal of Cell Biology 127 (6): 1965–1971. doi:10.1083/jcb.127.6.1965. PMC 2120284. PMID 7806574.
- Kikkawa, M., Metlagel, Z. (2006). "A molecular "zipper" for microtubules". Cell 127 (7): 1302–1304. doi:10.1016/j.cell.2006.12.009. PMID 17190594.
- Georgiev, D.D. (2007). "Falsifications of Hameroff-Penrose Orch OR model of consciousness and novel avenues for development of quantum mind theory". NeuroQuantology 5 (1): 145–174.
- Georgiev, D.D. (2009). "Remarks on the number of tubulin dimers per neuron and implications for Hameroff-Penrose Orch". NeuroQuantology 7 (4): 677–679. doi:10.1038/npre.2009.3860.1.
- Penrose, Roger (1989). The Emperor's New Mind: Concerning Computers, Minds and The Laws of Physics. Oxford University Press. p. 480. ISBN 0-19-851973-7.
- Hofstadter 1979, pp. 476–477, Russell & Norvig 2003, p. 950, Turing 1950 under “The Argument from Mathematics” where he writes “although it is established that there are limitations to the powers of any particular machine, it has only been stated, without sort of proof, that no such limitations apply to the human intellect.”
- Roger Penrose. Mathematical intelligence. In Jean Khalfa, editor, What is Intelligence?, chapter 5, pages 107-136. Cambridge University Press, Cambridge, United Kingdom, 1994.
- Bringsford, S. and Xiao, H. 2000. A Refutation of Penrose's Gödelian Case Against Artificial Intelligence. Journal of Experimental and Theoretical Artificial Intelligence 12: 307-329. The authors write that it is "generally agreed" that Penrose "failed to destroy the computational conception of mind."
- In an article at http://www.mth.kcl.ac.uk/~llandau/Homepage/Math/penrose.html L.J. Landau at the Mathematics Department of King's College London writes that "Penrose's argument, its basis and implications, is rejected by experts in the fields which it touches."
- Princeton Philosophy professor John Burgess writes in On the Outside Looking In: A Caution about Conservativeness (published in Kurt Gödel: Essays for his Centennial, with the following comments found on pp. 131-132) that "the consensus view of logicians today seems to be that the Lucas-Penrose argument is fallacious, though as I have said elsewhere, there is at least this much to be said for Lucas and Penrose, that logicians are not unanimously agreed as to where precisely the fallacy in their argument lies. There are at least three points at which the argument may be attacked."
- Dershowitz, Nachum 2005. The Four Sons of Penrose, in Proceedings of the Eleventh Conference on Logic Programming for Artificial Intelligence and Reasoning (LPAR; Jamaica), G. Sutcliffe and A. Voronkov, eds., Lecture Notes in Computer Science, vol. 3835, Springer-Verlag, Berlin, pp. 125-138.
- Marvin Minsky. "Conscious Machines." Machinery of Consciousness, Proceedings, National Research Council of Canada, 75th Anniversary Symposium on Science in Society, June 1991.
- Feferman, S. (1996). "Penrose's Gödelian argument". Psyche 2: 21–32.
- Searle, John R. The Mystery of Consciousness. 1997. ISBN 0-940322-06-4. pp 85–86.
- Penrose, Roger (1989). Shadows of the Mind: A Search for the Missing Science of Consciousness. Oxford University Press. p. 457. ISBN 0-19-853978-9.
- Marshall, W., Simon, C., Penrose, R., and Bouwmeester, D. (2003). "Towards quantum superpositions of a mirror". Physical Review Letters 91 (13): 130401. arXiv:quant-ph/0210001. Bibcode:2003PhRvL..91m0401M. doi:10.1103/PhysRevLett.91.130401. PMID 14525288.
- Hameroff, S.R., and Watt, R.C. (1982). "Information processing in microtubules". Journal of Theoretical Biology 98 (4): 549–561. doi:10.1016/0022-5193(82)90137-0. PMID 6185798.
- Hameroff, S.R. (1987). Ultimate Computing. Elsevier. ISBN 0-444-70283-0.
- Hameroff, Stuart (2008). "That's life! The geometry of π electron resonance clouds". In Abbott, D; Davies, P; Pati, A. Quantum aspects of life. World Scientific. pp. 403–434. Retrieved Jan 21, 2010.
- Roger Penrose & Stuart Hameroff (2011). "Consciousness in the Universe: Neuroscience, Quantum Space-Time Geometry and Orch OR Theory". Journal of Cosmology 14.
- Hameroff, S.R. (2006). "The entwined mysteries of anesthesia and consciousness". Anesthesiology 105 (2): 400–412. doi:10.1097/00000542-200608000-00024. PMID 16871075.
- Hameroff, S. (2009). "The "conscious pilot"—dendritic synchrony moves through the brain to mediate consciousness". Journal of Biological Physics 36 (1): 71–93. doi:10.1007/s10867-009-9148-x. PMC 2791805. PMID 19669425.
- Bennett, M.V.L., and Zukin, R.S. (2004). "Electrical Coupling and Neuronal Synchronization in the Mammalian Brain". Neuron 41 (4): 495–511. doi:10.1016/S0896-6273(04)00043-1. PMID 14980200.
- Buhl, D.L., Harris, K.D., Hormuzdi, S.G., Monyer, H., and Buzsaki, G. (2003). "Selective Impairment of Hippocampal Gamma Oscillations in Connexin-36 Knock-Out Mouse In Vivo". Journal of Neuroscience 23 (3): 1013–1018. PMID 12574431.
- Dermietzel, R. (1998). "Gap junction wiring: a 'new' principle in cell-to-cell communication in the nervous system?". Brain Research Reviews 26 (2–3): 176–183. doi:10.1016/S0165-0173(97)00031-3. PMID 9651521.
- Draguhn, A., Traub, R.D., Schmitz, D., and Jefferys, J.G.R. (1998). "Electrical coupling underlies high-frequency oscillations in the hippocampus in vitro". Nature 394 (6689): 189–192. Bibcode:1998Natur.394..189D. doi:10.1038/28184. PMID 9671303.
- Fries, P., Schroder, J.-H., Roelfsema, P.R., Singer, W., and Engel, A.K. (2002). "Oscillatory Neuronal Synchronization in Primary Visual Cortex as a Correlate of Stimulus Selection". Journal of Neuroscience 22 (9): 3739–3754. PMID 11978850.
- Galarreta, M., and Hestrin, S. (1999). "A network of fast-spiking cells in the neocortex connected by electrical synapses". Nature 402 (6757): 72–75. Bibcode:1999Natur.402...72G. doi:10.1038/47029. PMID 10573418.
- Gibson, J.R., Beierlein, M., and Connors, B.W. (1999). "Two networks of electrically coupled inhibitory neurons in neocortex". Nature 402 (6757): 75–79. Bibcode:1999Natur.402...75G. doi:10.1038/47035. PMID 10573419.
- Hormuzdi, S.G., Filippov, M.A., Mitropoulou, G., Monyer, H., and Bruzzone, R. (2004). "Electrical synapses: a dynamic signaling system that shapes the activity of neuronal networks". Biochimica et Biophysica Acta 1662 (1–2): 113–137. doi:10.1016/j.bbamem.2003.10.023. PMID 15033583.
- LeBeau, F.E.N., Traub, R.D., Monyer, H., Whittington, M.A., and Buhl, E.H. (2003). "The role of electrical signaling via gap junctions in the generation of fast network oscillations". Brain Research Bulletin 62 (1): 3–13. doi:10.1016/j.brainresbull.2003.07.004. PMID 14596887.
- Velazquez, J.L.P., and Carlen, P.L. (2000). "Gap junctions, synchrony and seizures". Trends in Neurosciences 23 (2): 68–74. doi:10.1016/S0166-2236(99)01497-6. PMID 10652547.
- Rozental, R., and de Carvalho, A.C.C. (2000). "Introduction". Brain Research Reviews 32 (1): 1–2. doi:10.1016/S0165-0173(99)00061-2. PMID 10751650.
- Hameroff, S.R. (1998). "Quantum Computation In Brain Microtubules? The Penrose-Hameroff "Orch OR" model of consciousness". Philosophical Transactions Royal Society London (A) 356: 1869–1896.
- F. J. Binmöller & C. M. Müller (1992). "Postnatal development of dye-coupling among astrocytes in rat visual cortex". Glia 6 (2): 127–137. doi:10.1002/glia.440060207. PMID 1328051.
- Georgiev, D. (2011). "Photons do collapse in the retina not in the brain cortex: Evidence from visual illusions". Neuroquantology 9 (2): 206–231. arXiv:quant-ph/0208053. Bibcode:2002quant.ph..8053G.
- Engel, G.S., Calhoun, T.R., Read, E.L., Ahn, T.-K., Mancal, T., Cheng, Y.-C., Blankenship, R.E., and Fleming, G.R. (2007). "Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems". Nature 446 (7137): 782–786. Bibcode:2007Natur.446..782E. doi:10.1038/nature05678. PMID 17429397.
- Cai, J.; Popescu, S.; Briegel, H. "Persistent dynamic entanglement from classical motion: How bio-molecular machines can generate non-trivial quantum states". Physical Review E 82: 021921. arXiv:0809.4906. Bibcode:2010PhRvE..82b1921C. doi:10.1103/PhysRevE.82.021921.
- Guerreschi, G.; Cai, J.; Popescu, S.; Briegel, H. (9 Nov 2011). Persistent dynamic entanglement for classical motion: How bio-molecular machines can generate non-trivial quantum states. arXiv:1111.2126vl.
- Hagan, S., Hameroff, S., and Tuszyński, J. (2002). "Quantum Computation in Brain Microtubules? Decoherence and Biological Feasibility". Physical Review E 65 (6): 061901. arXiv:quant-ph/0005025. Bibcode:2002PhRvE..65f1901H. doi:10.1103/PhysRevE.65.061901.
- Hameroff, S. (2006). "Consciousness, Neurobiology and Quantum Mechanics". In Tuszynski, Jack. The Emerging Physics of Consciousness. Springer. pp. 193–253
- De Zeeuw, C.I., Hertzberg, E.L., Mugnaini, E. (1995). "The dendritic lamellar body: A new neuronal organelle putatively associated with dendrodentritic gap junctions". Journal of Neuroscience 15 (2): 1587–1604. PMID 7869120.
- Reimers, J.R., McKemmish, L.K., McKenzie, R.H., Mark, A.E., and Hush, N.S. (2009). "Weak, strong, and coherent regimes of Fröhlich condensation and their applications to terahertz medicine and quantum consciousness". Proceedings of the National Academy of Sciences 106 (11): 4219–4224. Bibcode:2009PNAS..106.4219R. doi:10.1073/pnas.0806273106. PMC 2657444. PMID 19251667.
- McKemmish, L.K., Reimers, J.R., McKenzie, R.H., Mark, A.E., and Hush, N.S. (2009). "Penrose-Hameroff orchestrated objective-reduction proposal for human consciousness is not biologically feasible". Physical Review E 80 (2): 021912–021916. Bibcode:2009PhRvE..80b1912M. doi:10.1103/PhysRevE.80.021912.