Bohr suggests that thought involves such small
amounts of energy that quantum-theoretical
limitations play an essential role in
determining its character.
amounts of energy that quantum-theoretical
limitations play an essential role in
determining its character.
Thanks to Nature for publishing "Quantum Mechanics in the Brain," by Koch and Hepp. As one who has pursued this topic for 35 years, I feel confident that this article will come to be seen as a watershed in the evolution of the debate.
I must report that the authors (along with most of their peers) are thoroughly mistaken. They ask whether there is room for quantum computation in the brain. One might well reply, "Is there room for anything else?"
Thus, in his article on "Field Theory," Freeman Dyson tells us pretty plainly that "There is nothing else except these [quantum] fields: the whole of the material universe is built of them."  The brain is presumably part of the material universe; it seems to follow that the brain just is a collection of quantum fields—and, particularly, electromagnetic (EM) fields. Abdus Salam writes: "all chemical binding is electromagnetic in origin, and so are all phenomena of nerve impulses."  If conscious processes are phenomena of nerve impulses, then it would seem to follow that those processes are EM in origin.
Dyson informs us further: "A classical field is just a special large-scale manifestation of a quantum field." So, how might classical information survive, absent quantum information, as Koch and Hepp assert? How on earth do they suppose chemical interactions in the brain can happen, without photons—paradigmatically QM objects—to mediate those interactions? How do they suppose our eyes capture those photons?
The authors appear to have bought into the decoherence approach to the measurement problem, along with the notion that some form of coherence is necessary to the larger quantum-mind thesis. (Well, some people think along these lines, but I do not. Together with JS Bell and David Bohm, I have advocated a "hidden variables"* approach to this problem. Happily, a handful of our most prominent physicists have lately come around to this view.) If the decoherence view had an any merit, how might it explain nonlocal quantum computation? Or, why does the sea of virtual particles present in the vacuum not bring about decoherence?
Koch and Hepp write:
The power of quantum mechanics is often invoked for problems that brains solve efficiently. Computational neuroscience is a young field and theories of complex neural systems, with all the variability of living matter, will never reach the precision of physical laws of well-isolated simple systems.Well, our planet hosts quite a lot of living matter and yet Koch's former co-author, Francis Crick, helped find a physical mechanism beneath it all. And then, quantum computation is a younger field still, but the authors have already determined that it holds no hope for us in understanding the brain's computations—even though they seem to get that those computations must ultimately be carried out at the quantum level of neural activity. So there appears to be at least one source of incoherence.
It has already been demonstrated, however, that many previously mysterious aspects of perception and action are explainable in terms of conventional neuronal processing.One might well ask, "Demonstrated to the satisfaction of... whom, exactly?" Their peers in neuroscience, whose knowledge of QM is also largely scant?
The heart of light
Here we come to the nub of the matter:
Two examples are models for the rapid recognition of objects (for example, animals or faces) in natural scenes, with performance approaching that of human observers, and the attentional selection of objects in cluttered images. The necessary mathematical operations — such as changes in synaptic weights, evaluating the inner product between presynaptic activity and synaptic weight, multiplication and stationary nonlinearities — are available to neurons.
These "necessary mathematical operations" would seem to point toward operator theory, Heisenberg's matrix formulation of QM and tensor calculus—which just happen to be found not far away, doing just what we might expect them to be doing.
Indeed, there is an embarras de richesse of computational primitives implemented by synapses, dendrites and neurons. That is not to suggest that we understand how brains compute. But so far, there seems to be no need for quantum skyhooks.So... we don't understand how brains compute, but we can safely ignore the underlying physics? And then, their literary accomplishments notwithstanding, it seems a trifle odd, writing about computational primitives and then, in the same breath, dismissing any need for the physical primitives embodied in the mathematics of quantum theory. It is only in physics that we meet up with variables of comparable simplicity to the elements of perception. Thus, we regularly observe objects extended in space and enduring in time—sensory qualities represented in the metric of general relativity and so, presumably, in quantum field theory (QFT), which has been described by Shwinger, among others, as just being relativistic QM.
Why should evolution have turned to quantum computation, so fickle and capricious, if classical neural-network computations are evidently entirely sufficient to deal with the problems encountered by nervous systems?This borders on silliness. The evidence of our senses tells us that the world is full of color and sound—secondary qualities banished from the physical realm long ago by Democritus and, later, by Galileo, Newton and a handful of their contemporaries. These sensory qualities have found no representation in either classical physics or its quantum successor—much less contemporary neuroscience. (Paul Churchland thinks otherwise, but don't get me started.)
Are colors and sounds, perhaps, EPR's missing "elements of reality"?
Mention the notion to most learned heads living today and they will dismiss the idea out of hand. Press the point and they will tell you you're way off base, "not even wrong." Ask how, exactly, is this not thinkable and they will get quite irritated with you. Hands will wave, tempers will fly. (Try it!) Why do these gray eminences behave in this fashion? For the perfectly scientific reason that they haven't a clue. The existence of these properties (which we observe every waking moment), their exclusion from physics—this is the great invisible wall which contains them in an intellectual box, even as they brim with a smug certainty deriving from what "everybody knows," and even though Newton, Young, Helmholtz, Maxwell, Weyl, Schrodinger and Einstein all devoted serious thought to the problem.
The real deal
Umezawa, in a highly readable text on Advanced Field Theory, writes:
Among the many biological objects a particularly interesting one is the brain. For any theory to be able to claim itself as a brain theory, it should be able to explain the origin of such fascinating properties as the mechanism for creation and recollection of memories and consciousness.
For many years it was believed that brain function is controlled solely by the classical neuron system which provides the pathway for neural impulses. This is frequently called the neuron doctrine. The most essential one among many facts is the nonlocality of memory function discovered by Pribram [...]
There have been many models based on quantum theories, but many of them are rather philosophically oriented. The article by Burns [...] provides a detailed list of papers on the subject of consciousness, including quantum models. The incorrect perception that the quantum system has only microscopic manifestations considerably confused this subject. As we have seen in preceding sections, manifestation of ordered states is of quantum origin. When we recall that almost all of the macroscopic ordered states are the result of quantum field theory, it seems natural to assume that macroscopic ordered states in biological systems are also created by a similar mechanism. (My emphasis)
Koch and Hepp write that physicists are ignorant of neurobiologists' work, and conversely. An important exception must be Karl Pribram, who writes in a classic modern work that "the mathematical formulations that have been developed for quantum mechanics and quantum field theory can go a long way toward describing neural processes."  In this wise it is intriguing to note a passage from Lockwood's Mind, Brain & Quantum:
Consciousness, in other words, provides us with a kind of ‘window’ on to our brains, making possible a transparent grasp of a tiny corner of a material reality that is in general opaque to us, knowable only at one remove. The qualities of which we are immediately aware, in consciousness, precisely are some at least of the intrinsic qualities of the states and processes that go to make up the material world — more specifically, states and processes within our own brains.
The psychologist Pribram [...] has made an interesting attempt to revive an idea originally put forward around the turn of the century by the Gestalt psychologists: namely that it is certain fields, in the physicist’s sense, within the cerebral hemispheres, that may be the immediate objects of introspective awareness [...] What it would amount to, in terms of the present proposal, is that we have a ‘special’ or ‘privileged’ access, via some of our own brain activity, to the intrinsic character of, say, electromagnetism. Put like that, the idea sounds pretty fanciful. But make no mistake about it: whether about electromagnetism or about other such phenomena, that is just what the Russellian view ostensibly commits one to saying.
There are, however, two things that must now be emphasized. In the first place, it is a clear implication of the Russellian view that the material world, or more specifically, that part of it that lies within the skull, cannot possess less diversity than is exhibited amongst the phenomenal qualities that we encounter within consciousness. I am inclined to doubt whether the stock of fundamental attributes countenanced within contemporary physical science is, in principle, adequate to the task of accounting for the qualitative diversity that introspection reveals. The current trend, within physics, is towards ever greater unification of the fundamental forces.
This is, I think, just right. Lockwood and I arrived at this conclusion independently of one another, though by similar paths (private communication). More to the point, quantum theory easily accommodates this "qualitative diversity that introspection reveals," as Stapp and I have also argued at length.
I have taken the further step of pointing out, following Riemann, Maxwell and Weyl, that colors define a projective vector manifold. I may have been the first to call attention to the fact that the visual field can be described by assuming color space "fibers over" (sits over) the "points" of that field. This fact (readily open to inspection), taken together with the symmetries and phase relations of colors leads one by a direct path into gauge theory, Kaluza-Klein theory and, perhaps, M-theory, where "M" sometimes means "matrix."
Needless to add, I may well be dead before the general run of mankind comes around to accepting these notions. I recently attempted to make clear the fact that, given the vector character of color, we need a matrix to "rotate" one color vector into another — just as we do when engineering color TVs and computer monitors — in a manner demonstrably predictable, reliable and really quite quantifiable. Given the all-important symmetries of color, that matrix must be a tensor.
Here be dragons
So we have a tensor calculus, already in hand, whereby we can compute the appearance of color. And this is, I argue, of fundamental, foundational importance — because, although color is quite arguably an "element of reality" in the sense of EPR, it has yet to find suitable representation within the structure of physics, as Schrödinger tells us:
If you ask a physicist what is his idea of yellow light, he will tell you that it is transversal electromagnetic waves of wavelength in the neighborhood of 590 millimicrons. If you ask him: But where does yellow come in? he will say: In my picture not at all, but these kinds of vibrations, when they hit the retina of a healthy eye, give the person whose eye it is the sensation of yellow.
Having attempted to clarify the situation, I have been told by persons not wholly bereft of learning that it's probably all a coincidence, this predictive, mathematical correspondence between the model and the reality.
OK, now imagine that Albert Einstein has just explained that gravitational interactions can be modelled via a space-time curvature tensor. Only to be told that it's a coincidence. And so one takes comfort in despairing over the human race. Unhappily, there's not much future in futility.
On the other hand, I am heartened to see the debate breaking into the pages of Nature, even if most of the physics on view there thus far seems to have been gleaned from introductory texts. It is as it was with the publication of The Emperor's New Mind — it's not so much a matter of what Penrose had to say, but with the brute force of the fact that it was Penrose who was saying it. (Having said that, it strikes one as a tad ridiculous, when Nature compares the Encyclopedia Britannica to Wikipedia; a previous article by Crick and Koch contained a number of howlers, also—but then, the authors are Big Names, which surely counts for more in questions of science.)
Koch and Hepp rightly suggest that questions remain as to how brains compute. (They nonetheless feel confident that QM can't help us.) In this connection it is intriguing to note that the Churchlands argue for the tensor network theory of Pellionisz and Llinas. [4, 5] How are those tensors realized in the physics of the brain? Again, the operator formalism of quantum theory would seem to fit the bill admirably.
Given the fractal character of neural nets, we might expect to find this kind of self-similarity across spatio-temporal scales.
Koch and Hepp repeat the dogma that quantum mechanics (QM) is fundamentally indeterministic—a view nearly unquestioned, until recently.  Later, they note that the problem of qualia remains. Max Born, who fathered the statistical interpretation of QM, wrote at the time that "Anyone dissatisfied with these ideas may feel free to assume that there are additional parameters not yet introduced into the theory which determine the individual event."  Nowadays these parameters are called "hidden variables" and have lately been revived by such luminaries as 't Hooft, among others—a development of the highest importance, given that those qualia known as secondary qualities are not yet incorporated into the body of science and are only "hidden" in plain view.
A far more informed view of mind and matter comes from Wolfgang Pauli, who arguably knew something about QM, who also advocated a unitary description of mind and matter — and who also emphasised the centrality of symmetry in our understanding of nature:
For the invisible reality, of which we have small pieces of evidence in both quantum physics and the psychology of the unconscious, a symbolic, psychophysical unitary language must ultimately be adequate, and this is the far goal which I actually aspire. I am quite confident that the final objective is the same, independent of whether one starts from the psyche (ideas) or from physis (matter). Therefore, I consider the old distinction between materialism and idealism as obsolete. (My emphasis)
Then there is Eugene Wigner , whom Feynman called the most gifted physicist he ever met:
let us now turn to the assumption opposite to the 'first alternative' considered so far: that the laws of physics will have to be modified drastically if they are to account for the phenomena of life. Actually, I believe that this second assumption is the correct one.
Can arguments be adduced to show the need for modification? There seem to be two such arguments. The first is that, if one entity is influenced by another entity, in all known cases the latter one is also influenced by the former. The most striking and originally the least expected example for this is the influence of light on matter, most obviously in the form of light pressure. That matter influences light is an obvious fact — if it were not so, we could not see objects. The influence of light on matter is, however, a more subtle effect and is virtually unobservable under the conditions which surround us [...] Since matter clearly influences the content of our consciousness, it is natural to assume that the opposite influence also exists,
thus demanding the modification of the presently accepted laws of nature which disregard this influence.
Although I do not subscribe to Wigner's idea that consciousness causes collapse of the wave function, I believe his argument above will eventually persuade the world—the oracles at Nature notwithstanding.
Finally, why the (now familiar) rush to shut down this line of inquiry? Who can say, before the fact, what discoveries await us? Koch and Hepp appear to say that the staus quo works just fine and will continue to do so—trust us. Rather than explore the possibilities, they seem to have decided at the outset that we need not bother with QM... and then constructed an argument (of sorts) to bear out their preconceptions. Well, this is not science. It is wishful thinking.
* I am indebted to the SPIE for flying me out to Cambridge, MA to deliver this paper, if only because it allows me to establish my priority in these matters. Although the Penrose-Hameroff approach is the best known take on QM and the brain, it was not the first, nor is it, in my estimation, by any means the most plausible.
 Dyson, Freeman J., "Field Theory," pp. 58-60, Scientific American, 188: 1953.
 Salam, Abdus, Unification of Fundamental Forces. Cambridge, 1990.
 Pribram, Karl. Brain and Perception. Hillsdale, NJ: Lawrence Erlbaum, 1991.
 Churchland, P. M. A Neurocomputational Perspective. Cambridge, MA: MIT Press, 1989.
 Churchland, P. S. Neurophilosophy : Toward a Unified Understanding of the Mind-Brain. Cambridge, MA: MIT Press, 1986.
 Wheeler & Tegmark, "100 Years of Quantum Mysteries," Scientific American, 2/2001.
 Holland, Peter R. The Quantum Theory of Motion. Cambridge University Press, 1993.
 Wigner, “Physics and the Explanation of Life,” in Foundations of Physics, vol. 1, 1970, pp. 34-45.