Saturday, December 30, 2006

Smells Like Success

A recent article in Scientific American cites a paper accepted for publication in Physical Review Letters, positing a quantum basis for the olfactory sense:

The question: What property of an odor molecule (or odorant) do the receptors in our noses pick up? The reigning but still unproved explanation of smell supposes that the shape is the thing, with receptors fitting like a lock into the molecule's key. But the shape theory doesn't explain why some nearly identically shaped molecules smell vastly different, such as ethanol, which smells like vodka, and ethane thiol (rotten eggs).

Turin's more controversial theory, put forth in 1996 and now the subject of two popular books, holds instead that odorant receptors sense the way a molecule's atoms jiggle. The shape of the molecule still comes into play, Turin says, because it determines the odorant's overall vibrational frequency. But he didn't know how all the details fit together.

Physicist Marshall Stoneham and his colleagues at University College London report they have constructed a specific mechanism based on the properties of so-called G-protein coupled receptors, which project from olfactory cells inside the nose.

The researchers imagined that the odorant fits into a spot between a site that donates an electron and one that receives the electron. In this model, the receptor switches on when an electron hops from donor to acceptor. The group calculated that an electron could "tunnel" through the barrier imposed by the odorant, an effect made possible by quantum mechanics, they wrote in a preprint accepted for publication in Physical Review Letters.

I have not yet read the paper, but predict that some such mechanism will be established and that the "odorant's overall vibrational frequency" will be replaced by a vector in an EPR-complete Hilbert space, where by "EPR-complete" I mean a theory wherein all "elements of reality" are represented.

As I have long argued, QM is prima facie incomplete in that it does not explicitly represent the secondary properties or qualities, as Schrödinger tell us in the case of color:

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.

Clark makes the more general case in his admirable book on Sensory Qualities:
The world as described by natural science has no obvious place for colors, tastes, or smells. Problems with sensory qualities have been philosophically and scientifically troublesome since ancient times, and in modern form at least since Galileo in 1623 identified some sensory qualities as characterizing nothing real in the objects themselves...

The qualities of size, figure (or shape), number, and motion are for Galileo the only real properties of objects. All other qualities revealed in sense perception — colors, tastes, odors, sounds, and so on — exist only in the sensitive body, and do not qualify anything in the objects themselves. They are the effects of the primary qualities of things on the senses. Without the living animal sensing such things, these 'secondary' qualities (to use the term introduced by Locke) would not exist.

Much of modern philosophy has devolved from this fateful distinction. While it was undoubtedly helpful to the physical sciences to make the mind into a sort of dustbin into which one could sweep the troublesome sensory qualities, this stratagem created difficulties for later attempts to arrive at some scientific understanding of the mind. In particular, the strategy cannot be reapplied when one goes on to explain sensation and perception. If physics cannot explain secondary qualities, then it seems that any science that can explain secondary qualities must appeal to explanatory principles distinct from those of physics. Thus are born various dualisms.

I wrote above that QM does not explicitly represent colors and so forth. Yet physicists often speak of such things as monochromatic light, red giants, white dwarfs and so on.

Mendeleev, in composing the periodic table, was guided by the secondary properties reliably exhibited by the chemical elements.

Feynman, In his terrific little book on QED, speaks of "blue photons." And we all know what he means — until we start to think about it.

If pressed, scientists have traditionally fallen back on the dogma received from Galileo and Newton, who had it in turn from Democritus and the Greek atomists, that the secondary properties are produced in the mind... er, somehow or other. Yet the mind is yoked to the brain, a physical thing, and mental states are dependent on physical states.

The essence of the solution I have put forward flows from Mach, who wrote in his landmark work on Contributions to the Analysis of Sensations:

The traditional gulf between physical and psychological research... exist only for the habitual stereotyped method of observation. A color is a physical object so long as we consider its dependence upon its luminous source, upon other colors, upon heat, upon space and so forth. regarding, however, its dependence upon the retina... it becomes a psychological object, a sensation. Not the subject, but the direction of our investigation, is different in the two domains.

Mach's views are wholly compatible with mind/brain identity theory, as expressed in Chalmers:

The abstract notion of information, as put forward by Claude E. Shannon of MIT, is that of a set of separate states with a basic structure of similarities and differences between them. We can think of a 10-bit binary code as an information state, for example. Such information can be embodied in the physical world. This happens whenever they correspond to physical states (voltages, say); the differences between them can be transmitted along some pathway, such as a telephone line.

We can also find information embodied in conscious experience. The pattern of color patches in a visual field, for example, can be seen as analogous to that of pixels covering a display screen. Intriguingly, it turns out that we find the same information states embodied in conscious experience and in underlying physical processes in the brain. The three-dimensional encoding of color spaces, for example, suggests that the information state in a color experience correspond directly to an information state in the brain. We might even regard the two states as distinct aspects of a single information state, which is simultaneously embodied in both physical processing and conscious experience.

And before him by Feigl:

The solution that appears most plausible to me, and that is consistent with a thoroughgoing naturalism, is an identity theory of the mental and the physical, as follows: Certain neurophysiological terms denote (refer to) the very same events that are also denoted (referred to) by certain phenomenal terms. The identification of the objects of this twofold reference is of course logically contingent, although it constitutes a very fundamental feature of our world as we have come to conceive it in the modern scientific outlook. Using Frege's distinction between Sinn ('meaning', 'sense', 'intension'), and Bedeutung ('referent', 'denotatum', 'extension'), we may say that neurophysiological terms and the corresponding phenomenal terms, though widely differing in sense... do have identical referents. I take these referents to be the immediately experienced qualities, or their configurations in the various phenomenal fields.

I am pleased to announce that my recent paper on "The Unification of Mind & Matter," which treats these points in greater detail, has been accepted by a journal for a series on Men Who Made a New Science. I will supply a link at the appropriate time.

Tuesday, November 21, 2006

The Big Time

Thirty-six years ago, I became fascinated by the mind/body problem, the ancient question of how our thoughts, ideas, dreams and perceptions get hooked up to the gray matter inside our noggins.

A few years later, it came to me that, since the matter of our brains lives at the quantum level, then maybe that was a good place to look for mind. It was the luckiest hunch of my life. Now, this notion wasn't even on the lunatic fringe at the time -- it was nowhere near the radar.

Fast forward to Spring, 2007, when the American Association for Artificial Intelligence (AAAI) and Stanford University will host a symposium on the subject.

They seem to think this worth mentioning at Cambridge.

Well! This puts a different complexion on things, doesn't it? I have been pursuing R&D on the subject for all this while, with emphasis on the "R." I have some smarts and a healthy ego, but would never want anyone to take my word for all this "quantum mind" stuff -- should anyone be so foolish as to do so -- that is not what science is about & not what I'm about.

So I've been doing my research, thinking my thoughts and airing my views -- but mostly off-Broadway, not wishing to make a bigger fool of myself.

At one time, I co-moderated the q-mind forum under Stuart Hameroff, of the Penrose-Hameroff model. I have sharp disagreements with their approach, but Sir Roger, thanks to his prestige, put us on the map.

Ironically, it may be Hameroff's emphasis on microtubules which stands the test of time. On the other hand, their ideas about the importance of quantum gravity have never held any appeal for me; vastly more important, in my view, is quantum electrodynamics (QED).

Quanta & Consciousness

Are Perceptual Fields Quantum Fields?

Quantum Exchanges

Now, however... the AAAI and Stanford are august bodies -- rightfully conservative, protective of their reputations and not given to supporting wild speculations. They have a lot of real-world clout.

I believe the tide has turned.

Friday, April 21, 2006

Contrary to Nature

Bohr suggests that thought involves such small
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." [1] 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." [2] 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.

They continue:
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.

They inquire:
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 soundsecondary 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." [3] 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. [6] 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." [7] 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 [8], 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.


[1] Dyson, Freeman J., "Field Theory," pp. 58-60, Scientific American, 188: 1953.

[2] Salam, Abdus, Unification of Fundamental Forces. Cambridge, 1990.

[3] Pribram, Karl. Brain and Perception. Hillsdale, NJ: Lawrence Erlbaum, 1991.

[4] Churchland, P. M. A Neurocomputational Perspective. Cambridge, MA: MIT Press, 1989.

[5] Churchland, P. S. Neurophilosophy : Toward a Unified Understanding of the Mind-Brain. Cambridge, MA: MIT Press, 1986.

[6] Wheeler & Tegmark, "100 Years of Quantum Mysteries," Scientific American, 2/2001.

[7] Holland, Peter R. The Quantum Theory of Motion. Cambridge University Press, 1993.

[8] Wigner, “Physics and the Explanation of Life,” in Foundations of Physics, vol. 1, 1970, pp. 34-45.

Thursday, April 06, 2006

Before the Revolution

Einstein and Bohr Had a Debate

The aspects of things that are most important for us

are hidden because of their simplicity and familiarity.


Pity poor Einstein. O, he did good work in his youth, but could never fully embrace quantum theory--and history passed him by.

Thus, the conventional wisdom. Einstein and Bohr had a big debate. Bohr, the father of quantum theory, opined that cause-and-effect breaks down at the ground floor of the world: When a radioactive particle splits, it does so for no special reason--it's a flip of the coin.

Einstein said, "God does not play dice with the universe."

Bohr replied, "You're not him."

Einstein, Podolsky and Rosen wrote a landmark paper, known everywhere as EPR, where they argued that quantum mechanics was logically consistent but incomplete, meaning not every "element of reality" is represented in the theory. The missing elements, were they incorporated into the body of physical theory, would give us a better-than-statistical picture of reality.

And there matters remained. For 60 years. David Bohm tried to fill in the missing pieces--those mysterious (and surely nonexistent) hidden variables--but no one paid him any mind. Everyone who was anyone agreed on the main points.*

Little did we know

Except they didn't. Legendary physicists Schrödinger, Dirac, De Broglie and even Born all demurred from the status quo of quantum theory at one time or another. (Try finding that little item in the textbooks.) Schrödinger authored the eponymous equation governing the quantum realm. His well known remark about "those damn quantum jumps", referring to the sudden, almost mysterious process by which particles change energy levels, shows his frustration with the holes in quantum theory.

Dirac sired quantum field theory (QFT), the ongoing effort to meld relativity and quantum mechanics into one coherent theory. Dirac said: "It seems clear that the present quantum mechanics is not in its final form [...] I think it very likely, or at any rate quite possible, that in the long run Einstein will turn out to be correct." So maybe God really doesn't play dice.

De Broglie gave us wave-particle duality: Photons, electrons, protons--all elementary particles, everywhere--have aspects of both waves and particles. He also hit upon an alternative, "pilot wave" picture of quantum mechanics that Bohm later revived. De Broglie wrote: "The history of science shows that the progress of science has constantly been hampered by the tyrannical influence of certain conceptions that finally came to be considered as dogma." He suggests that the statistical interpretation is one such dogma, perhaps obscuring the truth at the most fundamental levels of Quantum Theory.

Max Born was Heisenberg's teacher. Born initially provided the statistical interpretation of Schrödinger's equation--one of the central pillars of the Copenhagen Interpretation, the body of theory that seemed to bring order to the bewildering quantum phenomena ruling the atomic world. Yet Born said 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."

What might Born's additional parameters be? Just EPR's missing "elements of reality," or, hidden variables. But that's all old hat and of no interest to anyone, aside from a few crackpots. Right?

Not precisely, no. In the last few years a curious rumbling has been heard on the horizon. Unknown to the public, a handful of the most respected voices in contemporary physics have recently published papers in serious journals on (wait for it) hidden variables. Including Gerard 't Hooft, James Hartle (who co-authors stuff with Hawking) and Lee Smolin, author of Three Roads to Quantum Gravity.

The stakes could scarcely be higher, the issue more fundamental: Einstein said that it was upon the resolution of this question, of whether or not God played dice, that the future history of physics would turn. The last time a shift this dramatic happened, we got nuclear power, lasers and transistors--the foundations of modern technology and with it the world economy. So that's kind of cool.

Where are the variables hiding?

If hidden variables exist, why don't we see them? This question is a very common one in contemporary physics, albeit from a different conversation. Thanks to Ed Witten at Princeton, the five different versions of string theory that once gave theorists fits are now known to be variations on a theme: M-theory.

M-theory's proponents are proud of its many achievements, most notably the fact that relativity naturally falls out of the equations--i.e., gravity doesn't have to be forced in by hand. (The theory's detractors hasten to point out that the theory makes no contact with observation.)

One of the fascinating things about M-theory is that it needs extra spatial dimensions for the numbers to come out right. If extra dimensions exist, though, why don't we see them? Are they related to hidden variables? Are they, perhaps, the same?

Now wrap your head around this one: General relativity tells us that gravity is the curvature of four-dimensional space-time. Einstein built directly upon the non-Euclidean geometry of Riemann, who, in his famous habilitation lecture, said this:

So few and far between are the occasions for forming notions whose specializations make up a continuous manifold, that the only simple notions whose specializations form a multiply extended manifold are the positions of perceived objects and colors.

Odd... you never hear about Riemann's remarks on color. But color is just the wavelength of light, right?

Vision and revision

No. Not according to bad boys Maxwell, Schrödinger and Feynman, who tell us that color is a vector, whereas a wavelength, being a length, is a scalar, needing only one number to specify it.

Hermann Weyl, a friend and colleague of Einstein's, gave us gauge theory, a vast subject dealing with the all-important symmetries of the universe. These symmetries are so fundamental that Steven Weinberg, another Nobel laureate, wrote that "it is pretty clear that the symmetries of nature are the deepest things we understand about nature today."

Scalars and vectors are kindergarten tensors, and all these mathematical beasties are useful to us in the main because they have the symmetries we want.

Weyl also thought about color:
Epistemologically it is not without interest that in addition to ordinary space there exists quite another domain of intuitively given entities, namely the colors, which forms a continuum capable of geometric treatment.

Weyl writes in another place that colors obey the laws of projective vector geometry. And this is curious, because the extra dimensions of M-theory are thought to obey those laws, too.

Then again, colors only exist in the mind, right?

Not according to Mach, whom Einstein regarded as one of his main influences. In his work on The Analysis of Sensations, Mach wrote:
A color is a physical object a soon as we consider its dependence, for instance, upon its luminous source, upon temperatures, and so forth. When we consider, however, its dependence upon the retina [...] it is a psychological object, a sensation.

So which is it? Are colors mental or physical? Are the mental and the physical perhaps akin to Bohr's complementary properties? Like wave and particle, two faces of the same thing? This is what Bohm thought: "One may then ask what is the relationship between the physical and the mental processes? The answer that we propose here is that there are not two processes. Rather, it is being suggested that both are essentially the same."

History teaches us

How did we come to think otherwise? It all goes back to the time when the foundations of modern science were being laid, by Galileo and Newton. Although they famously swept aside Greek ideas about motion, they kept an ancient division between the observed properties of nature, as Schrödinger relates:
I wish to demonstrate in a little more detail the very strange state of affairs already noticed in a famous fragment of Democritus of Abdera the strange fact that on the one hand all our knowledge of the world around us, both that gained in everyday life and that revealed by the most painstaking laboratory experiments, rests entirely on immediate sense perception, while on the other hand this knowledge fails to reveal the relations of the sense perceptions to the outside world, so that in the picture or model that we form of the outside world, guided by our scientific discoveries, all sensual qualities are absent.

Galileo took up the cry: "Hence I think that these tastes, odors, colors, etc., on the side of the object in which they seem to exist, are nothing else than mere names, but hold their residence solely in the sensitive body..."

Newton, who wrote that "the science of colors becomes a speculation as truly mathematical as any other part of physics," nonetheless acquiesced in this hoary dogma:
For the Rays (of light) to speak properly are not colored. In them there is nothing else than a certain Power and Disposition to stir up a Sensation of this or that Color [...] in the Rays they are nothing but their Dispositions to propagate this or that Motion into the Sensorium, and in the Sensorium they are Sensations of those Motions under the form of Colors.

How do the rays of light stir up color, exactly? Newton did not know. We do not know, today. And so with tastes, odors, sounds and so forth. Are these properties possibly the hidden variables of quantum theory?

The chasm yawning in the sub-cellar of physical theory has traditionally been papered over by a tissue of rationalizations of the sort a bright young philosophy student could readily puncture. Why? It worked. Splendidly so.

David Hume, that bright angel of reason, saw the problem right away.
Thus there is a direct and total opposition betwixt our reason and senses ... When we reason from cause and effect, we conclude, that neither color, sound, taste, nor smell have a continued and independent existence. When we exclude these sensible qualities there remains nothing in the universe, which has such an existence.

Still, it worked! Besides, if there did exist so fundamental a flaw in physics (our most precise science... if only because its objects are so simple), why then does it work so well? An excellent question, one our civilization has encountered before, in mathematics.

You see, Sherman, for Pythagoras and his disciples, number held sway above the flux of appearances. They thought the universe governed by the natural numbers (1, 2, 3...) and by simple fractions (½, 1/3, ¼). When they discovered that the square root of 2 could not be expressed by a simple fraction, a scandal ensued. (Everyone was talking. No one was saying.)

The process repeated itself when complex numbers were discovered, numbers involving the square root of -1, or i, though nowadays i holds a central place in quantum theory.

The natural numbers work in perfect precision--so long as everything comes in whole numbers.

Symmetry, symmetry

Traditional physics also works very well indeed--so long as we stick with silent, colorless entities in 4D space-time. The world we observe, however, is neither colorless nor silent--and yet colors and sounds appear to respect the fundamental symmetries of nature. That's why things look pretty much the same, day in, day out... even as our Earth, Solar System, Milky Way and Local Cluster fly through the interstellar regions, spinning merrily as they go.

Or, colors and sounds are symmetric under translations and rotations. Well, yes, obviously, so what? So relativity flows from the wellspring of this very kind of symmetry.

Colors and sounds are so simple, so elemental, it's hard to get a handle on them, even though--or perhaps just because--we observe or perceive them every day. And it is the business of science to make sense of what we observe. So says Uncle Albert:
Out of the multitude of our sense experiences we take, mentally and arbitrarily, certain repeatedly occurring complexes of sense impression... we attribute to them a meaning--the meaning of the bodily object. Considered logically this concept is not identical with the totality of sense impressions referred to; but it is an arbitrary creation of the human (or animal) mind. On the other hand, the concept owes its meaning and its justification exclusively to the totality of the sense impressions which we associate with it. (The first and last bits carry my emphasis.)

Where do we go from here? Freeman Dyson, another Nobelist, framed the worldview of contemporary physicists with stunning simplicity and clarity. In an article on "Field Theory" for Scientific American, he wrote: "There is nothing else except these fields: the whole of the material universe is built of them."

Quantum field theory (QFT) holds that all particles can best be described in much the same way that Maxwell described electromagnetism. His electromagnetic field inspired Einstein's work on the gravitational field. In QFT, the photon is the quantum of the electromagnetic field and so with the graviton and the gravitational field. QFT extends this picture to all particles, everywhere.

It is quite curious, then, that we commonly speak of the visual field. If, as Bohm and others have suggested, the mental and the physical are essentially the same, is the visual field then a quantum field? Are mind and body unified at the foundations of the world? Are the additional dimensions of M-theory only "hidden" in plain sight?

Is color invisible to science because of its simplicity and familiarity?

A speck in the visual field, though it need not be red must have some color;
it is, so to speak, surrounded by color-space. Notes must have some pitch,
objects of the sense of touch some degree of hardness, and so on.



* J.S. Bell at CERN had demonstrated by a simple proof that all "local" hidden variables have to respect certain conditions. Experiments by Aspect and others appeared to settle the matter. Unless, of course, the missing variables were nonlocal, but nobody much believed in that possibility. (OK, I did, but who cares?)