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.
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.
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?)