Only a moment ago, young James Clerk Maxwell asked Mrs. Murdoch to fetch his parents. Now all three are standing in the kitchen doorway, but he is watching the reflection that dances above the stove, across the ceiling. When he notices the adults, he mischievously flashes sunlight in their eyes.
Mr. Maxwell squints and raises a hand to block the glare, but his voice is indulgent. "What are you up to now, Jamesie?"
"It's the sun, papa. I got it in with this tin plate."
Before the afternoon is over, Jamesie will roll the plate around the pantry floor until Mrs. Murdoch sends him outside; beat it as a drum, marching against Napoleon with the Iron Duke; fill it with pink granite pebbles; empty it again, set it afloat on the duck pond, and bombard it with pebbles until it is swamped by the interlacing waves.
The antenna turns slowly against the spin of the earth, tracking a galaxy eight billion light-years away. That far away, that long ago, the galaxy's core was exploding with unimaginable violence. Here and now, the radio outburst is almost lost in background noise. Penzias and Wilson thought that the noise in their antenna might be caused by pigeon droppings. Instead, it was the echo of the Big Bang.
Where did the Big Bang go?
Waves in what?
In the field. The electromagnetic field. Maxwell's field.
What is the field?
It's like the water in ocean waves. It's like the air in sound waves. It's like the earth in seismic waves. It's like...
What is the field?
It's the sum of all the waves that ever were and all the waves that will ever be.
Penzias and Wilson weren't the first to have noise problems. Radio astronomy goes back to Karl Jansky, who hoped to trace the annoying static in long-range radio. Which goes back to Marconi, who made a revolution out of a laboratory curiosity. Which goes back to Heinrich Hertz in a darkened room at Karlsruhe, adjusting the gap between two brass spheres until he saw a spark: the first radio message. Which goes back to James Clerk Maxwell, who caused that spark as surely as Hertz's transmitter.
"One cannot escape the feeling," Hertz would write of Maxwell's equations, "that these formulae have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers, that we get more out of them than was originally put into them."
Poetic license, of course. Scientific piety. Out-and-out Pythagorean symbol worship.
"A more thorough mathematical study of Maxwell's equations," Einstein went on, "shows that new and really unexpected conclusions can be drawn and the whole theory submitted to a test on a much higher level..."
Come now; you can't really get more out of them than was originally put into them. According to information theory, you can't get even that much. "A great part of twentieth-century physics and mathematics could have been created in the nineteenth century," Freeman Dyson argues, "simply by exploring to the end the mathematical concepts to which Maxwell's equations naturally lead."
What are you up to, Jamesie?
At the moment, James Clerk Maxwell is staying too late at the Cavendish again. He watches young Glazebrook measure light refraction in prisms of Iceland spar. It is the spring of 1879, five years since the laboratory opened, but Professor Maxwell still supervises research as carefully as he planned and equipped the building.
The refraction measurements agree with theory to one part in ten thousand. It's good, sound work, as solid as anything they are doing in Germany. So much for the doubters at Nature who seemed to think it shameful for Fellows of Trinity to be messing about with apparatus!
Pain wrenches at his gut. He murmurs a word of encouragement for Glazebrook before retreating to his office for some carbonate of soda in a glass of water. He should go home to Katherine, but perhaps...yes, just a little more work on the latest proof sheets of the Cavendish book. How prescient the man was, anticipating so much of the work of Ohm, Ampere, even Faraday --- and publishing scarcely any of it, the d---l take him!
In a few months, An Account of the Electrical Researches of the Honourable Henry Cavendish, F.R.S., between 1771 and 1781 will go to press. A month after that, Professor James Clerk Maxwell will die of cancer of the stomach.
"You know in part, at least, how in this case the promise of youth was more than fulfilled, and how the man who, but a fortnight ago, was the ornament of the University, and --- shall I be wrong in saying it? --- almost the discoverer of a new world of knowledge, was even more loved than he was admired, retaining after twenty years of fame that mirth, that simplicity, that childlike delight in all that is fresh and wonderful, which we rejoice to think of as the surest accompaniment of scientific genius. You know, also..."
The Rev. Dr. Butler will prove in stately periods that science, Christianity, and eminence are compatible. But many in the chapel are remembering Maxwell's terrier, which would chase its tail until he gestured, then reverse direction, again and again, until he brought it to rest like the balance-wheel of a watch. Or the "d---l on two sticks," the gyroscopic toy that was never out of his hands for long. Or the pins and string he used to draw a new kind of ellipse when he was still a schoolboy.
Edinburgh, 11th March 1846
John Clerk Maxwell, Esq.
My Dear Sir ---
I am glad to find today, from Professor Kelland, that his opinion of your son's paper agrees with mine; namely, that it is most ingenious, most creditable to him and, we believe, a new way of considering higher curves with reference to loci. Unfortunately, these ovals appear to be curves of a very high and intractable order, so that possibly the elegant method of description may not lead to a corresponding simplicity in investigating their properties...
"Wheels within wheels," we say of a complex machination. It was the baroque epicyclic complexity of it all that doomed Ptolemaic astronomy. Kepler demolished the starry spheres. Descartes offered swirling intangible vortexes to replace them, but Newton needed only the reach of gravity to pull together a new cosmos of ellipses, parabolas, hyperbolas. He confessed misgivings: "...that one body may act on another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent facility for thinking can ever fall into it."
Yet it worked, and promised to make sense of electricity and magnetism, too. Until Faraday started messing about with apparatus, and saw lines of force, as real to him as iron filings, around every charge, magnet, and current. Newton's heirs were not amused. "I declare," sniffed the Astronomer Royal, "I can hardly imagine anyone, who knows the agreement between observation and calculation based on action at a distance, to hesitate an instant between this simple and precise action, on the one hand, and anything so vague and varying as lines of force on the other."
Worse was to come. In 1855, young James Clerk Maxwell began to extend Faraday's ideas in a ten-year campaign. "I was at first almost frightened when I saw such mathematical force made to bear upon the subject," Faraday admitted, "and then wondered to see that the subject stood it so well." Maxwell modeled not just lines of force, but sheets and surfaces of it, rotating tubes of invisible fluids, particles of electricity spinning between the tubes, wheels within wheels that put Ptolemy and Descartes to shame. Yet it worked.
And Maxwell didn't believe it for a minute. He borrowed from mechanics, he said, "to allow the mind at every step to lay hold of a clear physical conception, without being committed to any theory founded on the physical science from which that conception is borrowed." By 1865, in A Dynamical Theory of the Electromagnetic Field, he abandoned the gears and the plumbing.
What remained was the field. It needed no properties that were not in his beautifully symmetric equations. It accounted for all known phenomena of electrical charges, magnets, and their motions. It carried waves at a speed he could calculate.
Hertz understood, and a few others. Most were like C.J. Monro, who wrote to Maxwell: "The coincidence between the observed velocity of light and your calculated velocity of a transverse vibration in your medium seems a brilliant result. But I must say, I think a few such results are wanted before you can get people to think that, every time an electric current is produced, a little file of particles is squeezed along between rows of wheels..."
There was no need to think that. The Cheshire Cat vanishes once it has smiled.
Where did the cat go?
Into the field. The electromagnetic field. Maxwell's field.
After a pigeon?
After a transverse undulation in the luminiferous ether.
We all know about the ether, the supposed medium for electromagnetic waves. One of those weird substances people used to believe in, like phlogiston or caloric, right? It had to be infinitely rigid yet infinitely tenuous. Michelson and Morley mounted their instruments on a stone slab, set the slab afloat in mercury, and took their readings on tiptoe, after midnight (no fluid waves, no sound waves, no seismic waves, please). All the world of physics held its breath, and... no ether. Nothing but light itself.
Too bad about Maxwell. After all, he had written right there for all to see in the Britannica --- hell, he and Huxley were the science editors, ninth edition, 1878! --- "there can be no doubt that the interplanetary and interstellar spaces are not empty, but are occupied by a material substance..."
It's a good thing Michelson and Morley set us straight, right?
FitzGerald, 1878: "If the Maxwell theory induced us to emancipate ourselves from the thralldom of a material ether, it might possibly lead to most important results in the theoretic interpretation of nature."
Einstein, 1938: "It was, indeed, a long time before the full content of Maxwell's theory was recognized. The field was at first considered as something which might later be interpreted mechanically with the help of ether. By the time it was realized that this program could not be carried out, the achievements of the field theory had already become too striking and important for it to be exchanged for a mechanical dogma..."
Feinberg, 1968: "The notion that light is fundamentally just another kind of matter is likely to persist in any future theory."
You can still read in textbooks that Einstein created special relativity to account for the Michelson-Morley results. In fact, he was not thinking of that at all. He was thinking instead that the most important property of Maxwell's equations was their symmetry. What would happen to the symmetry if you could ride on a wave of light?
While the others were trying to explain where the cat had gone, Einstein was looking very hard at that smile.
There was much more to Maxwell than "mathematical force," although in that he ranks behind only Newton and Gauss. True, he calculated for two happy, exhausting years to prove that Saturn's rings must be made of separate particles. True, his work on kinetic theory set physics firmly on the statistical path to quantum mechanics.
But he was also the Jamesie who had never been satisfied with anyone's answers to his everlasting "What's the go of it?", persisting: "But what's the particular go of it?" He stoked fires and hauled ice while his wife took meter readings. (They were measuring the viscosity of gases in a tube that ran through the garret of their London home.) He projected a color photograph in 1861, while Matthew Brady was still mastering black and white. (It shouldn't have worked, because the plates he called "red" and "green" were in fact insensitive to those wavelengths. Unknown to him, they did capture two bands of ultraviolet light, which just happened to give the same effect. A lucky coincidence, if you like.) His stamp would still be on the Cavendish when Rutherford began messing about with atoms.
He lectured at workmen's evening classes, and contributed private essays as a luminary of the Cambridge Apostles. Then there was the Britannica , of course; some physicists today cherish copies of that ninth edition as a bibliophile would treasure a First Folio. And he found time for poetry that ranged from hymn to parody to philosophic doggerel:
Till in the twilight of the Gods,
When earth and sun are frozen clods,
When, all its energy degraded,
Matter to ether shall have faded,
We, that is, all the work we've done
As waves in ether shall forever run
In ever widening spheres through heavens beyond the sun.
Now: do you understand about the ether? About the waves? Not if you still believe that history runs by textbook time, one-way.
Look: the full symmetry of the equations, still unfolding, yields two kinds of waves. There are the waves that spread and fade into noise, ever-widening spheres around every star, every spark, every quantum jump. The others, the time-reversed mirror images Wheeler and Feynman called the "advanced" waves, are strange, but at least as real as iron filings. They begin as noise at the edge of space-time and converge, strengthening, coming into phase, arriving all at once to be sucked into the star, quench the spark, cause (if you like) the quantum jump.
Reflect: does the radio telescope help collapse a galaxy? Does a photon leap from John Clark Maxwell's retina to the shiny toy, bounce to the nearest star, burrow inward to split helium into hydrogen?
"It's the sun, papa. I got it in with this tin plate."
In The Field With James Clerk Maxwell