Einstein and the Quantum (6 page)

That task was left to the Scottish physicist/mathematician James Clerk Maxwell. Maxwell was a deeply religious man, related to minor nobility, who showed an Einsteinian fascination with natural phenomena from a young age. As early as age three he would wander around the family estate asking how things worked, or as he put it, “
What's the go o' that
?” He is widely regarded as the third-greatest physicist of all time, after Newton and Einstein, although he is surely much less known to the public. He wrote his first important scientific paper at the age of sixteen and attended Cambridge University, where he excelled and became a Fellow shortly after graduation. One of his contemporaries wrote of him, “
He was the one acknowledged genius
… it was certain that he would be one of that small but sacred band to whom it would be given to enlarge the bounds of human knowledge.” At the age of twenty-three Maxwell expressed his philosophy of science in terms that prefigure similar sentiments of both Planck and Einstein:

Happy is the man
who can recognize in the work of today a connected portion of the work of life, and an embodiment of the work of Eternity. The foundations of his confidence are unchangeable, for he has been made
a partaker of Infinity. He strenuously works out his daily enterprises, because the present is given to him for a possession.

Maxwell had a full beard and a certain reserved presence that was hard to warm up to (very unlike Einstein, the mensch); however, he was a loyal friend and an almost saintly husband—in all, a man of character and integrity. Despite his diffidence, he possessed a rapier-like wit, which he would only occasionally display, as in the following. In his forties, having “retired” to his Scottish country estate for health and personal reasons, he was convinced to return to England to head the new Cavendish Laboratory at Cambridge; he did a superb job and became an important administrative figure in British science. In this capacity he was asked to explain to Queen Victoria the importance of creating a very high vacuum. He described the encounter thus:

I was sent for to London
to be ready to explain to the Queen why Otto von Guerike devoted himself to the discovery of nothing, and to show her the two hemispheres in which he kept it … and how after 200 years W. Crookes has come much nearer to nothing and has sealed it up in a glass globe for public inspection. Her majesty however let us off very easily and did not make much ado about nothing, as she had much heavy work cut out for her all the rest of the day.

The young Maxwell came to know the much older Faraday personally as well as through his work and realized that his experimental discoveries, which Faraday had framed qualitatively, could be cast into a set of equations that describe all electromagnetic phenomena in four compact formulas, now universally known as Maxwell's equations. Like Newton's Second Law these are four differential equations, not describing masses and forces but rather electrical fields, magnetic fields, electrical charges and currents. If Maxwell had used only Faraday's law and the previously known laws of electrostatics and magnetism, he would have found similar equations but with a disturbing asymmetry between the role of the electric and magnetic fields. Maxwell decided in 1861 that these two fields were different expressions of the same unified force, and had the
brilliant insight to add a new term to one of the equations describing the magnetic field, which had the effect of making the full set of equations perfectly symmetric in regions of space where there were no electrical charges or currents (as in vacuum). Thus he essentially added a major clause to the laws of electromagnetism. The new term gave rise to new effects, called “displacement currents,” which were verified experimentally. They also made the equations structurally perfect. Boltzmann, quoting Goethe, said of Maxwell's equations, “
was it God that wrote
those lines?”

FIGURE 4.1.
James Clerk Maxwell at roughly the age at which he proposed the fundamental laws of classical electromagnetism. Courtesy of the Master and Fellows of Trinity College Cambridge.

Having added his new contribution to the electromagnetic laws, Maxwell made a historic discovery: electric and magnetic fields could propagate through the vacuum in the form of a wave that carried energy and could exert both electric and magnetic forces. In physics the term
wave
refers to a disturbance in a medium (e.g., water or air) that oscillates in time and typically is extended, at any single instant, over a large region of space. In this case the strength of the disturbance is measured by the strength of the electric field, so that if an electric charge sat at one point in space the electric field would push the charge alternately up and then down, like a rubber ball bobbing on surface waves propagating through water. Moreover, if you moved along with the wave, like a surfer, the field would always push you in one direction, just as the surfboard stays at the leading edge of a water wave (for a while).

Maxwell showed that the distance between crests of the electromagnetic waves could be made arbitrarily large or small; that is, any
wavelength was possible. Thus he discovered what we now call the electromagnetic spectrum, extending, for example, from radio waves having a wavelength of a meter, to thermal radiation (as we saw earlier) at ten millionths of a meter, visible light at half a millionth of a meter, and on to x-rays at ten billionths of a meter. This was a spectacular finding; but the epiphany, the earthshaking revelation, was the speed of the waves: all of them traveled at the same speed, the speed of light! Suddenly disparate phenomena involving man-made electrical devices, natural electric and magnetic phenomena, color, and vision were unified into one phenomenon, the propagation of electromagnetic waves at 186,000 miles per second.

The beauty and significance of this discovery has awed physicists ever since. One of the greatest modern theoretical physicists, Richard Feynman, wrote of this event: “
From the long view
of the history of mankind … the most significant event of the nineteenth century will be judged as Maxwell's discovery of the laws of electrodynamics. The American Civil War will pale into provincial insignificance in comparison with this important scientific event of the same decade.” Maxwell himself, with typical understatement, wrote to a friend in 1865, “
I have also a paper afloat
, with an electromagnetic theory of light, which, until I am convinced of the contrary, I hold to be great guns.”

Maxwell would go on to make other major contributions to physics, specifically with his statistical theory of gases, which will be of great relevance below, but he was not recognized as a transcendent figure during his lifetime. He died of abdominal cancer in 1879 at the age of forty-eight, still at the peak of his scientific powers. While in hindsight we view Maxwell as poorly rewarded in his time for his genius and service to society (he was never knighted, for example), Maxwell did not see it that way. On his deathbed he told his doctor, “
I have been thinking
how very gently I have always been dealt with. I have never had a violent shove in my life. The only desire which I can have is, like David, to serve my generation by the will of God and then fall asleep.”

Maxwell's achievement particularly captivated Einstein. Maxwell, Faraday, and Newton were the three physicists whose picture he had on the wall in his study later in life. Of Maxwell he wrote, “[
the purely mechanical world
picture was upset by] the great revolution forever linked with the names of Faraday, Maxwell and Hertz. The lion's share of this revolution was Maxwell's … since Maxwell's time physical reality has been thought of as represented by continuous fields…. this change in the conception of reality is the most profound and fruitful that physics has experienced since the time of Newton.” Elsewhere he said, “
Imagine his feelings when
the differential equations he had formulated proved to him that electromagnetic fields spread in the form of … waves and with the speed of light”; and, “
to few men in the world
has such an experience been vouchsafed.”

Maxwell had completed the second pillar of classical physics, what we now call classical electrodynamics, to go along with the first pillar, classical mechanics. But neither his nor Newton's equations in themselves answered the fundamental question: what is the universe made of? One knew that there were masses and charges and forces and fields, but what were the building blocks of the everyday world? The enormous challenge was to extend these physical laws down to this conjectured “atomic” scale. Were there new, microscale forces not detectable at everyday dimensions? Did Newton's and Maxwell's laws still hold there? Were atoms little billiard balls with mass and electrical charge obeying classical mechanics and electrodynamics? Were there atoms at all, or were they just “theoretical constructs,” as many physicists and chemists maintained until the end of the nineteenth century?

At the time of Maxwell there was no way to probe the internal structure of atoms or molecules directly. As Maxwell put it, “
No one has ever seen
or handled a single molecule. Molecular science therefore … cannot be subjected to direct experiment.” However physicists, led by Maxwell and Boltzmann, were beginning to use the atomic concept to explain in great depth the macroscopic behavior of gases. In doing so they were inferring properties of atoms and their interactions. This was the work that Einstein never forgave Herr Weber, his erstwhile mentor, for ignoring. It is here that Einstein first put his shoulder to the wheel.

 

¹
This wonderful incident may well be apocryphal, as there is no contemporaneous account of it.

CHAPTER 5

THE PERFECT INSTRUMENTS OF THE CREATOR

“
The Boltzmann is magnificent
,” Einstein wrote to Maric in September of 1900. “I am firmly convinced that the principles of his theory are right, … that in the case of gases we are really dealing with discrete particles of definite finite size which are moving according to certain conditions … the hypothetical forces between molecules are not an essential component of the theory, as the whole energy is kinetic. This is a step forward in the dynamical explanation of physical phenomena.” Einstein was reading Boltzmann's
Lectures on the Theory of Gases
. The Viennese physicist Ludwig Boltzmann and Maxwell had developed a theory of gases in the 1860s with much the same content, but with the difference that Boltzmann wrote long, difficult-to-decode treatises, while Maxwell's work was much more succinct. Maxwell commented on this drily: “
By the study of Boltzmann
I have been unable to understand him. He was unable to understand me on account of my shortness, and his length was and is an equal stumbling block to me.” Einstein, despite the enthusiasm he expressed to his fiancée in 1900, was later to warn students, “
Boltzmann … is not easy
reading. There are very many great physicists who do not understand it.” It is likely that Einstein had no access to Maxwell's work on gases in 1900, and as he did not read English until much later in life, he would not have been able to benefit from it anyway (in contrast, Maxwell's electrodynamics was available to Einstein in German textbooks).

Maxwell beautifully described the scientific advance he had made in atomic theory in an address to the Royal Society in 1873 titled, simply, “Molecules.”

An atom is a body
which cannot be cut in two. A molecule is the smallest possible portion of a particular substance. The mind of man has perplexed itself with many hard questions…. [Among them] do atoms exist, or is matter infinitely divisible? …

According to Democritus and the atomic school, we must answer in the negative. After a certain number of sub-divisions, [a piece of matter] would be divided into a number of parts each of which is incapable of further sub-division. We should thus, in imagination, arrive at the atom, which, as its name literally signifies, cannot be cut in two. This is the atomic doctrine of Democritus, Epicurus, and Lucretius, and, I may add, of your lecturer.

Maxwell goes on to describe how chemists had already learned that the smallest amount of water is a molecule made up of two “molecules” of hydrogen and one “molecule” of oxygen (here he has decided, somewhat confusingly, to use molecule to refer to both atoms and molecules). Then he arrives at his current research.

Our business this evening
is to describe some researches in molecular science, and in particular to place before you any definite information which has been obtained respecting the molecules themselves. The old atomic theory, as described by Lucretius and revived in modern times, asserts that the molecules of all bodies are in motion, even when the body itself appears to be at rest…. In liquids and gases, … the molecules are not confined within any definite limits, but work their way through the whole mass, even when that mass is not disturbed by any visible motion…. Now the recent progress of molecular science began with the study of the mechanical effect of the impact of these moving molecules when they strike against any solid body. Of course these flying molecules must beat against whatever is placed among them, and the constant succession of these strokes is, according to our theory, the sole cause of what is called the pressure of air and other gases.