Surfaces and Essences: Analogy as the Fuel and Fire of Thinking (110 page)

Einstein, recognizing that there was nothing to do but accept the image so clearly suggested by his analogy, came to the staggering hypothesis, flying in the face of the most solidly established facts, that the electromagnetic radiation in a blackbody cavity consisted of small corpuscles — small packets of energy, analogous to the
N
molecules in an ideal gas (and, to show how far ahead of his times Einstein was, we point out that at that moment in physics, even the existence of atoms and molecules was still considered suspect by some skeptical holdouts!). Each of these mysterious “lumps of radiation” would necessarily possess exactly the energy
hν
, which thus had to be the
minimal
amount of energy associated with the frequency
ν
. Called “light quanta” by Einstein, such particles are known today as “photons”.

Although not in the least controversial today, Einstein’s bold suggestion in 1905 that light must consist of particles was harshly and unanimously dismissed by his colleagues. Later in life, he declared this hypothesis, based on but the shakiest of analogies, to be the most daring idea of his entire career; indeed, it was so daring that it unleashed, among his colleagues, a barrage of scorn and hostility whose magnitude, duration, and ferocity he surely could not have anticipated.

In the conclusion of his light-quantum article, the young “Technical Expert, Third Class” (the lowest rank at the Swiss patent office) had both the cleverness and the courage to suggest three possible experimental ways to confirm or refute his theory, thus taking the risk of handing weapons to his enemies, with which they could potentially shoot him down! In particular, the second of his suggestions involved looking at the photoelectric effect, in which, when electromagnetic radiation (such as light) falls on a piece of metal, some electrons come flying out of the metal. It was an odd little effect but was considered of no great moment for physics, and had been observed for the first time, but only very crudely, in 1887 by the German physicist Heinrich Hertz, in a series of experiments in which he conclusively demonstrated the existence of electromagnetic waves, thus brilliantly confirming Maxwell’s equations.

Einstein realized that his theory of light quanta yielded precise predictions for the photoelectric effect. In particular, in a very simple equation, it predicted the rate of ejection of electrons as a function of the wavelength of the incident light, and this prediction was in stark contradiction with predictions based on Maxwell’s universally accepted equations. Einstein could not know, nor could any other physicist of the time, what would be revealed by precise measurements of the photoelectric effect, but it was clear to him that such experiments would be decisive and might lead to a great battle, because if his prediction turned out to be correct, the world of physics would be forced to reject Maxwell’s equations as the basis of electromagnetism. This was among the most paradoxical moments in the entire history of physics, for Hertz’s experiments, which had so triumphantly
confirmed
Maxwell’s equations, were also the source of the tiny anomaly that now threatened to
undermine
those very equations. However, the investigation that Einstein suggested in his conclusion was very difficult to carry out, and it took quite a number of years before the experiments yielded clear results.

In 1905, though, no one paid the least attention to the light-quantum hypothesis, as everyone but Einstein was completely convinced of the validity of Maxwell’s equations. Light was made of waves; that was that. To doubt it was simply insanity. Even Max Planck, who had dreamt up the idea of
quanta of energy of vibrating atoms
, proclaimed that the new hypothesis of
quanta of light
was senseless. (It is of note that Planck, some years earlier, had also declared that the hypothesis of atoms was senseless, but by 1905 he greatly regretted having done so.) Despite his colleagues’ unanimous scorn, the young Einstein had an unshakable faith in his own ideas, and was not discouraged. (Actually, calling them “his colleagues” is a bit of a stretch, since until 1908, Einstein was merely an amateur physicist, his official job being that of Technical Expert in the patent office.)

In 1907, Einstein pushed his quantum ideas yet further. He proposed a new analogy that built both on Max Planck’s idea of
energy
quanta in vibrating atoms and on his own idea of
light
quanta. This analogy had to do with sound waves inside solids. Essentially, Einstein came up with the idea of
sound quanta
, although he never used this terminology. (Today, the quanta making up sound waves are called “phonons”, echoing “photon”; they play a key role in the physics of matter.) With his new way of conceiving of vibrations inside solids, Einstein was able to resolve a major mystery concerning the heat capacity of solids. This time, most curiously, the world of physics, even as it disdainfully continued to reject
light
quanta, unanimously accepted the validity of Einstein’s explanation of the heat capacity of solids, based on
sound
quanta, and in 1909 the Dutch physicist Peter Debye deepened Einstein’s theory and created a very powerful theory of heat capacities, which physicists quickly and warmly welcomed, all while still giving the cold shoulder to Einstein’s light-quantum hypothesis.

A strong friendship and great mutual respect developed between Albert Einstein and Max Planck, and in 1913, the latter nominated Einstein for membership in the Prussian Academy of Sciences, which was one of the most distinguished scientific societies in the world. In his nomination letter, Planck sang Einstein’s praises, but when it came to the subject of light quanta, which Einstein had continued to champion, Planck commented, “That he may sometimes have missed the target in his speculations, as, for example, in his hypothesis of light quanta, cannot be held too much against him, for it is not possible to introduce really new ideas even in the most exact sciences without sometimes taking a risk.”

In the decade from 1906 to 1915, the distinguished American physicist Robert Millikan carried out a long and very careful series of experiments on the photoelectric effect. From the start, he was convinced that Einstein’s ideas on the subject were worthless, since they directly contradicted the century-old finding, due to Thomas Young in England and Augustin Fresnel in France, and spectacularly confirmed in 1887 by Heinrich Hertz in Germany, that light consists of waves, and this fact precluded particles of light. For Millikan as for nearly everyone else, the idea of light being
both
particulate and wavelike was inconceivable. Nonetheless, his experiments wound up confirming Einstein’s predictions perfectly, which plunged Millikan into deep cognitive dissonance. In a major book summarizing his work, published in 1917, Millikan admitted that his results supported Einstein’s revolutionary predictions to the hilt, but he insisted that one should beware of Einstein’s “reckless” ideas about light because they had no theoretical underpinning. Put otherwise, although Einstein’s conjectural explanation of the photoelectric effect had furnished impeccable predictions, one should give it no credence because it had not been rigorously derived from previously known physical laws. Millikan even had the temerity to declare in his article that Einstein himself no longer believed in his own “erroneous theory” about light (a pure speculation on Millikan’s part, without the slightest basis in fact).

To add insult to injury, although the 1921 Nobel Prize in Physics was awarded to Albert Einstein, it was not for his theory of light quanta but “for his discovery of the law of the photoelectric effect”. Weirdly, in the citation there was no mention of the ideas
behind
that law, since no one on the Nobel Committee (or in all of physics) believed in them! Light quanta had been unanimously rejected by the members of the community of physicists, even the most adventurous among them. For example, the following year, Niels Bohr, the great Danish physicist and admirer of Einstein, in his acceptance speech for his own Nobel Prize, which had just been awarded to him for his contributions to quantum theory, brusquely dismissed Einstein’s ideas about the corpuscularity of light as “not able to throw light on the nature of radiation”.

And thus Albert Einstein’s revolutionary ideas on the nature of light, that most fundamental and all-pervading of natural phenomena, were not what won him the only Nobel Prize that he would ever receive; instead, it was just his little equation concerning the infinitely less significant photoelectric effect. It’s as if the highly discriminating Guide Michelin, in awarding its tiptop rank of three stars to Albert’s Auberge, had systematically ignored its chef’s consistently marvelous five-course meals and had cited merely the fact that the Auberge serves very fine coffee afterwards.

The turning point when light quanta at last emerged from the shadows came only in 1923, when the American physicist Arthur Holley Compton astonished the world of physics with his experimental discovery that when an electromagnetic wave approaches an electrically charged particle (an electron in an atom, for instance), it transfers to the particle some of its kinetic energy and momentum, but does not do so as Maxwell’s equations predicted. In fact, Compton found that the wave–particle “collision” that takes place in such a situation obeyed the long-known mathematical rules of collisions between
two particles
, with the energies of the incoming and outgoing waves matching exactly what Einstein had predicted in his 1905 paper about light quanta. And thus, at long last, light became particulate!

It still took three more years for the catchier word “photon” to be coined by the American chemist Gilbert Lewis, but in any case, today the notion of a photon — that is, a “wave packet” of light — is a completely familiar denizen of the physics world, and no physicist would dream of denying its reality.

It thus took almost twenty years before the idea of light quanta, the fruit of an analogy conceived in 1905, was taken seriously by physicists — and even after the Compton effect, it still took a bitter battle before the idea was universally accepted. Today, oddly enough, this story is hardly remembered; indeed, most contemporary physicists have the erroneous impression that this first of Einstein’s five great articles in 1905 was written solely in order to explain the “famous” photoelectric effect, basing it all on Max Planck’s idea that the atoms in the walls of a black body can only take on quantized amounts of vibrational energy. But that is
not
what Einstein’s article was written for. Indeed, in 1905 the photoelectric effect was so new and so unexplored that there were not enough data to call for a precise explanation. And thus, in his article, Einstein didn’t propose an
explanation
of a famous, well-charted effect; rather, he made a precise
prediction
of the behavior of a barely-known effect, suggesting in a very clear way
how his prediction might be tested; however, all of this occupied but two pages near the very end, since his article’s
main
topic was the radical idea of light quanta, which had very little in common with what Max Planck had hypothesized in 1900 (as Planck’s violent rejection of the idea shows). In sum, Einstein’s light-quantum article was nothing but the dogged pursuit of a subtle analogy linking a black body to an ideal gas. Once he had glimpsed this analogy, Einstein went way out on a limb, placing all of his chips on it, in a move that to his colleagues seemed crazy, and then he patiently waited nearly twenty years before being vindicated by Compton’s experiments.

This saga, rather troubling but at the same time enlightening, beautifully illustrates Einstein’s ability to put his finger on the true essence of a physical situation where his colleagues either saw nothing of special interest or saw only a fog without any recognizable landmarks. For us, the story of this analogy constitutes an example of human intelligence at its very finest.

What is the most famous equation in the world? The most plausible candidate, other than “1 + 1 = 2”, would surely be “
E = mc
²
”, the celebrated formula by which Albert Einstein revealed a profound but unsuspected relationship between the concepts of
mass
and
energy.
In the next several sections of this chapter, we will concentrate our attention mainly on the process by which the Technical Expert, Third Class gradually deepened his understanding of the meaning of his discovery. It took him two full years — from 1905 till 1907 — to come to see the unsuspected depths hidden in these five little symbols. How this conceptual evolution took place in Einstein’s mind is a fascinating but surprisingly little-known story.

But one must begin at the beginning — that is, the origins of
E = mc
²
. To set the stage, we need to describe how the mechanisms of analogical category extension and vertical category leaps can be used in scientific discovery. Both types of process played key roles in the intellectual style of Albert Einstein, and together they carried him to fantastic destinations.

To illustrate the scientific role of analogical category extension, we will consider for a moment the
annus minimus
(“minimal year”) of Doctor Ellen Ellenbogen. It was in 1905 that Doctor Ellenbogen, who was not yet employed as a physician but rather as Dishwasher, Third Class in a restaurant in Bellinzona, Switzerland, made not several, alas, but just one medical discovery, and a very modest one, at that. To be specific, shortly after Doctor Ellenbogen had read an article about a marvelous yet very simple treatment that had been recently discovered by Doctor Knut von Knie for an acute
knee
disease, it occurred to her that Doctor von Knie’s method might well be also applied to afflicted
elbows.
Here are the words with which, many years later, the Dishwasher Third Class explained her bold mental leap: