einstein

quirk in the cosmos. For him, these quanta of energy (which in 1926 were named photons) 20 existed even when light was moving through a
vacuum. “We wish to show that Mr. Planck’s determination of the elementary quanta is to some extent independent of his theory of blackbody
radiation,” he wrote. In other words, Einstein argued that the particulate nature of light was a property of the light itself and not just some description
of how the light interacts with matter. 21
Even after Einstein published his paper, Planck did not accept his leap. Two years later, Planck warned the young patent clerk that he had gone
too far, and that quanta described a process that occurred during emission or absorption, rather than some real property of radiation in a vacuum. “I
do not seek the meaning of the ‘quantum of action’ (light quantum) in the vacuum but at the site of absorption and emission,” he advised. 22
Planck’s resistance to believing that the light quanta had a physical reality persisted. Eight years after Einstein’s paper was published, Planck
proposed him for a coveted seat in the Prussian Academy of Sciences. The letter he and other supporters wrote was filled with praise, but Planck
added: “That he might sometimes have overshot the target in his speculations, as for example in his light quantum hypothesis, should not be
counted against him too much.” 23
Just before he died, Planck reflected on the fact that he had long recoiled from the implications of his discovery. “My futile attempts to fit the
elementary quantum of action somehow into classical theory continued for a number of years and cost me a great deal of effort,” he wrote. “Many of
my colleagues saw in this something bordering on a tragedy.”
Ironically, similar words would later be used to describe Einstein. He became increasingly “aloof and skeptical” about the quantum discoveries
he pioneered, Born said of Einstein. “Many of us regard this as a tragedy.” 24
Einstein’s theory produced a law of the photoelectric effect that was experimentally testable: the energy of emitted electrons would depend on the
frequency of the light according to a simple mathematical formula involving Planck’s constant. The formula was subsequently shown to be correct.
The physicist who did the crucial experiment was Robert Millikan, who would later head the California Institute of Technology and try to recruit
Einstein.
Yet even after he verified Einstein’s photoelectric formulas, Millikan still rejected the theory. “Despite the apparently complete success of the
Einstein equation,” he declared, “the physical theory on which it was designed to be the symbolic expression is found so untenable that Einstein
himself, I believe, no longer holds to it.” 25
Millikan was wrong to say that Einstein’s formulation of the photo-electric effect had been abandoned. In fact, it was specifically for discovering
the law of the photoelectric effect that Einstein would win his only Nobel Prize. With the advent of quantum mechanics in the 1920s, the reality of the
photon became a fundamental part of physics.
However, on the larger point Millikan was right. Einstein would increasingly find the eerie implications of the quantum—and of the wave-particle
duality of light—to be deeply unsettling. In a letter he wrote near the end of his life to his dear friend Michele Besso, after quantum mechanics had
been accepted by almost every living physicist, Einstein would lament, “All these fifty years of pondering have not brought me any closer to
answering the question, What are light quanta?” 26
Doctoral Dissertation on the Size of Molecules, April 1905
Einstein had written a paper that would revolutionize science, but he had not yet been able to earn a doctorate. So he tried one more time to get
a dissertation accepted.
He realized that he needed a safe topic, not a radical one like quanta or relativity, so he chose the second paper he was working on, titled “A
New Determination of Molecular Dimensions,” which he completed on April 30 and submitted to the University of Zurich in July. 27
Perhaps out of caution and deference to the conservative approach of his adviser, Alfred Kleiner, he generally avoided the innovative statistical
physics featured in his previous papers (and in his Brownian motion paper completed eleven days later) and relied instead mainly on classical
hydrodynamics. 28 Yet he was still able to explore how the behavior of countless tiny particles (atoms, molecules) are reflected in observable
phenomena, and conversely how observable phenomena can tell us about the nature of those tiny unseen particles.
Almost a century earlier, the Italian scientist Amedeo Avogadro (1776–1856) had developed the hypothesis—correct, as it turned out—that
equal volumes of any gas, when measured at the same temperature and pressure, will have the same number of molecules. That led to a difficult
quest: figuring out just how many this was.
The volume usually chosen is that occupied by a mole of the gas (its molecular weight in grams), which is 22.4 liters at standard temperature and
pressure. The number of molecules under such conditions later became known as Avogadro’s number. Determining it precisely was, and still is,
rather difficult. A current estimate is approximately 6.02214 x 10 23 . (This is a big number: that many unpopped popcorn kernels when spread
across the United States would cover the country nine miles deep.) 29
Most previous measurements of molecules had been done by studying gases. But as Einstein noted in the first sentence of his paper, “The
physical phenomena observed in liquids have thus far not served for the determination of molecular sizes.” In this dissertation (after a few math and
data corrections were later made), Einstein was the first person able to get a respectable result using liquids.
His method involved making use of data about viscosity, which is how much resistance a liquid offers to an object that tries to move through it.
Tar and molasses, for example, are highly viscous. If you dissolve sugar in water, the solution’s viscosity increases as it gets more syrupy. Einstein
envisioned the sugar molecules gradually diffusing their way through the smaller water molecules. He was able to come up with two equations, each
containing the two unknown variables—the size of the sugar molecules and the number of them in the water—that he was trying to determine. He
could then solve for these unknown variables. Doing so, he got a result for Avogadro’s number that was 2.1 x 10 23 .
That, unfortunately, was not very close. When he submitted his paper to the Annalen der Physik in August, right after it had been accepted by
Zurich University, the editor Paul Drude (who was blissfully unaware of Einstein’s earlier desire to ridicule him) held up its publication because he
knew of some better data on the properties of sugar solutions. Using this new data, Einstein came up with a result that was closer to correct: 4.15 x
10 23 .
A few years later, a French student tested the approach experimentally and discovered something amiss. So Einstein asked an assistant in
Zurich to look at it all over again. He found a minor error, which when corrected produced a result of 6.56 x 10 23 , which ended up being quite
respectable. 30
Einstein later said, perhaps half-jokingly, that when he submitted his thesis, Professor Kleiner rejected it for being too short, so he added one
more sentence and it was promptly accepted. There is no documentary evidence for this. 31 Either way, his thesis actually became one of his most
cited and practically useful papers, with applications in such diverse fields as cement mixing, dairy production, and aerosol products. And even