Einstein and the Quantum (3 page)

Thus, when Planck stepped to the podium that night, his aim was not scientific revolution but damage control. Nonetheless, he was a truth seeker; he was not willing to run away from unpleasant facts. Later he scorned the English theorist James Jeans for just such behavior: “
He is the model of the theorist
as he should
not
be…, [because
he believes] so much the worse for the facts if they don't fit.” Planck stood up and faced the music: “
The interesting results of long wavelength
spectral energy measurements … confirm the statement … that Wien's energy distribution law is not generally valid…. Since I myself
even in this Society
have expressed the opinion that Wien's law must be necessarily true, I may perhaps be permitted to explain briefly the relationship between the … theory developed by me and the experimental data.”

The “relationship” between them of course is that the Planck-Wien theory is wrong; Planck could not quite bring himself to say
that
in his remarks. But he did identify a weak point in his earlier arguments and admitted that the Second Law of thermodynamics does not have enough power, on its own, to answer the question. There had to be some further new principle involved. Having lost his guideposts for the journey, but being under such intense pressure to come up with an answer, Planck did something highly uncharacteristic. Planck was not a man to leap impulsively into the unknown; by his own description he was “
by nature … peacefully inclined
, and reject[s] all doubtful adventures.” Nonetheless, on that October night he had decided to wing it. What followed was the most fateful improvisation in the history of science.

Planck had been fortunate that his friend Rubens had given him warning of the failure of his theory. Moreover Rubens's data provided a huge clue to what was wrong. Earlier experiments had shown that the Plank-Wien law worked very well for
visible
EM radiation emitted by very hot bodies, that is, for the shorter wavelengths. The new experiments of Rubens and Kurlbaum showed not only that the law failed for the longer, infrared wavelengths emitted by less hot objects, but also showed exactly
how
it failed. That nice, straight line in the data told Planck that at long wavelengths, contrary to the prediction of the Planck-Wien law, the radiation energy must be proportional to temperature. To Planck the challenge was similar to filling in a line in a crossword puzzle for which the end of the word was known, and now someone had filled in the first letter for him, telling him his original guess was wrong. With a little inspired mathematical insight on the very Sunday night, twelve days earlier, that Rubens had warned him of the problem, Planck had
guessed
the correct mathematical formula for
the law of thermal radiation. Now, at the meeting, he unveiled his new formula, soon to become immortalized as the Planck radiation law.
²
Moreover he took the liberty of sketching how his new law compared to the Rubens-Kurlbaum data; it produced a line perfectly matching the data points. He concluded, “
I should therefore be permitted
to draw your attention to this new formula, which I consider to be the simplest possible, apart from Wien's expression.”

With this great leap of intuition Planck had achieved a draw, but not a victory. Theorists are not supposed to just
guess
the correct formulas to describe data; they are supposed to
derive
these formulas from the fundamental laws of physics, which at the time were Newton's laws of mechanics and of gravity, Maxwell's electromagnetic theory, and the laws of thermodynamics. For Planck's new law to be anything more than a “curiosity” (as he himself put it), he would have to connect it to the more general laws of physics. As Planck himself said, “
even if the absolutely precise
validity of the radiation formula is taken for granted, so long as it had merely the standing of a law disclosed by a lucky intuition, it could not be expected to possess more than a formal significance. For this reason, on the very day when I formulated this law, I began to devote myself to the task of investing it with true physical meaning.”

The details of Planck's new reasoning will be fully explained later in our story. For the moment it suffices to say that after “
some weeks of the most strenuous
work” of his life, “some light came into the darkness,” and Planck again went before the German Physical Society to justify his radiation law. In the course of that presentation, on December 14, 1900, he uttered two sentences of incalculable significance for humankind:

We consider, however
—this is the most essential point of the whole calculation—[the energy]
E
to be composed of a very definite number
of equal parts and use thereto the constant of nature
h
= 6.55 × 10
^−27
erg-sec. This constant, multiplied by the frequency
ν
… gives us the energy element,
ε
.

Planck showed that, from this assumption and the then-controversial statistical theory of atoms, his new law of thermal radiation followed. But with this cryptic phrase natural science had crossed a philosophical Rubicon: ultimately the exquisitely sharp Newtonian photograph of the natural world would fall out of focus, becoming blurred and uncertain. The even flow of natural processes would give way to an atomic world of sudden jumps and collapses. Light itself would become grainy, belying its wave properties, so brilliantly wrung from the nineteenth-century triumphs of Maxwell and others. And all who look to science to elucidate the universe would have to get used to a worldview that sanctioned “
spooky action at a distance
,” the modern quantum view of reality.

Planck's insight was beyond brilliant; it was an act of genius. The new law he introduced will bear his name and will be used by scientists as long as there is technologically advanced human civilization. In fact, as far as we know, it may be in use right now in nonhuman civilizations.
³
The theory that arose from this insight, the quantum theory, is unquestionably the most important theoretical advance in physical science since Newton.

So by December 1900 Planck had changed everything in physics and chemistry. The only problem was he didn't realize it. Planck was still recovering from his near-death experience as a reputable theorist. He later described his arrival at the quantum hypothesis as “
an act of desperation
.” Now he breathed a deep sigh of relief and put the “energy element” out of his mind: “
I considered the [quantum hypothesis]
a purely formal assumption, and I did not give it much thought except for this: that I had obtained a positive result under any circumstances and at whatever cost.” And the entire physics community went along
with this denial, like a family with an unspoken agreement to never again discuss a traumatic event.

Although he didn't realize it, Planck had removed a foundation stone from the edifice of classical physics; it would take another twenty-five years for the entire structure to collapse. However, the immediate reaction was … nothing. For the next five years neither Planck nor any of the great physicists of the era took up the meaning and extension of Planck's ideas. Not the revered Hendrik Lorentz in Holland, nor the profound but impenetrable Ludwig Boltzmann in Vienna, nor any of Planck's close colleagues picked up the challenge. That was left to a twenty-five-year-old patent examiner and maverick theorist living in Bern, Switzerland. Like Planck, thermodynamics and statistical mechanics had been his first love as a physicist. In addition he had been fascinated from an early age by Maxwell's equations and EM radiation. Unlike Planck however,
he
had been rejected by academe and had no reputation to lose. He was on the verge of taking the leap that Planck and the other great physicists of the time had not even considered. He was about to give Planck's radiation law the most radical interpretation possible: that it implied the discontinuity of motion on the atomic scale. He would begin this uprising with a paper that he himself termed “revolutionary.” His name was Albert Einstein.

 

¹
Electromagnetic radiation is not the only way heat is transmitted over distances; quite commonly a hot body (e.g., a heating coil in your stove) directly heats the air, which, as it moves around (“convects”), comes in contact with other bodies and heats them up.

²
Moreover, the old terminology referring to the incorrect law, the “Planck-Wien law,” was quickly adjusted to simply the “Wien law,” erasing from the physics canon the evidence of Planck's original error.

³
Surprisingly, the staid Planck had some things to say about extraterrestrials, as we will see in
chapter 14
.

CHAPTER 2

THE IMPUDENT SWABIAN

We do not know the exact moment when Heinrich Weber began to despise Albert Einstein. It definitely was not at first sight. Professor Weber was the head of the Physics Department of the Federal Institute of Technology, an up-and-coming engineering school in Zurich, Switzerland, now known worldwide as ETH Zurich. In 1895, when Weber and Einstein first met, the “Poly” (as it was called by the locals) had the immense advantage for the young Einstein that it did not require a high school diploma for admission. This was particularly pertinent for Einstein because he had rather recently and without the consent of his parents “excused himself” from the final two years of his well-regarded German high school (the Luitpold Gymnasium in Munich) on the basis of a nebulous medical condition, “
neurasthenic exhaustion
.” In fact he had hated the school, and once his parents had left Munich for Italy for financial reasons he saw no reason to stick it out. In late December of 1894 the fifteen-year-old Einstein showed up on their doorstep in Milan and “
assured them most resolutely
” that he would self-school himself in order to qualify for admission to the Zurich Poly by the next fall.

Indeed Einstein was already an accomplished autodidact, having taught himself differential and integral calculus well ahead of the school curriculum; to qualify for the Poly he had taken the precaution of obtaining a letter of advanced mathematical achievement from his teacher in Munich. Armed with this certificate, he presented himself to Albin Herzog, principal of the Zurich Poly, in October of 1895, as a “
prodigy
” who should be allowed to take the entrance exams a full year and a half before he would attain the required minimum age. It
was at this time that he encountered Professor Weber, a reserved and dignified scientist, who, while not a physicist of historic stature, was a respected experimental researcher in thermodynamics.

On the entrance exams Einstein confirmed the judgment of his mathematics teacher, performing brilliantly on the math and physics portions of the test. However, he was neither fond of nor talented in subjects requiring a great deal of memorization, so he failed the general sections of the exam, which covered subjects such as literature, French, and politics. He thus failed to gain admission to the Poly. Yet his strong showing in math and physics so impressed Weber that he invited Einstein, against regulations, to attend his own lectures for second-year physics students. But there was still the minor matter of qualifying for admission, which could not be met by auditing lectures in the subjects where Einstein already excelled. So, at the suggestion of Herzog, Einstein enrolled in the cantonal high school in nearby Aarau for an additional year of formal schooling. He thrived there, finishing first in the final exams and gaining automatic admission to the Poly in October of 1896.

It was then that his intense relationship with Weber began. Weber was the primary physics instructor, and Einstein took fifteen courses from him, ten in the classroom and five in the lab. He did well in all of them. His very first physics course was with Weber, who immediately impressed him. “
Weber lectured on heat
… with great mastery. I am looking forward from one of his lectures to the next,” Einstein wrote in 1898 to his fellow student and future wife, Mileva Maric. Einstein had been fascinated with physics since he was a young boy, beginning with his experience of “wonder” at a compass that he received at age five, which revealed to him the existence of unseen forces. Initially at the Poly his youthful love of physics was nurtured, and he responded with a strong academic performance: at the end of his first two years he passed the intermediate diploma exam with an overall grade of 5.7 out of 6, placing him first in his class.

But a problem was emerging. Einstein was aware of the great advances in physical theory that had taken place in the previous twenty years, and specifically of the world-changing electromagnetic theory
of Maxwell and the bold statistical theory of gases due to Boltzmann. In vain he awaited the appearance of these exciting ideas in his classroom. Weber was a conservative scientist and had no intention of teaching these recent and highly mathematical developments in his lectures. A fellow student remarked: “
[Weber's] lectures were outstanding
but … [modern developments] were simply ignored. At the conclusion of one's studies one was acquainted with the history of physics, but not with its present or future.” In particular, “
Einstein's hopes of learning
something decisive about Maxwell's electromagnetic theory were not realized.” When, in his very last semester, Einstein heard a lecture from the mathematician Hermann Minkowski on modern formulations of Newton's laws he remarked to a classmate, “
this is the first lecture on mathematical
[theoretical] physics we have heard at the Poly.” This refusal to admit the existence of newer ideas in physics apparently revived in Einstein a long-standing characteristic of his personality, his disrespect for authority in the classroom.

In later life Einstein spoke many times about how regimented his early education had been, and how he had particularly disliked the German system, as exemplified by the Luitpold Gymnasium, which he had fled in 1894. But contemporaries of his, even those with the same Jewish background, did not recall this school as being oppressive. In fact there seems to have been something in Einstein's own manner that contributed to the conflicts he recalled; he had a knack for driving his teachers to distraction. At the gymnasium his frustrated Latin teacher, Joseph Degenhart, offered one of history's great erroneous predictions: that “
[Einstein] would never get anywhere
in life.” When Einstein maintained that he had committed no offense to elicit such an opinion, Degenhart replied, “your mere presence here undermines the class's respect for me.” After leaving the gymnasium and ending up at Aarau, despite his much greater affinity for this school, his tendency to be less than respectful to his teachers did not change. While on a field trip he was questioned by his geology teacher, Mühlberg, as to whether the strata they were observing ran upward or down; he replied, “
It is pretty much the same
to me which way they run, Professor.” An Aarau classmate recalled the impression made by the young
Einstein. “
A cold wind of skepticism
was blowing [that suited] the impudent Swabian…. Sure of himself, his grey felt hat pushed back from his thick black hair, he strode energetically up and down in the rapid, I might almost say crazy tempo of a restless spirit which carries a whole world in itself. Nothing escaped the sharp gaze of his large brown eyes. Whoever approached him came immediately under the spell of his superior personality. A sarcastic curl of his lip did not encourage Philistines to fraternize with him…. his witty mockery pitilessly lashed any conceit or pose.”