Einstein and the Quantum (5 page)

As early as March of 1899 Einstein wrote to Maric and told of showing her photograph to his mother and of the tense interchange that ensued (his mother's deep antipathy to Maric would plague the couple for many years). However, he ends the letter with an intriguing hint: “
My broodings about radiation
are starting to get on a somewhat firmer ground & I am curious whether something will come out of them.” By the summer of that year he had begun addressing her with the affectionate nickname “Dolly” (Doxerl). In one letter, after explaining
to her, complete with equations, why he believes the present electrodynamic theory cannot be correct, he ends with: “
If only you would be again
with me a little! We both understand each other's black souls so well & also drinking coffee & eating sausages, etc.” (Among Einstein's inventions at that time was the suggestive form of etcetera.) The summer of 1900 brought twin disappointments: Einstein's lack of success in landing an assistant's position, and Maric's failure to pass the final exams and receive her degree. If anything this seemed to bring them closer together, and in July Einstein, during a visit home, announced his intention to marry Mileva, eliciting a “scene” of anger and disapproval from his mother.

Einstein was unmoved by this display, but as often happened, he found solace in reading physics papers, in this case the works of Gustav Kirchoff, the first physicist to understand the importance of the thermal radiation law. Both of Einstein's parents continued the barrage of disapproval of Maric over the summer, but Einstein held firm: “
Mama and Papa are very phlegmatic
people and have less stubbornness in their whole body than I have in my little finger.” By the fall of 1900 it was clear that for the immediate future it would be Albert and Mileva against the world, both the world of bourgeois society and the world of the physics establishment. In October Einstein wrote his fiancée from Milan: “
You too don't like the philistine
life any longer, do you! He who tasted freedom cannot stand the chains any longer. How lucky I am to have found in you a creature who is my equal, who is as strong and independent as I am myself!”

It was not immediately obvious to Einstein how serious his plight was as he cheerily expected something to turn up any day. He even had the temerity to turn down an insurance job that his friend Ehrat had lined up for him, saying “
One must shun
such stultifying affairs.” Initially he clung to the naive hope that he could land a job with the mathematician Hurwitz, whose courses he had avoided rather brazenly. When this didn't work out, he wrote to a friend: “
Neither of us have gotten a job
and we support ourselves by private lessons, when we can pick up some, which is still very questionable. Is this not a journeyman's or even a gypsy's life? But I believe we will be happy in it nonetheless.”

CHAPTER 4

TWO PILLARS OF WISDOM

The man loved mysterious Nature
as a lover loves his distant beloved. In his day there did not exist the dull specialization that stares with self-conceit through horn-rimmed glasses and destroys poetry.

—ALBERT EINSTEIN, ON MICHAEL FARADAY

“
About Max Planck's studies
on radiation, misgivings of a fundamental nature have arisen in my mind, so that I am reading his article with mixed feelings.” So Einstein wrote to his Dolly from Milan in April of 1901, a scant four months after Planck's “act of desperation” in Berlin had saved his own reputation but failed to alert the physics community to the storm ahead. In the same letter Einstein ruefully admits, “
soon I will have honored
all physicists from the North Sea to the southern tip of Italy with my [job inquiry].” Emboldened by his first published article, which had appeared in the prestigious journal
Annalen Der Physik
, Einstein had sent a slew of postcards requesting an assistant's position to the well-known physicists and chemists of Europe. None of these missives bore fruit, and as far as we know few of them were even graced with a reply. Although Einstein was convinced that Weber was behind the rejections, Einstein's indifferent final academic record and his failure to receive the pro forma job offer from the Poly would likely have been enough.

Despite these disappointments he was scraping together a living through part-time jobs and private lessons and forging ahead with his independent thinking about the current state of theoretical physics. For much of this time he would be separated from his fiancée, but
writing to her frequently. In his very next letter to Maric he continues discussing Planck: “
Maybe his newest theory
is more general. I intend to have a go at it.” A little later in the letter he comments, “I have also somewhat changed my idea about the nature of the latent heat in solids, because my views on the nature of radiation have again sunk back into the sea of haziness. Perhaps the future will bring something more sensible.” His last words were prescient; his views on radiation would emerge from haziness to enlarge the Planck radiation theory in a revolutionary manner, while the latent (or specific) heat of solids, a seemingly mundane topic, would provide Planck's theory with the radical physical interpretation that it currently lacked. But before this could occur, Einstein needed to plumb deeply into thermodynamics, Planck's specialty, and the newer atomistic discipline of statistical mechanics, which attempted to explain and extend the laws of thermodynamics. His main scientific motivation at the time was not to unravel the puzzles of relative motion. Einstein's famous insight, that resolving these puzzles would require a major reshaping of our conceptions of time and space, would not occur to him for four more years. Rather, his primary scientific focus from his student days was “
to find facts which would attest
to the existence of atoms of a definite size.” Proving the existence of atoms and understanding the physical laws governing their behavior was the original quest of the Valiant Swabian.

The atomic world was the frontier of physics at the beginning of the twentieth century. The disciplines of what is now called classical physics had all developed without a need to delve too deeply into the question of the nature of the microscopic constituents of matter. That situation had now changed. If physics was going to progress, it would be essential to understand the fundamental origin of electromagnetic phenomena, of heat flow, of the properties of solids (e.g., electrical conductivity, thermal conduction and insulation, transparency, hardness), and the physical laws leading to chemical reactions. The answers to these questions would only be found by understanding the makeup of the atom and the physical interactions between atoms and molecules.

Modern physics had begun with the work of Sir Isaac Newton in the second half of the seventeenth century. He introduced a new
paradigm for the motion of objects (masses) in space: first by the bold assertion that the natural state of motion of a solid body is to move at a constant speed in a straight line (Newton's First Law), and then by the statement that the state of motion changes in a predictable manner when “forces” are acting on the body (Newton's Second Law). If one knew the force and mass of the body, the Second Law would determine the instantaneous acceleration of the mass,
a
, via the relation
F
/
m
=
a
. What it meant to speak of the
instantaneous
rate of change of any quantity wasn't (and isn't) obvious, but Newton cleared this up by means of a mathematical innovation, the invention of calculus. From this point forward, mechanics came to mean the study of the motion of masses under the influence of forces described by elaborations of Newton's Second Law, which could now be written as a “differential equation” using calculus.

For this law to be useful, scientists would need to have a mathematical representation of the forces in nature, the
F
on the left-hand side of
F
=
ma
. The forces of nature cannot be deduced; they can only be hypothesized (okay, guessed) and tested for whether their consequences make sense and agree with experimental measurements. No amount of mathematical legerdemain can get around that. Newton's Second Law was an empty tautology unless one had an independent mathematical expression for the forces that mattered in a given situation.

Newton gained eternal fame by divining the big one, the one we all know from infancy: the force of gravity. His universal law of gravitation stated that two masses are attracted to each other along the line between their centers, and the strength of that attraction is proportional to the product of their masses and inversely proportional to the square of the distance between them. Of course this attraction is very weak between normal-size masses like two people, but between the earth and a person or the earth and the sun it is a big deal. From this law of gravitation and his Second Law, Newton was able to calculate all kinds of solid-body motion: the orbits of the planets in the solar system, the relation between the moon and tides, the trajectories of cannonballs. Thus Newton had published the first major section of the
“book of Nature,” which was, Galileo famously declared, “written in the language of mathematics.”

Along with the stunning mathematical insights of Newton and their vast practical applications came an ontology, a view of what the fundamental categories of nature were, and how events in the world were related. As Einstein put it in his autobiographical notes, “
In the beginning—if such a thing
existed—God created Newton's laws of motion together with the necessary masses and forces. That is all. Anything further is the result of suitable mathematical methods through deduction. What the nineteenth century achieved on this basis … must arouse the admiration of any receptive man … we must not therefore be surprised that … all the physicists of the last century saw in classical mechanics a firm and empirical basis for all … of natural science.”

At the core of the Newtonian view of nature was the concept of rigid determinism, majestically expressed by the Marquis de Laplace:

We may regard the present
state of the universe as the effect of its past and the cause of its future. An intellect which at any given moment knew all of the forces that animate nature and the mutual positions of the beings that compose it, if this intellect were vast enough to submit these data to analysis, could condense into a single formula the movements of the greatest bodies of the universe and that of the lightest atom; for such an intellect nothing could be uncertain and the future just like the past would be present before its eyes.

This Marquis Pierre Simon de Laplace was one of the great masters of classical mechanics in the nineteenth century and became known as the “French Newton.” He was willing to literally put his neck on the line for his natural philosophy. When he presented his five-volume study of celestial mechanics to Napoleon, he was greeted with the intimidating question: “Monsieur Laplace, they tell me you have written this large book on the system of the universe and have never even mentioned its Creator.” Laplace, normally quite politic in his dealings with influential men, in this case drew himself up and replied bluntly, “I have no need of that hypothesis.”

While the relation between mass and the force of gravity was the only fundamental law discovered by Newton, he and other physicists knew that there must be other forces with associated laws, for example, the pressure exerted by a gas (pressure is force per unit area), which surely must have a microscopic origin. Near the end of the eighteenth century Charles Augustin de Coulomb, using a sensitive instrument known as the torsion balance, definitively measured another type of force, also of invisible origin: the electrical force. Coulomb and others determined that, in addition to mass, there is another important property of matter, electrical charge, and that two charged bodies exert forces on each other in a manner similar to the way gravity works in Newton's Second Law, that is, proportional to the product of their charges and inversely proportional to the square of the distance between them. However, there is a major difference between this electrostatic force and gravity; charges come in two types, positive and negative. Opposite charges attract each other, but like charges repel. Matter is usually electrically neutral (that is, made up of an equal number of positive and negative charges) or very nearly neutral, so two chunks of matter don't usually exert much long-range electrical force on each another. Therefore, despite the fact that the electrical force is much stronger than the gravitational force (when appropriately compared), it doesn't have the same kind of macroscopic effects as gravity.

Early in the nineteenth century it became clear that the story was even more complicated. Moving charges (i.e., electrical currents) create yet another force, known to the ancients but not understood as related to electricity: magnetism. Primarily through the work of the English experimental physicist Michael Faraday, it became clear that electricity and magnetism were intimately related because, for example, magnetic fields could be used to create electrical currents. Exploiting this principle, discovered in 1831 and now known as Faraday's law, Faraday was able to build the first electrical generator (he had earlier made the first functioning electric motor). Faraday's discovery would lead to an expansion of the classical ontology of physics, because it implied that electrical charges and currents gave rise to unseen electric and magnetic
fields
, which permeated space and were not associated
with matter at all but rather represented a
potential
to exert a force on charged matter. These were the “unseen forces” that moved the compass needle, which had fascinated Einstein as a child. Besides masses, forces, and charges, there were now fields as well.

Faraday had risen from the status of a lowly bookbinder's apprentice to become Fullerian Professor of Chemistry at the Royal Institution (during his life he rejected a knighthood and twice declined the presidency of the Royal Society). When asked by the four-time prime minister William Gladstone the value of electricity, he is said to have quipped,
¹
“One day sir, you may tax it.” He had little formal mathematical education and showed by experiment that his ideas were correct but did not formulate them into a rigorous theory.