Einstein (26 page)

A new concept appeared in physics, the most important invention since Newton’s time: the field. It needed great scientific imagination to realize that it is not the charges nor the particles but the field in the space between the charges and the particles that is essential for the description of physical phenomena. The field concept proved successful when it led to the formulation of Maxwell’s equations describing the structure of the electromagnetic field.
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At first, the electromagnetic field theory developed by Maxwell seemed compatible with the mechanics of Newton. For example, Maxwell believed that electromagnetic waves, which include visible light, could be explained by classical mechanics—if we assume that the universe is suffused with some unseen, gossamer “light-bearing ether” that serves as the physical substance that undulates and oscillates to propagate the electromagnetic waves, comparable to the role water plays for ocean waves and air plays for sound waves.

By the end of the nineteenth century, however, fissures had begun to develop in the foundations of classical physics. One problem was that scientists, as hard as they tried, could not find any evidence of our motion through this supposed light-propagating ether. The study of radiation—how light and other electromagnetic waves emanate from physical bodies—exposed another problem: strange things were happening at the borderline where Newtonian theories, which described the mechanics of discrete particles, interacted with field theory, which described all electromagnetic phenomena.

Up until then, Einstein had published five little-noted papers. They had earned him neither a doctorate nor a teaching job, even at a high school. Had he given up theoretical physics at that point, the scientific
community would not have noticed, and he might have moved up the ladder to become the head of the Swiss Patent Office, a job in which he would likely have been very good indeed.

There was no sign that he was about to unleash an
annus mirabilis
the like of which science had not seen since 1666, when Isaac Newton, holed up at his mother’s home in rural Woolsthorpe to escape the plague that was devastating Cambridge, developed calculus, an analysis of the light spectrum, and the laws of gravity.

But physics was poised to be upended again, and Einstein was poised to be the one to do it. He had the brashness needed to scrub away the layers of conventional wisdom that were obscuring the cracks in the foundation of physics, and his visual imagination allowed him to make conceptual leaps that eluded more traditional thinkers.

The breakthroughs that he wrought during a four-month frenzy from March to June 1905 were heralded in what would become one of the most famous personal letters in the history of science. Conrad Habicht, his fellow philosophical frolicker in the Olympia Academy, had just moved away from Bern, which, happily for historians, gave a reason for Einstein to write to him in late May.

Dear Habicht,

Such a solemn air of silence has descended between us that I almost feel as if I am committing a sacrilege when I break it now with some inconsequential babble . . .

So, what are you up to, you frozen whale, you smoked, dried, canned piece of soul ...? Why have you still not sent me your dissertation? Don’t you know that I am one of the 1½ fellows who would read it with interest and pleasure, you wretched man? I promise you four papers in return. The first deals with radiation and the energy properties of light and is very revolutionary, as you will see if you send me your work first. The second paper is a determination of the true sizes of atoms ... The third proves that bodies on the order of magnitude 1/1000 mm, suspended in liquids, must already perform an observable random motion that is produced by thermal motion. Such movement of suspended bodies has actually been observed by physiologists who call it Brownian molecular motion. The fourth paper is only a rough draft at this point, and is an electrodynamics of moving bodies which employs a modification of the theory of space and time.
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As Einstein noted to Habicht, it was the first of these 1905 papers, not the famous final one expounding a theory of relativity, that deserved the designation “revolutionary.” Indeed, it may contain the most revolutionary development in the history of physics. Its suggestion that light comes not just in waves but in tiny packets—quanta of light that were later dubbed “photons”—spirits us into strange scientific mists that are far murkier, indeed more spooky, than even the weirdest aspects of the theory of relativity.

Einstein recognized this in the slightly odd title he gave to the paper, which he submitted on March 17, 1905, to the
Annalen der Physik:
“On a Heuristic Point of View Concerning the Production and Transformation of Light.”
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Heuristic? It means a hypothesis that serves as a guide and gives direction in solving a problem but is not considered proven. From this first sentence he ever published about quantum theory until his last such sentence, which came in a paper exactly fifty years later, just before he died, Einstein regarded the concept of the quanta and all of its unsettling implications as heuristic at best: provisional and incomplete and not fully compatible with his own intimations of underlying reality.

At the heart of Einstein’s paper were questions that were bedeviling physics at the turn of the century, and in fact have done so from the time of the ancient Greeks until today: Is the universe made up of particles, such as atoms and electrons? Or is it an unbroken continuum, as a gravitational or electromagnetic field seems to be? And if both methods of describing things are valid at times, what happens when they intersect?

Since the 1860s, scientists had been exploring just such a point of intersection by analyzing what was called “blackbody radiation.” As anyone who has played with a kiln or a gas burner knows, the glow from a material such as iron changes color as it heats up. First it appears to radiate mainly red light; as it gets hotter, it glows more orange, and then white and then blue. To study this radiation, Gustav Kirchhoff and others devised a closed metal container with a tiny hole to let a little
light escape. Then they drew a graph of the intensity of each wavelength when the device reached equilibrium at a certain temperature. No matter what the material or shape of the container’s walls, the results were the same; the shape of the graphs depended only on the temperature.

There was, alas, a problem. No one could fully account for the basis of the mathematical formula that would produce the hill-like shape of these graphs.

When Kirchhoff died, his professorship at the University of Berlin was given to Max Planck. Born in 1858 into an ancient German family of great scholars, theologians, and lawyers, Planck was many things that Einstein was not: with his pince-nez glasses and meticulous dress, he was very proudly German, somewhat shy, steely in his resolve, conservative by instinct, and formal in his manner. “It is difficult to imagine two men of more different attitudes,” their mutual friend Max Born later said. “Einstein a citizen of the whole world, little attached to the people around him, independent of the emotional background of the society in which he lived—Planck deeply rooted in the traditions of his family and nation, an ardent patriot, proud of the greatness of German history and consciously Prussian in his attitude to the state.”
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His conservatism made Planck skeptical about the atom, and of particle (rather than wave and continuous field) theories in general. As he wrote in 1882, “Despite the great success that the atomic theory has so far enjoyed, ultimately it will have to be abandoned in favor of the assumption of continuous matter.” In one of our planet’s little ironies, Planck and Einstein would share the fate of laying the groundwork for quantum mechanics, and then both would flinch when it became clear that it undermined the concepts of strict causality and certainty they both worshipped.
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In 1900, Planck came up with an equation, partly using what he called “a fortuitous guess,” that described the curve of radiation wavelengths at each temperature. In doing so he accepted that Boltzmann’s statistical methods, which he had resisted, were correct after all. But the equation had an odd feature: it required the use of a constant, which was an unexplained tiny quantity (approximately 6.62607 x
10
^–34
joule-seconds), that needed to be included for it to come out right. It was soon dubbed Planck’s constant,
h,
and is now known as one of the fundamental constants of nature.

At first Planck had no idea what, if any, physical meaning this mathematical constant had. But then he came up with a theory that, he thought, applied not to the nature of light itself but to the action that occurred when the light was absorbed or emitted by a piece of matter. He posited that the surface of anything that was radiating heat and light—such as the walls in a blackbody device—contained “vibrating molecules” or “harmonic oscillators,” like little vibrating springs.
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These harmonic oscillators could absorb or emit energy only in the form of discrete packets or bundles. These packets or bundles of energy came only in fixed amounts, determined by Planck’s constant, rather than being divisible or having a continuous range of values.

Planck considered his constant a mere calculational contrivance that explained the process of emitting or absorbing light but did not apply to the fundamental nature of light itself. Nevertheless, the declaration he made to the Berlin Physical Society in December 1900 was momentous: “We therefore regard—and this is the most essential point of the entire calculation—energy to be composed of a very definite number of equal finite packages.”
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Einstein quickly realized that quantum theory could undermine classical physics. “All of this was quite clear to me shortly after the appearance of Planck’s fundamental work,” he wrote later. “All of my attempts to adapt the theoretical foundation of physics to this knowledge failed completely. It was as if the ground had been pulled out from under us, with no firm foundation to be seen anywhere.”
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In addition to the problem of explaining what Planck’s constant was really all about, there was another curiosity about radiation that needed to be explained. It was called the photoelectric effect, and it occurs when light shining on a metal surface causes electrons to be knocked loose and emitted. In the letter he wrote to Mari
right after he learned of her pregnancy in May 1901, Einstein enthused over a “beautiful piece” by Philipp Lenard that explored this topic.

Lenard’s experiments found something unexpected. When he increased the
frequency
of the light—moving from infrared heat and red
light up in frequency to violet and ultraviolet—the emitted electrons sped out with much more energy. Then, he increased the
intensity
of the light by using a carbon arc light that could be made brighter by a factor of 1,000. The brighter, more intense light had a lot more energy, so it seemed logical that the electrons emitted would have more energy and speed away faster. But that did not occur. More intense light produced more electrons, but the energy of each remained the same. This was something that the wave theory of light did not explain.

Einstein had been pondering the work of Planck and Lenard for four years. In his final paper of 1904, “On the General Molecular Theory of Heat,” he discussed how the average energy of a system of molecules fluctuates. He then applied this to a volume filled with radiation, and found that experimental results were comparable. His concluding phrase was, “I believe that this agreement must not be ascribed to chance.”
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As he wrote to his friend Conrad Habicht just after finishing that 1904 paper, “I have now found in a most simple way the relation between the size of elementary quanta of matter and the wavelengths of radiation.” He was thus primed, so it seems, to form a theory that the radiation field was made up of quanta.
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In his 1905 light quanta paper, published a year later, he did just that. He took the mathematical quirk that Planck had discovered, interpreted it literally, related it to Lenard’s photoelectric results, and analyzed light as if it
really was
made up of pointlike particles—light quanta, he called them—rather than being a continuous wave.

Einstein began his paper by describing the great distinction between theories based on particles (such as the kinetic theory of gases) and theories that involve continuous functions (such as the electromagnetic fields of the wave theory of light). “There exists a profound formal difference between the theories that physicists have formed about gases and other ponderable bodies, and Maxwell’s theory of electromagnetic processes in so-called empty space,” he noted. “While we consider the state of a body to be completely determined by the positions and velocities of a very large, yet finite, number of atoms and electrons, we make use of continuous spatial functions to describe the electromagnetic state of a given volume.”
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