Einstein (71 page)

In other words, Einstein had said that light should be regarded not only as a wave but also as a particle. Likewise, according to de Broglie, a particle such as an electron could also be regarded as a wave. “I had a sudden inspiration,” de Broglie later recalled. “Einstein’s wave-particle dualism was an absolutely general phenomenon extending to all of
physical nature, and that being the case the motion of all particles—photons, electrons, protons or any other—must be associated with the propagation of a wave.”
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Using Einstein’s law of the photoelectric affect, de Broglie showed that the wavelength associated with an electron (or any particle) would be related to Planck’s constant divided by the particle’s momentum. It turns out to be an incredibly tiny wavelength, which means that it’s usually relevant only to particles in the subatomic realm, not to such things as pebbles or planets or baseballs.
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In Bohr’s model of the atom, electrons could change their orbits (or, more precisely, their stable standing wave patterns) only by certain quantum leaps. De Broglie’s thesis helped explain this by conceiving of electrons not just as particles but also as waves. Those waves are strung out over the circular path around the nucleus. This works only if the circle accommodates a whole number—such as 2 or 3 or 4—of the particle’s wavelengths; it won’t neatly fit in the prescribed circle if there’s a fraction of a wavelength left over.

De Broglie made three typed copies of his thesis and sent one to his adviser, Paul Langevin, who was Einstein’s friend (and Madame Curie’s). Langevin, somewhat baffled, asked for another copy to send along to Einstein, who praised the work effusively. It had, Einstein said, “lifted a corner of the great veil.” As de Broglie proudly noted, “This made Langevin accept my work.”
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Einstein made his own contribution when he received in June of that year a paper in English from a young physicist from India named Satyendra Nath Bose. It derived Planck’s blackbody radiation law by treating radiation as if it were a cloud of gas and then applying a statistical method of analyzing it. But there was a twist: Bose said that any two photons that had the same energy state were absolutely indistinguishable, in theory as well as fact, and should not be treated separately in the statistical calculations.

Bose’s creative use of statistical analysis was reminiscent of Einstein’s youthful enthusiasm for that approach. He not only got Bose’s paper published, he also extended it with three papers of his own. In them, he applied Bose’s counting method, later called “Bose-Einstein statistics,” to actual gas molecules, thus becoming the primary inventor of quantum-statistical mechanics.

Bose’s paper dealt with photons, which have no mass. Einstein extended the idea by treating quantum particles
with mass
as being indistinguishable from one another for statistical purposes in certain cases. “The quanta or molecules are not treated as structures statistically independent of one another,” he wrote.
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The key insight, which Einstein extracted from Bose’s initial paper, has to do with how you calculate the probabilities for each possible state of multiple quantum particles. To use an analogy suggested by the Yale physicist Douglas Stone, imagine how this calculation is done for dice. In calculating the odds that the roll of two dice (A and B) will produce a lucky 7, we treat the possibility that A comes up 4 and B comes up 3 as one outcome, and we treat the possibility that A comes up 3 and B comes up 4 as a different outcome—thus counting each of these combinations as different ways to produce a 7. Einstein realized that the new way of calculating the odds of quantum states involved treating these not as two different possibilities, but only as one. A 4-3 combination was indistinguishable from a 3-4 combination; likewise, a 5-2 combination was indistinguishable from a 2-5.

That cuts in half the number of ways two dice can roll a 7. But it does not affect the number of ways they could turn up a 2 or a 12 (using either counting method, there is only one way to roll each of these totals), and it only reduces from five to three the number of ways the two dice could total 6. A few minutes of jotting down possible outcomes shows how this system changes the overall odds of rolling any particular number. The changes wrought by this new calculating method are even greater if we are applying it to dozens of dice. And if we are dealing with billions of particles, the change in probabilities becomes huge.

When he applied this approach to a gas of quantum particles, Einstein discovered an amazing property: unlike a gas of classical particles, which will remain a gas unless the particles attract one another, a gas of
quantum particles can condense into some kind of liquid even without a force of attraction between them.

This phenomenon, now called Bose-Einstein condensation,
*
was a brilliant and important discovery in quantum mechanics, and Einstein deserves most of the credit for it. Bose had not quite realized that the statistical mathematics he used represented a fundamentally new approach. As with the case of Planck’s constant, Einstein recognized the physical reality, and the significance, of a contrivance that someone else had devised.
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Einstein’s method had the effect of treating particles as if they had wavelike traits, as both he and de Broglie had suggested. Einstein even predicted that if you did Thomas Young’s old double-slit experiment (showing that light behaved like a wave by shining a beam through two slits and noting the interference pattern) by using a beam of gas molecules, they would interfere with one another as if they were waves. “A beam of gas molecules which passes through an aperture,” he wrote, “must undergo a diffraction analogous to that of a light ray.”
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Amazingly, experiments soon showed that to be true. Despite his discomfort with the direction quantum theory was heading, Einstein was still helping, at least for the time being, to push it ahead. “Einstein is thereby clearly involved in the foundation of wave mechanics,” his friend Max Born later said, “and no alibi can disprove it.”
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Einstein admitted that he found this “mutual influence” of particles to be “quite mysterious,” for they seemed as if they should behave independently. “The quanta or molecules are not treated as independent of one another,” he wrote another physicist who expressed bafflement. In a postscript he admitted that it all worked well mathematically, but “the physical nature remains veiled.”
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On the surface, this assumption that two particles could be treated as indistinguishable violated a principle that Einstein would nevertheless try to cling to in the future: the principle of separability, which as serts that particles with different locations in space have separate, independent realities. One aim of general relativity’s theory of gravity had been to avoid any “spooky action at a distance,” as Einstein famously called it later, in which something happening to one body could instantly affect another distant body.

Once again, Einstein was at the forefront of discovering an aspect of quantum theory that would cause him discomfort in the future. And once again, younger colleagues would embrace his ideas more readily than he would—just as he had once embraced the implications of the ideas of Planck, Poincaré, and Lorentz more readily than they had.
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An additional step was taken by another unlikely player, Erwin Schrödinger, an Austrian theoretical physicist who despaired of discovering anything significant and thus decided to concentrate on being a philosopher instead. But the world apparently already had enough Austrian philosophers, and he couldn’t find work in that field. So he stuck with physics and, inspired by Einstein’s praise of de Broglie, came up with a theory called “wave mechanics.” It led to a set of equations that governed de Broglie’s wavelike behavior of electrons, which Schrödinger (giving half credit where he thought it was due) called “Einstein–de Broglie waves.”
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Einstein expressed enthusiasm at first, but he soon became troubled by some of the ramifications of Schrödinger’s waves, most notably that over time they can spread over an enormous area. An electron could not, in reality, be waving thus, Einstein thought. So what, in the real world, did the wave equation really represent?

The person who helped answer that question was Max Born, Einstein’s close friend and (along with his wife, Hedwig) frequent correspondent, who was then teaching at Göttingen. Born proposed that the wave did not describe the behavior of the particle. Instead, he said that it described the
probability
of its location at any moment.
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It was an approach that revealed quantum mechanics as being, even more than previously thought, fundamentally based on chance rather than causal certainties, and it made Einstein even more squeamish.
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Meanwhile, another approach to quantum mechanics had been developed in the summer of 1925 by a bright-faced 23-year-old hiking enthusiast, Werner Heisenberg, who was a student of Niels Bohr in
Copenhagen and then of Max Born in Göttingen. As Einstein had done in his more radical youth, Heisenberg started by embracing Ernst Mach’s dictum that theories should avoid any concepts that cannot be observed, measured, or verified. For Heisenberg this meant avoiding the concept of electron orbits, which could not be observed.

He relied instead on a mathematical approach that would account for something that
could
be observed: the wavelengths of the spectral lines of the radiation from these electrons as they lost energy. The result was so complex that Heisenberg gave his paper to Born and left on a camping trip with fellow members of his youth group, hoping that his mentor could figure it out. Born did. The math involved what are known as matrices, and Born sorted it all out and got the paper published.
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In collaboration with Born and others in Göttingen, Heisenberg went on to perfect a matrix mechanics that was later shown to be equivalent to Schrödinger’s wave mechanics.

Einstein politely wrote Born’s wife, Hedwig, “The Heisenberg-Born concepts leave us breathless.” Those carefully couched words can be read in a variety of ways. Writing to Ehrenfest in Leiden, Einstein was more blunt. “Heisenberg has laid a big quantum egg,” he wrote. “In Göttingen they believe in it. I don’t.”
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Heisenberg’s more famous and disruptive contribution came two years later, in 1927. It is, to the general public, one of the best known and most baffling aspects of quantum physics: the uncertainty principle.

It is impossible to know, Heisenberg declared, the precise
position
of a particle, such as a moving electron, and its precise
momentum
(its velocity times its mass) at the same instant. The more precisely the position of the particle is measured, the less precisely it is possible to measure its momentum. And the formula that describes the trade-off involves (no surprise) Planck’s constant.

The very act of observing something—of allowing photons or electrons or any other particles or waves of energy to strike the object—affects the observation. But Heisenberg’s theory went beyond that. An electron does not have a definite position or path until we observe it. This is a feature of our universe, he said, not merely some defect in our observing or measuring abilities.

The uncertainty principle, so simple and yet so startling, was a stake in the heart of classical physics. It asserts that there is no objective reality—not even an objective position of a particle—outside of our observations. In addition, Heisenberg’s principle and other aspects of quantum mechanics undermine the notion that the universe obeys strict causal laws. Chance, indeterminacy, and probability took the place of certainty. When Einstein wrote him a note objecting to these features, Heisenberg replied bluntly, “I believe that indeterminism, that is, the nonvalidity of rigorous causality, is necessary.”
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When Heisenberg came to give a lecture in Berlin in 1926, he met Einstein for the first time. Einstein invited him over to his house one evening, and there they engaged in a friendly argument. It was the mirror of the type of argument Einstein might have had in 1905 with conservatives who resisted his dismissal of the ether.

“We cannot observe electron orbits inside the atom,” Heisenberg said.“A good theory must be based on directly observable magnitudes.”

“But you don’t seriously believe,” Einstein protested, “that none but observable magnitudes must go into a physical theory?”

“Isn’t that precisely what you have done with relativity?” Heisenberg asked with some surprise.

“Possibly I did use this kind of reasoning,” Einstein admitted, “but it is nonsense all the same.”
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In other words, Einstein’s approach had evolved.

Einstein had a similar conversation with his friend in Prague, Philipp Frank. “A new fashion has arisen in physics,” Einstein complained, which declares that certain things cannot be observed and therefore should not be ascribed reality.

“But the fashion you speak of,” Frank protested, “was invented by you in 1905!”

Replied Einstein: “A good joke should not be repeated too often.”
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The theoretical advances that occurred in the mid-1920s were shaped by Niels Bohr and his colleagues, including Heisenberg, into what became known as the Copenhagen interpretation of quantum mechanics. A property of an object can be discussed only in the context of how that property is observed or measured, and these observations
are not simply aspects of a single picture but are complementary to one another.

In other words, there is no single underlying reality that is independent of our observations. “It is wrong to think that the task of physics is to find out how nature
is,
” Bohr declared. “Physics concerns what we can
say
about nature.”
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This inability to know a so-called “underlying reality” meant that there was no strict determinism in the classical sense. “When one wishes to calculate ‘the future’ from ‘the present’ one can only get statistical results,” Heisenberg said, “since one can never discover every detail of the present.”
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