Einstein: His Life and Universe

wrote.⁴⁸

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.⁴⁹

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.”⁵⁰

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.”⁵¹

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.”⁵²

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, Poincare, and Lorentz more readily than they had.⁵³

An additional step was taken by another unlikely player, Erwin Schrodinger, 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 Schrodinger (giving half credit where he thought it was due) called “Einstein–de Broglie waves.”⁵⁴

Einstein expressed enthusiasm at first, but he soon became troubled by some of the ramifications of Schrodinger’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 Gottingen. 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.⁵⁵ 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.⁵⁶

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 Gottingen. 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.⁵⁷ In collaboration with Born and others in Gottingen, Heisenberg went on to perfect a matrix mechanics that was later shown to be equivalent to Schrodinger’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 Gottingen they believe in it. I don’t.”⁵⁸

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.