einstein

Unlike the development of relativity theory, which was largely the product of one man working in near solitary splendor, the development of
quantum mechanics from 1924 to 1927 came from a burst of activity by a clamorous congregation of young Turks who worked both in parallel and
in collaboration. They built on the foundations laid by Planck and Einstein, who continued to resist the radical ramifications of the quanta, and on the
breakthroughs by Bohr, who served as a mentor for the new generation.
Louis de Broglie, who carried the title of prince by virtue of being related to the deposed French royal family, studied history in hopes of being a
civil servant. But after college, he became fascinated by physics. His doctoral dissertation in 1924 helped transform the field. If a wave can behave
like a particle, he asked, shouldn’t a particle also behave like a wave?
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.” 46
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.*
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.” 47
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. 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, Poincaré, and Lorentz more readily than they had. 53