he called invariances—based on the combination of space and time into one four-dimensional fabric. Quantum mechanics, on the other hand, would be based on true underlying uncertainties in nature, events that could be described only in terms of probabilities.
On a visit to Berlin in 1920, Niels Bohr, who had become the Copenhagen-based ringleader of the quantum mechanics movement, met Einstein for the first time. Bohr arrived at Einstein’s apartment bearing Danish cheese and butter, and then he launched into a discussion of the role that chance and probability played in quantum mechanics. Einstein expressed his wariness of “abandoning continuity and causality.” Bohr was bolder about going into that misty realm. Abandoning strict causality, he countered to Einstein, was “the only way open” given the evidence.
Einstein admitted that he was impressed, but also worried, by Bohr’s breakthroughs on the structure of the atom and the randomness it implied for the quantum nature of radiation. “I could probably have arrived at something like this myself,” Einstein lamented, “but if all this is true then it means the end of physics.”40
Although Einstein found Bohr’s ideas disconcerting, he found the gangly and informal Dane personally endearing. “Not often in life has a human being caused me such joy by his mere presence as you did,” he wrote Bohr right after the visit, adding that he took pleasure in picturing “your cheerful boyish face.” He was equally effusive behind Bohr’s back.“Bohr was here, and I am just as keen on him as you are,” he wrote their mutual friend Ehrenfest in Leiden. “He is an extremely sensitive lad and moves around in this world as if in a trance.”41
Bohr, for his part, revered Einstein. When it was announced in 1922 that they had won sequential Nobel Prizes, Bohr wrote that his own joy had been heightened by the fact that Einstein had been recognized first for “the fundamental contribution that you made to the special field in which I am working.”42
On his journey home from delivering his acceptance speech in Sweden the following summer, Einstein stopped in Copenhagen to see Bohr, who met him at the train station to take him home by streetcar. On the ride, they got into a debate. “We took the streetcar and talked so animatedly that we went much too far,” Bohr recalled. “We got off and traveled back, but again rode too far.” Neither seemed to mind, for the conversation was so engrossing. “We rode to and fro,” according to Bohr, “and I can well imagine what the people thought about us.”43
More than just a friendship, their relationship became an intellectual entanglement that began with divergent views about quantum mechanics but then expanded into related issues of science, knowledge, and philosophy. “In all the history of human thought, there is no greater dialogue than that which took place over the years between Niels Bohr and Albert Einstein about the meaning of the quantum,” says the physicist John Wheeler, who studied under Bohr. The social philosopher C. P. Snow went further. “No more profound intellectual debate has ever been conducted,” he proclaimed.44
Their dispute went to the fundamental heart of the design of the cosmos: Was there an objective reality that existed whether or not we could ever observe it? Were there laws that restored strict causality to phenomena that seemed inherently random? Was everything in the universe predetermined?
For the rest of their lives, Bohr would sputter and fret at his repeated failures to convert Einstein to quantum mechanics.
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
