Stepping down from the train into Berlin’s Lehrte Station, Einstein was back in catastrophe’s homeland. Sweden had been confident, Denmark assured, but agonized Germany was walled off from the world of postwar normalcy and wanted someone to blame. Its money had become worse than worthless. Any counterfeiter who transformed a blank sheet of paper into a million German marks would have been reducing the paper’s value. Once Einstein would have needed a separate valise just to carry the money to pay the porters who carried his bags, but Germany had responded to the hyperinflation by printing bills of enormous denominations, so the famous scenes of Germans carting wheelbarrow loads of money just to do their grocery shopping were no longer necessary. Indeed, the train station still looked clean and prosperous. That summer Hemingway reported from Germany that tourists, even those who traveled extensively, saw no suffering. “There are no beggars. No horrible examples on view. No visible famine sufferers nor hungry children that besiege the railway stations.” So Einstein was able to make his way home, without having to step over pitiable neighbors.
“The tourist leaves Germany wondering what all this starving business is about,” Hemingway added, “The country looks prosperous. On the contrary in Naples he has seen crowds of ragged beggars, sore-
eyed children, a hungry-looking horde. Tourists see the professional beggars, but they do not see the amateur starvers. For every ten professional beggars in Italy there are a hundred amateur starvers in Germany. An amateur starver does not starve in public. On the contrary no one knows the amateur is starving until they find him. They usually find him in bed.”
But the wall between Germany’s ruin and the rest of the world’s indifference was not quite an iron curtain. The money rot had begun to spread. In the capitals of the victorious powers, economics ministers were alarmed. The value of the French franc was sinking and the British pound had started to wobble.—Good! was the normal, suffering Berliner’s reaction. Let them find out what we have been suffering.—Good! thought the more conspiratorially minded. Now they will taste what they have done to us.—Good! cursed the bitterest cynics. Now that it is threatening them, they will put an end to it.
Who were them and they? The Jews took some of the blame, but the French probably took more. The war had been over for almost five years, but neither the French nor the Belgians seemed to have lost any of their fury or instinct for revenge. They had sent troops deep into Germany to seize and hold the Rhine Valley and were agitating to create a separate Rhine republic, splintering Germany into smaller units of despair. “Germany will wait in vain for us to vacillate even a moment,” France’s prime minister declared during the dedication of a war memorial, “France will walk this road to its end.” Unable to fight back, Germans quarreled among themselves about how to explain their continuing agony. God’s punishment. An allied conspiracy. Jewish thievery. Socialist bungling. Capitalist greed.
Most explanations for the catastrophe required some kind of leap. On the one side towered the unprecedented, unimaginable destruction of money and everything money supports. On the other sat the fully precedented, frequently imagined things that one fears. The money catastrophe served as a kind of hieroglyph in which readers saw the name of their own personal dread, and everybody had one. Einstein tended to believe more in humanity’s general folly than in conspiracies and he blamed the chaos on Germany’s soul rather than on foreigners or internal plotting. “Germany had the misfortune of
becoming poisoned,” he wrote in a note to himself, “first because of plenty, and then because of want.”
Einstein was one of the very few in Germany who had crossed the line, gone into France, examined the remains of the western front, and returned, deeply shaken, to Berlin. That visit, a year before his journey to Scandinavia, had shown him just how high the wall between Germany and victorious Europe still stood. Einstein had been cheered in America and Britain, but his reception in France was mixed. France’s most distinguished physicists welcomed him, but he decided against speaking at the French Academy because some of its members threatened a walkout if a German tried to speak before them. The Society of French Physicists also snubbed him, but Madame Curie showed her support by attending his lecture at the College de France and the prime minister, Paul Painlevé, who had also been a professor of mathematics, ushered at the door.
A French physicist, Henri Bouasse, an expert on acoustics and hydrodynamics, announced that “the French spirit, with its desire for Latin lucidity, will never understand the theory of relativity.” Remarkably, Bouasse did not think he was slandering France, “It is a product of the Teutonic tendency toward mystical speculation.”
But the other side was just as visible. On the morning he left France, Einstein got into a car with three distinguished Frenchmen—Maurice Solovine, Paul Langevin, and Charles Nordmann. Solovine was a friend from the patent-office days in Switzerland, a mathematician and Einstein’s French translator. Langevin was a leading physicist and expert on magnetism. Einstein later said that Langevin would have surely discovered special relativity for himself, “had that not been done elsewhere.” Nordmann’s title was astronomer of the Paris Observatory. He had written a wonderful little book about relativity. All three citizens had accomplished what Bouasse proclaimed impossible for Frenchmen. They understood relativity.
The countryside they passed through between Paris and the German border had been murdered. It was not just that the ground had been torn open by artillery shells, or that the houses were blasted apart, or that chunks of human bone seeded the fields. Even the trees had been gassed to death. Their roots still propped them up, but the
branches had been barren for years. In Reims, the heart of Champagne country, they stopped for lunch in a restaurant where two high ranking French officers were dining. This area had been the front itself, with French forces entrenched in and around Reims, while Germans held the high ground. The region had endured a steady pummeling over the four years of war, with some of their heaviest dueling going on while Einstein was in his creative frenzy, solving general relativity. The Reims cathedral, one of the symbols of traditional France, where many kings had been crowned, was now a ruin. The city’s homes were as devastated as the dwelling places of the ancient Trojans.
In the restaurant, the officers recognized Einstein at once and sent glances his way. None in Einstein’s party could be sure what would happen. The world’s most famous German was seated among supposedly enemy veterans and surrounded by devastated lands and towns. But they ate without disruption. Einstein’s trio of escorts were puzzled to learn their guest was such a teetotaler that even in Reims he refused to down a glass of Champagne. “I do not need wine,” he explained, “because my brain is acquainted with intellectual drunkenness.” They stood to leave the officers and their woman companion rose, too, and then bowed toward the celebrated physicist-pacifist. So even among veterans there could be respect for Einstein as a man and as a champion of reason.
But the wall between the two societies was still very strong. After leaving the restaurant, Einstein’s party continued eastward, crossing the ground that had been the no man’s land between trench lines. Even with the machine guns and artillery removed, those no-man’s barriers lived in many hearts. Trade between the once-enemy neighbors had still barely resumed. Before the war, France had bought about 8 percent of Germany’s exports. In 1923, with Germany’s export trade slashed by 40 percent, France was buying barely 1 percent of that output. Trafficking in ideas and courtesies was weaker still.
The wall also blocked Einstein’s professional reach. He had ready news of the ideas coming from Göttingen and Copenhagen, where his photons were viewed without sympathy and where research focused on other matters. Remarkably, it was in Paris that interest in the meaning of hυ continued. The seeds had been sown at the great Solvay
Conference of 1911. One of the conference secretaries was Maurice de Broglie, an experimental physicist based in Paris. He returned from that first Solvay as an enthusiast for Einstein’s light quanta, although, as an experimentalist, he had no clear way of theorizing about them. The theorist in Paris who was most energetic about trying to understand wave-particle duality was Marcel Brillouin, father of Leon, the physicist who worked to maintain the French-German wall by demanding to exclude Einstein, “whatever his genius,” from international meetings.
Paris’s work had no influence on Göttingen’s side of the wall and could not have seemed more remote if it had been carried out in Nairobi or Bengal. Yet it was in Paris that in September, 1923—while members of the Göttingen-Copenhagen alliance stiffened themselves for their final dual over light particles—that physics at last began to grapple with the mystery of wave-particle duality.
Maurice de Broglie’s younger brother, Louis, had been greatly impressed by Maurice’s enthusiasm after Solvay 1911. Louis had planned to study humanist subjects in preparation for a career in the French civil service, but his brother’s work and the writings of Poincaré persuaded him to take up physics. He quickly showed a keen interest in and appreciation for the toolkit of ideas, equations, and techniques that Einstein had given physicists.
Louis was working on his doctoral paper in September when he used Einstein’s toolkit to gain a Detective Columbo hunch about what must be proved if the quantum mystery was ever to be explained. Instinctively, de Broglie concentrated on the experimental evidence that most clearly illustrated the wave-particle paradox. De Broglie hoped for a “synthetic theory of radiation,” that is, a theory that combined waves and particles into one thing. This hunt for the nature of light kept getting more complicated. Ancients had thought light might be something in us, a ray sent out from the eye, but a medieval Arab scholar known in the west as Alhazen studied pinholes of light and their ability to project images against a dark wall. He concluded that light did not come from the eye but consisted of particles moving in straight lines. Newton, too, studied single beams of light and came to a similar conclusion. Then Young did his two-slit experiments showing
the interference patterns typical of waves. Maxwell’s optics ended all dispute. Anything Alhazen and Newton studied could be explained by waves.
But now we have a complicating explanation in which light again acts like a particle to produce the photoelectric effect and Compton effect. Set up a two-slit experiment as described by Young to show the wave interference, but have the light land on a metal wall. Now the wave interference will be visible on the metal, but at the same time the light will knock out electrons in the manner of particles and produce a photoelectric effect. Here you have light moving like a wave yet interacting like a particle. It is the photon’s primal mystery.
De Broglie attacked this puzzle by imagining a photon as a kind of clock. Alarm clocks are solid things, but they have some sort of internal ticking that makes them different from solids like soccer balls and bricks. The photon is bricklike enough to carry momentum and produce the Compton effect, but something about it is always ticking. Just what might be acting so regularly, de Broglie could not guess.
Reaching again into Einstein’s toolkit, de Broglie pulled out Einstein’s two most famous equations: E = mc2 and E = hυ. To the untrained eye, the E’s in both of these equations look identical, but the physicist knows better. The first E refers to energy available in a particle of matter (mc2). An electron, for example, can somehow be transformed into pure energy, consuming the electron in the process. We can call that the material E. The second E defines radiant energy, the energy carried by a massless quantum of light (hυ). That word “massless” is important here. Mathematically it means that mass (m) equals zero. So if you use mc2 to calculate how much material energy you can get from a photon you find that m = 0; so E = 0c2, or just plain old nothing.
De Broglie, of course, knew of these differences, but he combined the two equations anyway, saying mc2 = hυ, material energy equals radiant energy. This was as bold a union as Einstein’s assertion that inertial mass and gravitational mass were physically equivalent. Einstein’s bravado had ultimately yielded new insights into both gravity and acceleration. If de Broglie’s match-up proved correct, physicists could anticipate insights into particles with masses, like electrons, as
well as into those without masses, like photons. If material energy (in electrons) was equivalent to radiant energy, then perhaps electrons, like photons, were waves as well as particles. If so, then it should be possible to shoot a beam of electrons through two slits and see an interference pattern. De Broglie’s theory, then, was subject to experimental testing.
De Broglie reached yet again into Einstein’s toolkit. The most versatile of Einstein’s yardsticks was, of course, relativity and its ability to compute the way things look to different observers. Using his combined Einstein equation, de Broglie derived two equations for a particle’s internal clockwork. One figured the clockwork relative to the particle’s own reference frame, while the other defined the clockwork from an outside perspective. De Broglie found what Einstein had already shown: thanks to the peculiarities of time’s relativity, the outside observer sees time slow down. Einstein had described the process in his theory that gravity produces a “red shift,” but the red shift is a feature of radiation. By combining Einstein’s two great equations, de Broglie was implying that the same rules apply to atomic particles. It is not just photons that are going to show a red shift; electrons should show it, too.
At this point in the story the difference between electron and photon has started to grow a little hazy. Electrons have mass, photons do not. That is something, but by emphasizing the differences, we miss what de Broglie was beginning to suspect—the great similarities between atomic particles and photons. De Broglie used the word “mobile” for both particle-like waves and wave-like particles. The ambiguous term let him speak of electrons and photons together without worrying about whether they were waves or particles.
De Broglie focused his effort on the difference in a mobile’s frequency as seen by the mobile itself and the frequency as seen by an outside observer. The mobile’s measure of frequency differs from the outsider’s measure, but remember, we are talking about the same mobile. The frequencies are relative, just as speed is relative or pathways are relative. Looking for something that could link the two relative frequencies, de Broglie imagined “a fictitious wave.” Anybody who knew that Einstein had been thinking about “ghost waves” might rise to attention here. De Broglie suggested that this fictitious wave mov-
ing with the mobile is in harmony—“in phase,” to use the technical jargon—with both the particle’s view and the outside observer’s view. He concluded that “this harmony of phase will always persist,” and then he generalized in a manner worthy of Einstein that “any moving body may be accompanied by a wave” and it is impossible to distinguish between “motion of body and propagation of wave.”
In de Broglie’s mobile, wave-motion and body-motion are joined together like lovers on an opera house stage. They remain individual yet are united through the harmony of their music. The difference between de Broglie’s wave and Einstein’s hard-sought ghost wave is that de Broglie’s is like a duet, while Einstein had been looking for a separate item, something like a bullwhip, that could carry a wave but did not have two-ness built into its nature.
Duets, of course, can join more than two singers in harmony. The instruments in the orchestra pit play their parts as well, and all these sounds join together into something that, for all its richness, can be reduced to a single groove on a record. The tenor’s voice, the soprano’s sweetness, the violin’s contribution along with those of the cello and oboe are distinct to the ear and yet they all combine to describe one solitary line on an old recording disc. De Broglie imagined that the harmonies of many photons could also be described by a single wave, which he called a phase wave.
Einstein had missed this musicality of the quanta, and as he so much loved music, it is natural to wonder why he missed it. Einstein’s skree-skree, however, was not harmonious, and he had no sympathy for teams that acted in unison. His strength lay in the statistical effects of individuals acting individually—of, say, water molecules crashing independently against isolated specks of dust. Even as a child, unified action held no appeal for him. Watching a military parade in Munich as a boy, he was unmoved by the music, the color, and the thousand men tramping as one. Horrified, he told his parents, “When I grow up I don’t want to be one of those poor people.”
De Broglie, however, hoped even the photon’s primal mystery might become comprehensible if he thought of a light beam as a phase wave of photons moving in step. Suppose someone behind a curtain throws an alarm clock. We cannot see the clock move behind
the curtain; however, if our ears are keen enough, we can hear it move. Each tick will sound from a different place. If we take the ticking sound as the whole story, we will become confused. The clock will seem to jump between different points without going through the space between, but if we consider this ticking as a clue to the clock’s general activity we can begin to make sense of it: Something moving gives us a regular report—but not a continuous one—on its where-abouts.
De Broglie thought light could be considered similarly. It is moving continuously through space but can interact with matter only when the elements of its phase wave are in harmony. Those harmonious moments mark when the light’s presence can be discovered, just as ticking sounds periodically reveal a clock behind a curtain.
If de Broglie’s phase wave was to survive, it had to explain not only the mystery of wave-particle duality, but Alhazen’s pinhole image and Young’s interference. There are two standard techniques for analyzing light motion. One is geometric, drawing lines to show how light travels or is bent by a lens or reflected by a mirror. Alhazen had used that method to argue that light is a particle, so de Broglie’s problem was to explain how it could be created by a mobile. De Broglie’s hunch was that the light moved in a continuous wave while the light’s “ticking” occurs at the same point on each wave. Suppose an alarm clock rides a small roller-coaster that carries the clock up and down along a continuous track. It takes one second to cross one full roller-coaster hill and the clock only ticks once a second, so the clock will always be at the same point on each hill when it ticks and a person tracking the motion by the sound will suppose that the clock is moving along a straight line.
There is an old military joke about a sergeant drilling recruits. He has them parading back and forth, but then he makes a mistake. He is too slow in giving an order to turn and the squad marches straight into a wall. Not flummoxed for even a second, the sergeant barks, “If you were real soldiers, you would have all hit that wall together.” The same principle applies to photons hitting the wall of a pinhole camera. Only those that are in step when they hit the wall will “tick” and
reveal their presence, so only evidence of straight line motion will be observable.
Young’s two-slit experiment reversed de Broglie’s problem. Alhazen’s geometric optics were no help here. Wave dynamics were needed to account for this interference. Could de Broglie’s mobile also explain it? This time it was not quite so easy. He had to add a few extra hypotheses to his account (something Einstein in particular was always loath to do), but the essence was basic. If the slits are sufficiently tiny, passage through them disrupts the light, bending it so that it scatters a bit, just as soldiers marching through an obstacle will be disrupted. Trained soldiers will reform their group and resume marching, but of course if some soldiers cross one obstacle and some cross a different obstacle, the separated groups will no longer be in step with one another. A physicist would say they have gotten out of phase. And, of course, photons are not trained soldiers who can alertly keep together. Howsoever the slit distorted their paths, that is how the photons travel, and when they hit the wall, some will be “ticking” and reveal their presence while others will be out of phase and interact with nothing. The interference pattern on the screen does not reveal where light is absent and where it strikes; it only shows where “ticking” light strikes. And that pattern matches perfectly with the dynamic analysis of how waves will interfere with one another. De Broglie was naturally happy to have found in the interaction of light and matter a “fundamental bond that unites the two great principles of geometrical optics and dynamics.”
De Broglie had created an agenda for quantum physicists. Instead of trying to explain away the troubling paradox of wave-particle duality, physics should weave it into the heart of any explanation of how matter and energy interact. The wave theory was good, but it placed too much emphasis on continuity and missed out on the tick-tock way that mobiles interact with the larger world. Particle theory was good too, but it was overly mechanical and assumed that every particle interacts with everything it touches. If a particle hits a wall, it makes a bang. So if the wall is not banging, there cannot be any particles hitting it. This dogma missed the way mobiles can strike a wall between ticks and not interact at all. The new physics would have to be a
science of discontinuous interactions between mobiles that move continuously, or at least it would if de Broglie’s hunch proved right.
Like any poet or sculptor, de Broglie thought his creation too beautiful to be false, but others might want harder evidence. In particular they might want proof that electrons are really mobiles and can create interference patterns when fired through narrow enough slits. De Broglie was cautious enough to close the final paper of his miracle September with a voice of controlled excitement, “Many of these ideas may be criticized and perhaps reformed, but it seems no little doubt should remain of the existence of light quanta. Moreover if our opinions are received, as they are grounded in the relativity of time, all of the enormous experimental evidence of the ‘quantum’ will turn in favor of Einstein’s conceptions.”
A closing like that would normally have come to Einstein’s attention immediately, but the wall between Paris and Berlin had put the two cities out of phase and they no longer interacted coherently. In Paris, de Broglie’s paper was seen as remarkable, but probably crazy. In Berlin, people were concentrating on matters like the price of milk, which one fine morning stood at 15 million marks and the next day had jumped to 30 million.