Seen from a ferry, Copenhagen appeared first as a smoky cloud, then as factory chimneys poking above the horizon. Einstein was coming from Sweden where he had given his delayed Nobel lecture. The Swedes had cheered him, of course. He had spoken before an audience of 2,000 souls in the port city of Göteborg, which was celebrating its tercentenary jubilee.

Beneath the smoking chimneys, as Copenhagen’s green-copper domes and red roofs rose into view, Bohr was waiting for Einstein to land in Denmark. As the ferry moved into the harbor, Bohr was still refusing to follow Compton’s stride into the world of light quanta. Bohr dismissed Compton’s effect as an illusion. His assistant, Kramers, compared the theory of light quanta with “medicine which will cause the disease to vanish but kill the patient.” He meant, perhaps, that the theory would explain the data but abolish coherence. Even so, Bohr found plenty to talk about when Einstein landed. Presumably they said Hello and maybe something about the brief voyage and perhaps something about Sweden, but very quickly they were deep into physics. They were lost to the world even before the tram delivered them to Bohr’s home.

Regrettably, even though by that time Einstein was very well known and apt to be recognized wherever he went, no passengers aboard the tram have left an onlooker’s account of how these two men

conversed, or rather spewed speech at one another. Both were well known to be compulsive talkers; neither was distinguished as a compulsive listener. Einstein did not demand that the so-called listener actually comprehend what he was saying. A politely open pair of eyes was good enough. Elsa could be good enough. Bohr liked to turn listeners into secretaries, asking them to transcribe his words as he spoke. In neither case was audience participation required or looked for. Undoubtedly, therefore, as the two men spoke they sometimes stepped on each other’s sentences and often interrupted with ”Yes, buts” that soared off on tangents.

Bohr, sober and long-winded, still insisted that the light quanta idea was irrational and therefore false.

Einstein, direct and witty, thought contradictions in nature were mysteries to be explained.

Bohr saw the light quantum as more impossible than mysterious. X-rays were waves, period. The light quanta formula even included the υ for a frequency and frequency could be measured only by an apparatus that treated the X-rays as waves.

Of course Einstein had recognized these puzzles when Bohr was still a college student. He knew too that the h was just as much a part of the quantum formula, a little, unshrinkable, unvibrating number.

The two men were pipe smokers, although it is a challenge to talk energetically and keep a pipe lit. It is even harder to light a pipe bowl while interrupting a fast-paced talker, so their smoking rituals would have forced each man from time to time to listen quietly to the other.

Bohr, too, was used to the quantum oddities. He knew that in classical theory a wave could shrink to something so small that it was just an infinitesimal burp away from being nothing at all, but energy that weak cannot support an electron in its orbit, just as wings cannot keep a too-slow airplane in the sky. Bohr did not look for any physical reality behind his symbols; h was just a number and hυ was just a combination of numbers that was not to be taken as something’s name.

Einstein did look for a symbol’s meaning and once used the metaphor of a beer stein in a statistical analysis to prove that beer never comes as a free fluid but is always packaged in steins. Bohr was never impressed by either the humor or the quantitative abstraction behind

the beer-stein metaphor. He held that although beer was served only in multiples of pint-sizes (steins of a pint, quart, half gallon, and so on.), beer was still only a fluid and never a mug.

Looking outside the tram Bohr noticed that they had been conversing so intensely they had missed their stop, and not by just a block or two. The two men hurried to the exit and made their way across the tram tracks to take another ride back. Bohr was the younger man and still had a full head of hair, but Einstein was the more imposing—taller, stronger, and he sported that great head. If our regrettably silent passenger had been on the tram and had watched the two men go, Einstein would likely have been the one to seize the stranger’s eye.

Copenhagen’s port district was busy, but away from its commercial heart the city quickly felt snug and provincial. The two physicists were not surrounded by a Berlin-like metropolitan vigor as they waited for an electric tram. Bicyclists were sprinkled all over Copenhagen streets.

For years, Bohr had been dubious about the conservation of energy at the quantum level. Now the Compton effect was forcing a crisis. Compton and Debye’s analyses worked only if energy conservation held true.

Einstein saw no reason to try anything as radical as rejecting the conservation of energy.

Bohr considered rejecting energy conservation to be far less radical than marrying particles to waves.

Einstein disagreed, believing that physical sense itself depended on keeping energy conservation.

The issue seems abstract, remote from anyone’s life, but the problem was as fundamental as the need for air. How shall we understand our lives? Lions and lambs seem never to worry about that, but humans always do. Judges anguish over how to apply the law. Believers kneeling in front of a candle grapple with some private hope or fear. An artist twisting colors on a pallet looks fiercely for the mixture that is true to the moment. Bohr’s and Einstein’s concerns were just as personal and just as universal.

Bohr’s heart grasped things metaphorically, seeing abstractions as tools that distracted from the particular.

Einstein’s soul relied on abstractions that clarified concrete experience’s ambiguities.

Yet both men were physicists, great physicists, and even in their seemingly infinite disagreement they shared some common ground. Einstein published a paper that summer, one he had written with his chum Paul Ehrenfest, which Bohr thought correct. Compton had suggested that light quanta ricochet like billiard balls and jump from one frequency to another. Einstein, Ehrenfest, and Bohr, too, agreed that when the incoming X-rays hit an electron it was absorbed. The electron emitted new light at a lower frequency. They disagreed over how and when the new X-ray was emitted.

For Bohr the emission was unrelated in either space or time to the absorbed X-ray.

Einstein believed that the absorption and emission was instantaneous.

Bohr could not avoid one weakness in his position. He had instinctively rejected the Compton effect, but he had no better way to explain Compton’s data. All he could do was voice his doubt.

Einstein knew his own weakness too. He still had no good idea how to synthesize waves and particles into one comprehensible, concrete thing.

Matchboxes in Denmark had the king’s portrait on them. Christian X looked on quietly whenever Bohr relit his bowl.

Oh my God! They had missed their stop again. The tram was approaching their starting point. There was not much to do beyond exchanging sheepish grins, dismounting their public conveyance, crossing the tracks, and trying again. The two men stood at the tram stop, the very picture of absurd genius. Many would have said they were the two smartest men in the world, but they stood side by side at an anonymous way station, yo-yoing back and forth across Copenhagen because they were too distracted by their own intelligence to find their way home.

Of course there was more at stake in their endless talk than truth, physics, and nature’s way. Both men were risking their reputations and achievements. Bohr’s research since 1913 had concentrated on atomic structure. He held that hυ limited electron orbits, and that to get from

one possible orbit to another the electrons “jumps” from one place to another without going through space or time.

Einstein’s ambition was to unite his general theory of relativity with the atom’s electromagnetism. For that scheme to work, he was going to have to express the unity in terms of space and time.

Bohr did not like Einstein’s effort at a spatial mapping. If light quanta can bang into electrons like meteors colliding into planets, space and time stay firmly in the story.

Einstein was pleased with the way the Compton effect’s X-rays scatter in a positively Newtonian manner that allows for measuring scatter angles, energy exchanges, and momentum transfers without ever having to perform a “jump.”

As it moved, the tram passed bicyclists, but the cyclists sometimes caught up with the tram again when it paused to take on and release riders.

By arguing against energy conservation, Bohr defended his own contribution. Bohr’s orbiting electrons could be mapped in space and time, of course, but space posed no limits on how “far” an electron could jump when it shifted from one fixed orbit to another, and no clock determined when it was time to make a jump. These jumps just happened. The electron was here, now it is there; it did not travel between here and there; it just changed. Instead of a calculus of continuous changes, the ultimate quantum theory would have to predict the discontinuous states that electrons “jumped” to.

Perhaps Bohr’s success was why Einstein never predicted the Compton effect. Bohr’s electron did not use space and time in a classical way. Einstein was skeptical about the Bohr atom, but skeptical physicists had for years been making progress by accepting jumps and ignoring the continuity of space-time. Maybe Einstein had finally lost his nerve, like a poker player who thinks his full house looks good but wonders why the other fellow keeps raising. Maybe Einstein had seen the whole thing—light quanta scattering, their energy changing, the angle of scatter providing the decisive link between changes in frequency—and yet he had hesitated. It would be terrible to announce a decisive experiment and then have it fail, not because there was some-

thing wrong with light quanta, but because space-time does not hold at subatomic distances.

Bohr, too, had been growing nervous. His theory’s initial success had, in recent years, become increasingly problematic. Despite his explanation of chemistry’s periodic table of the elements, Bohr’s theory had yet to work in all its details for any atom more complicated than those with a lone electron.

If Einstein, usually so cocky, had grown nervous, the Compton effect restored him to full confidence. His defiant insistence on light quanta’s reality had finally been rewarded.

Meanwhile Bohr’s long perch on a pedestal had grown precarious. The Compton effect’s success at describing continuous change brought the whole discontinuous structure of the atom into crisis.

So Bohr and Einstein both had their excuses for riding back and forth through Copenhagen on the city’s tram system while puffing their pipes. Both were slaves to time and space, but they disagreed profoundly over how tightly space-time bound the atom.