When Bohr got it wrong: the impact of a little-known paper on the development of quantum theory
One hundred and one years ago, Danish physicist Niels Bohr proposed a radical theory together with two young colleagues – Hendrik Kramers and John Slater – in an attempt to resolve some of the most perplexing issues in fundamental physics at the time. Entitled “The Quantum Theory of Radiation”, and published in the Philosophical Magazine, their hypothesis was quickly proved wrong, and has since become a mere footnote in the history of quantum mechanics.
Despite its swift demise, their theory perfectly illustrates the sense of crisis felt by physicists at that moment, and the radical ideas they were prepared to contemplate to resolve it. For in their 1924 paper Bohr and his colleagues argued that the discovery of the “quantum of action” might require the abandonment of nothing less than the first law of thermodynamics: the conservation of energy.
As we celebrate the centenary of Werner Heisenberg’s 1925 quantum breakthrough with the International Year of Quantum Science and Technology (IYQ) 2025, Bohr’s 1924 paper offers a lens through which to look at how the quantum revolution unfolded. Most physicists at that time felt that if anyone was going to rescue the field from the crisis, it would be Bohr. Indeed, this attempt clearly shows signs of the early rift between Bohr and Albert Einstein about the quantum realm, that would turn into a lifelong argument. Remarkably, the paper also drew on an idea that later featured in one of today’s most prominent alternatives to Bohr’s “Copenhagen” interpretation of quantum mechanics.
Genesis of a crisis
The quantum crisis began when German physicist Max Planck proposed the quantization of energy in 1900, as a mathematical trick for calculating the spectrum of radiation from a warm, perfectly absorbing “black body”. Later, in 1905, Einstein suggested taking this idea literally to account for the photoelectric effect, arguing that light consisted of packets or quanta of electromagnetic energy, which we now call photons.
Bohr entered the story in 1912 when, working in the laboratory of Ernest Rutherford in Manchester, he devised a quantum theory of the atom. In Bohr’s picture, the electrons encircling the atomic nucleus (that Rutherford had discovered in 1909) are constrained to specific orbits with quantized energies. The electrons can hop in “quantum jumps” by emitting or absorbing photons with the corresponding energy.
Bohr had no theoretical justification for this ad hoc assumption, but he showed that, by accepting it, he could predict (more or less) the spectrum of the hydrogen atom. For this work Bohr was awarded the 1922 Nobel Prize for Physics, the same year that Einstein collected the prize for his work on light quanta and the photoelectric effect (he had been awarded it in 1921 but was unable to attend the ceremony).
After establishing an institute of theoretical physics (now the Niels Bohr Institute) in Copenhagen in 1917, Bohr’s mission was to find a true theory of the quantum: a mechanics to replace, at the atomic scale, the classical physics of Isaac Newton that worked at larger scales. It was clear that classical physics did not work at the scale of the atom, although Bohr’s correspondence principle asserted that quantum theory should give the same results as classical physics at a large enough scale.
Quantum theory was at the forefront of physics at the time, and so was the most exciting topic for any aspiring young physicist. Three groups stood out as the most desirable places to work for anyone seeking a fundamental mathematical theory to replace the makeshift and sometimes contradictory “old” quantum theory that Bohr had cobbled together: that of Arnold Sommerfeld in Münich, of Max Born in Göttingen, and of Bohr in Copenhagen.
Dutch physicist Hendrik Kramers had hoped to work on his doctorate with Born – but in 1916 the First World War ruled that out, and so he opted instead for Copenhagen, in politically neutral Denmark. There he became Bohr’s assistant for ten years: as was the case with several of Bohr’s students, Kramers did the maths (it was never Bohr’s forte) while Bohr supplied the ideas, philosophy and kudos. Kramers ended up working on an impressive range of problems, from chemical physics to pure mathematics.
Reckless and radical
One of the most vexing question for Bohr and his Copenhagen circle in the early 1920s was how to think about electron orbits in atoms. Try as they might, they couldn’t find a way to make the orbits “fit” with experimental observations of atomic spectra.
Perhaps, in quantum systems like atoms, we have to abandon any attempt to construct a physical picture at all
Bohr and others, including Heisenberg, began to voice a possibility that seemed almost reckless: perhaps, in quantum systems like atoms, we have to abandon any attempt to construct a physical picture at all. Maybe we just can’t think of quantum particles as objects moving along trajectories in space and time.
This struck others, such as Einstein, as desperate, if not crazy. Surely the goal of science had always been to offer a picture of the world in terms of “things happening to objects in space”. What else could there be than that? How could we just give it all up?
But it was worse than that. For one thing, Bohr’s quantum jumps were supposed to happen instantaneously: an electron, say, jumping from one orbit to another in no time at all. In classical physics, everything happens continuously: a particle gets from here to there by moving smoothly across the intervening space, in some finite time. The discontinuities of quantum jumps seemed to some – like Austrian physicist Erwin Schrödinger in Vienna – bordering on the obscene.
Worse still was the fact that while the old quantum theory stipulated the energy of quantum jumps, there was nothing to dictate when they would happen – they simply did. In other words, there was no causal kick that instigated a quantum jump: the electron just seemed to make up its own mind about when to jump. As Heisenberg would later proclaim in his 1927 paper on the uncertainty principle (Zeitschrift für Physik 43 172), quantum theory “establishes the final failure of causality”.
Such notions were not the only source of friction between the Copenhagen team and Einstein. Bohr didn’t like light quanta. While they seemed to explain the photoelectric effect, Bohr was convinced that light had to be fundamentally wave-like, so that photons (to use the anachronistic term) were only a way of speaking, not real entities.
To add to the turmoil in 1924, the French physicist Louis de Broglie had, in his doctoral thesis for the Sorbonne, turned the quantum idea on its head by proposing that particles such as electrons might show wave-like behaviour. Einstein had at first considered this too wild, but soon came round to the idea.
Go where the waves take you
In 1924 these virtually heretical ideas were only beginning to surface, but they were creating such a sense of crisis that it seemed anything was possible. In the 1960s, science historian Paul Forman suggested that the feverish atmosphere in physics was part of an even wider cultural current. By rejecting causality and materialism, the German quantum physicists, Forman said, were attempting to align their ideas with a rejection of mechanistic thinking while embracing the irrational – as was the fashion in the philosophical and intellectual circles of the beleaguered Weimar republic. The idea has been hotly debated by historians and philosophers of science – but it was surely in Copenhagen, not Munich or Göttingen, that the most radical attitudes to quantum theory were developing.
Then, just before Christmas in 1923, a new student arrived at Copenhagen. John Clarke Slater, who had a PhD in physics from Harvard, turned up at Bohr’s institute with a bold idea. “You know those difficulties about not knowing whether light is old-fashioned waves or Mr Einstein’s light particles”, he wrote to his family during a spell in Cambridge that November. “I had a really hopeful idea… I have both the waves and the particles, and the particles are sort of carried along by the waves, so that the particles go where the waves take them.” The waves were manifested in a kind of “virtual field” of some kind that spread throughout the system, and they acted to “pilot” the particles.
Bohr was mostly not a fan of Slater’s idea, not least because it retained the light particles that he wished to dispose of. But he liked Slater’s notion of a virtual field that could put one part of a quantum system in touch with others. Together with Slater and Kramers, Bohr prepared a paper in a remarkably short time (especially for him) outlining what became known as the Bohr-Kramers-Slater (BKS) theory. They sent it off to the Philosophical Magazine (where Bohr had published his seminal papers on the quantum atom) at the end of January 1924, and it was published in May (47(281) 785). As was increasingly characteristic of Bohr’s style, it was free of any mathematics (beyond Einstein’s quantum relationship E=hν).
In the BKS picture, an excited atom about to emit light can “communicate continually” with the other atoms around it via the virtual field. The transition, with emission of a light quantum, is then not spontaneous but induced by the virtual field. This mechanism could solve the long-standing question of how an atom “knows” which frequency of light to emit in order to reach another energy level: the virtual field effectively puts the atom “in touch” with all the possible energy states of the system.
The problem was that this meant the emitting atom was in instant communication with its environment all around – which violated the law of causality. Well then, so much the worse for causality: BKS abandoned it. The trio’s theory also violated the conservation of energy and momentum – so they had to go too.
Causality and conservation, abandoned
But wait: hadn’t these conservation laws been proved? In 1923 the American physicist Arthur Compton in Cambridge had shown that when light is scattered by electrons, they exchange energy, and the frequency of the light decreases as it gives up energy to the electrons. The results of Compton’s experiments agreed perfectly with predictions made on the assumptions that light is a stream of quanta (photons) and that their collisions with electrons conserve energy and momentum.
Ah, said BKS, but that’s only true statistically. The quantities are conserved on average, but not in individual collisions. After all, such statistical outcomes were familiar to physicists: that was the basis of the second law of thermodynamics, which presented the inexorable increase in entropy as a statistical phenomenon that need not constrain processes involving single particles.
The radicalism of the BKS paper got a mixed reception. Einstein, perhaps predictably, was dismissive. “Abandonment of causality as a matter of principle should be permitted only in the most extreme emergency”, he wrote. Wolfgang Pauli, who had worked in Copenhagen in 1922–23, confessed to being “completely negative” about the idea. Born and Schrödinger were more favourable.
But the ultimate arbiter is experiment. Was energy conservation really violated in single-particle interactions? The BKS paper motivated others to find out. In early 1925, German physicists Walther Bothe and Hans Geiger in Berlin looked more closely at Compton’s X-ray scattering by electrons. Having read the BKS paper, Bothe felt that “it was immediately obvious that this question would have to be decided experimentally, before definite progress could be made.”
Experimental arbitrators German physicists Walther Bothe and Hans Geiger (right) conducted an experiment to explore the BKS paper, that looked at X-ray scattering from electrons to determine the conservation of energy at microscopic scales. (IPP/© Archives of the Max Planck Society)
Geiger agreed, and the duo devised a scheme for detecting both the scattered electron and the scattered photon in separate detectors. If causality and energy conservation were preserved, the detections should be simultaneous; while any delay between them could indicate a violation. As Bothe would later recall “The ‘question to Nature’ which the experiment was designed to answer could therefore be formulated as follows: is it exactly a scatter quantum and a recoil electron that are simultaneously emitted in the elementary process, or is there merely a statistical relationship between the two?” It was incredibly painstaking work to seek such coincident detections using the resources then available. But in April 1925 Geiger and Bothe reported simultaneity within a millisecond – close enough to make a strong case that Compton’s treatment, which assumed energy conservation, was correct. Compton himself, working with Alfred Simon using a cloud chamber, confirmed that energy and momentum were conserved for individual events (Phys. Rev. 26 289).
Revolutionary defeat… singularly important
Bothe was awarded the 1954 Nobel Prize for Physics for the work. He shared it with Born for his work on quantum theory, and Geiger would surely have been a third recipient, if he had not died in 1945. In his Nobel speech, Bothe definitively stated that “the strict validity of the law of the conservation of energy even in the elementary process had been demonstrated, and the ingenious way out of the wave-particle problem discussed by Bohr, Kramers, and Slater was shown to be a blind alley.”
Bohr was gracious in his defeat, writing to a colleague in April 1925 that “It seems… there is nothing else to do than to give our revolutionary efforts as honourable a funeral as possible.” Yet he was soon to have no need of that particular revolution, for just a few months later Heisenberg, who had returned to Göttingen after working with Bohr in Copenhagen for six months, came up the first proper theory of quantum mechanics, later called matrix mechanics.
“In spite of its short lifetime, the BKS theory was singularly important,” says historian of science Helge Kragh, now emeritus professor at the Niels Bohr Institute. “Its radically new approach paved the way for a greater understanding, that methods and concepts of classical physics could not be carried over in a future quantum mechanics.”
The Bothe-Geiger experiment that [the paper] inspired was not just an important milestone in early particle physics. It was also a crucial factor in Heisenberg’s argument [about] the probabilistic character of his matrix mechanics
The BKS paper was thus in a sense merely a mistaken curtain-raiser for the main event. But the Bothe-Geiger experiment that it inspired was not just an important milestone in early particle physics. It was also a crucial factor in Heisenberg’s argument that the probabilistic character of his matrix mechanics (and also of Schrödinger’s 1926 version of quantum mechanics, called wave mechanics) couldn’t be explained away as a statistical expression of our ignorance about the details, as it is in classical statistical mechanics.
Rather, the probabilities that emerged from Heisenberg’s and Schrödinger’s theories applied to individual events: they were, Heisenberg said, fundamental to the way single particles behave. Schrödinger was never happy with that idea, but today it seems inescapable.
Over the next few years, Bohr and Heisenberg argued that the new quantum mechanics indeed smashed causality and shattered the conventional picture of reality as an objective world of objects moving in space–time with fixed properties. Assisted by Born, Wolfgang Pauli and others, they articulated the “Copenhagen interpretation”, which became the predominant vision of the quantum world for the rest of the century.
Failed connections
Slater wasn’t at all pleased with what became of the idea he took to Copenhagen. Bohr and Kramers had pressured him into accepting their take on it, “without the little lump carried along on the waves”, as he put it in mid-January. “I am willing to let them have their way”, he wrote at the time, but in retrospect he felt very unhappy about his time in Denmark. After the BKS theory was disproved, Bohr wrote to Slater saying “I have a bad conscience in persuading you to our views”.
Slater replied that there was no need for that. But in later life – after he had made a name for himself in solid-state physics – Slater admitted to a great deal of resentment. “I completely failed to make any connection with Bohr”, he said in a 1963 interview with the historian of science Thomas Kuhn. “I fought with them [Bohr and Kramers] so seriously that I’ve never had any respect for those people since. I had a horrible time in Copenhagen.” While most of Bohr’s colleagues and students expressed adulation, Slater’s was a rare dissenting voice.
But Slater might have reasonably felt more aggrieved at what became of his “pilot-wave” idea. Today, that interpretation of quantum theory is generally attributed to de Broglie – who intimated a similar notion in his 1924 thesis, before presenting the theory in more detail at the famous 1927 Solvay Conference – and to American physicist David Bohm, who revitalized the idea in the 1950s. Initially dismissed on both occasions, the de Broglie-Bohm theory has gained advocates in recent years, not least because it can be applied to a classical hydrodynamic analogue, in which oil droplets are steered by waves on an oil surface.
Whether or not it is the right way to think about quantum mechanics, the pilot-wave theory touches on the deep philosophical problems of the field. Can we rescue an objective reality of concrete particles with properties described by hidden variables, as Einstein had advocated, from the fuzzy veil that Bohr and Heisenberg seemed to draw over the quantum world? Perhaps Slater would at least be gratified to know that Bohr has not yet had the last word.
This article forms part of Physics World‘s contribution to the 2025 International Year of Quantum Science and Technology (IYQ), which aims to raise global awareness of quantum physics and its applications.
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