The most famous photograph in the history of physics was taken in Brussels in October 1927. Twenty nine scientists sit and stand in three rows: Einstein in the front center, Marie Curie the only woman, Planck, Bohr, Heisenberg, Schrödinger, Dirac, Born, de Broglie, Pauli and more. By a common count, seventeen of them won or would win a Nobel Prize. The meeting is remembered less for its formal sessions than for a conversation that went on over breakfast and dinner, and for years afterward.

Como, then Brussels

A month earlier, Bohr had given a lecture in Como, Italy, at a meeting marking the centenary of Alessandro Volta's death. There he set out for the first time his idea of complementarity: that wave and particle descriptions are both needed, though never in the same experimental arrangement. Brussels would be the first meeting of the two men on the new theory.

The Solvay conferences were funded by Ernest Solvay, a Belgian industrial chemist who had grown rich from a process for making soda. The first, in 1911, had discussed radiation and quanta. The fifth, in 1927, had the theme "Electrons and Photons," and it was chaired by Hendrik Lorentz, the Dutch physicist whom nearly everyone admired. He died a few months later.

The formal program

The reports covered experiments and theory. De Broglie presented a version of his ideas later called the pilot wave theory, in which a real particle is guided by a real wave. Pauli raised objections, and the theory was received coolly, and de Broglie soon set it aside; it would be revived only decades later. Born and Heisenberg gave a joint report on matrix mechanics and its interpretation. They ended with a striking claim: they regarded quantum mechanics as a closed theory, whose basic assumptions no longer needed changing.

Breakfast challenges

The real drama happened outside the sessions. According to later recollections by Otto Stern and Heisenberg, Einstein would come to breakfast at the hotel with a new imagined experiment designed to show that the uncertainty relations could be beaten, that position and motion could both be pinned down. Bohr, Heisenberg and Pauli would work on it during the day, and by dinner Bohr usually had an answer. Ehrenfest, a friend of both men, is said to have told Einstein he was ashamed of him, since Einstein was now resisting the new theory just as his own critics had resisted relativity.

The photon box

The contest continued at the sixth Solvay conference in 1930, where Einstein brought his most ingenious challenge. Imagine a box full of light, with a clock inside that opens a shutter for an instant and lets out a single photon. Weigh the box before and after, and the mass lost tells you the photon's energy, since mass and energy are equivalent. The clock tells you the exact moment it left. Energy and time would then both be known precisely, defeating one of Heisenberg's relations.

Bohr was badly shaken and, by the accounts of those present, spent an anxious evening on it. By morning he had a reply, built on Einstein's own general relativity. To weigh the box, you must let it move slightly in the earth's gravity, and according to general relativity a clock's rate depends on its height in a gravitational field. The uncertainty in the box's position therefore makes the clock's reading uncertain by just the right amount. Einstein accepted the answer.

From inconsistency to incompleteness

After 1930 Einstein largely stopped trying to show that quantum mechanics contradicted itself. Instead he argued that it was true as far as it went but did not go far enough. His objection moved from inconsistency to incompleteness, the claim that the theory leaves out something real. That line of argument led to a famous paper in 1935 and, much later, to experiments that tested it.

Despite their disagreement the two men remained close friends. Much of what we know about the debates comes from Bohr's own essay, written in 1949 for a volume honoring Einstein's seventieth birthday. Historians read it carefully, since it was written two decades later by one of the two parties, and some think it smooths over moments where Bohr's answers were less decisive than the essay suggests.

Worked example: the photon box step by step

Walk through the argument as a judge might. Einstein's claim: one apparatus can fix both the energy of an escaping photon and its moment of escape. His evidence: the clock gives the time, and the change in weight gives the energy. Bohr's reply does not deny any step directly. Instead it asks what weighing really involves. A scale reads a weight by letting the box shift until a spring or counterweight balances it. That shift moves the clock up or down a little in the earth's gravity, and general relativity says this changes the clock's rate. The more precisely you weigh, the less you know about the clock's position, and so about its time.

The exchange shows good arguing in action. Each man took the other's strongest case seriously, and the answer drew on a theory the challenger himself had created. Notice too how much depends on the historical record. The tidy version comes largely from Bohr's later account, so a careful reader treats it as testimony from one side, valuable but not final.