Moving on to the middle row, again from the the left we see another Nobel Laureate, Dutch chemist Peter Debye (1884–1966), who is known primarily for his application of the concept of dipole moment to the charge distribution in asymmetric molecules. On his immediate left, we see Martin Knudsen (1871–1949), the Danish physicist known for his study of molecular gas flow and the development of the Knudsen cell, and Lawrence Bragg (1890–1971), the British physicist, pioneering x-ray crystallographer and 1915 Nobel Laureate. Also present, next to Dirac, is the 1927 Nobel Laureate, the American physicist Arthur Compton (1892–1962), known both for his discovery of the Compton effect which demonstrated the particle nature of electromagnetic radiation and for his later contributions to the Manhattan Project. Louis de Broglie (1892–1987), student of Paul Langevin (front row) was also there. de Broglie was the person who first (in his 1924 PhD thesis) postulated the wave nature of electrons and suggested that all matter has wave properties. Known now as the “de Broglie hypothesis”, it was de Broglie’s idea that Schrödinger had used in his formulation of wave mechanics. Following its experimental verification in 1927 by the Davisson-Germer experiment, de Broglie was awarded his Nobel Prize in physics in 1929.

In addition to these brilliant men, we again focus our attention towards a handful of individuals who were especially prominent in the formulation of early quantum theory. Therein

Niels Bohr (1885–1962)

Hendrik Kramers (1894–1952)

Max Born (1882–1970)

Paul Dirac (1902–1984)

Niels Bohr

Niels Bohr, 42 years old at the time of the conference, was of course the Danish physicist most well known for his (and Ernest Rutherford’s) 1913 formulation of the Bohr model of the atom which proposes that energy levels of electrons are discrete and that the electrons revolve in stable orbits around the atomic nucleus but can jump from one energy level (orbit) to another. The model won Bohr the Nobel Prize in Physics in 1922. In the 30s, he was instrumental in helping refugees escape Nazism. After Denmark was occupied by the Germans, personally lobbied Heisenberg (by then the head of the German nuclear weapons program) about the implications of nuclear war (accounts differ on the exact content of their conversation). He was also part of the British mission to the Manhattan project and later involved in the establishment of CERN in Geneva.

Left: Niels Bohr (1885–1962). Right: Bohr’s 1913 paper On the Constitution of Atoms and Molecules, Part II Systems Containing Only a Single Nucleus, where Bohr introduced what is now known as the Bohr model of the atom.

Prior to the conference, Heisenberg had been working as a lecturer at Bohr’s Institute for Theoretical Physics at the University of Copenhagen. Bohr had forwarded Heisenberg’s paper introducing the uncertainty principle to Einstein. During the conference, Bohr led the charge to defend the implications of Heisenberg’s work by debating Einstein over his criticism illustrated through the now-famous “slit experiment”:

Thought Experiment: The Slit Experiment

Consider a particle passing through a slit of width d. The slit introduces uncertainty in momentum of approximately h/d because the particle passes through the wall. But, let us determine the momentum of the particle by measuring the recoil of the wall. In doing so, we find the momentum of the particle to arbitrary accuracy by conservation of momentum.

Bohr’s elegant response was simple: He argued that the wall which the photon passes through is indeed a quantum mechanical system as well. As such, in order to measure the recoil of the wall to an accuracy of Δp, the momentum of the wall must also be known to this accuracy before the particle passes through. The implication is that at this degree of accuracy, the position of the wall is in fact uncertain as well, just as it is for the particle passing through it. As such, the position of the slit is equal to h/Δp and if the wall’s momentum is known precisely enough to measure the recoil, the slit’s position is uncertain enough to disallow a measurement of its position, in accordance with Heisenberg’s uncertainty principle.

Bohr’s triumph in the debate and his close relationship with Heisenberg at the University of Copenhagen led to the colloquial naming of the non-deterministic view spearheaded by Heisenberg, Bohr, Born and others as the “Copenhagen interpretation” of quantum physics.

Hendrik A. Kramers

Also present in the middle row was the Dutch physicist Hendrik Kramers (1894–1952), who had worked under Bohr in Copenhagen as a Ph.D. candidate and later with Ehrenfest in Leiden. Prior to the advent of quantum mechanics by Heisenberg in 1925, Kramers worked with him on the so-called Kramers-Heisenberg dispersion formula, which expresses the cross section for scatting of a photon by an electron and was fundamental to the establishment of Heisenberg’s 1926 result.

Left: Hendrik “Hans” A. Kramers (1894–1952). Right: Kramers’ 1925 co-authored paper with Heisenberg Über die Streuung von Strahlung durch Atome (“On the Scattering of Radiation by Atoms”) which introduces the Kramers-Heisenberg dispersion formula

Paul Dirac

One of the more, by now, well-known physicists present was Paul Dirac, then aged 25 and a researcher under Ralph Fowler (back row) in Cambridge. The year before, he had completed his Ph.D with the first ever thesis on Heisenberg’s quantum mechanics.

Left: Paul Dirac (1902–1984). Right: Dirac’s 1928 paper The Quantum Theory of the Electron in which he introduced the Dirac equation as a relativistic equation of motion for the wave function of the electron

Dirac’s contribution that led to his Ph.D. occurred in 1925. His supervisor (Fowler) had received a proof copy of Heisenberg’s paper where he introduced matrix mechanics for the first time, and gave it to Dirac for him to examine. Dirac noticed a curious mathematical relationship which he later realized had the same structure as the Poisson brackets that occur in the classical dynamics of particle motion. The realization led to his introduction of a quantum theory based on non-commuting dynamic variables, which allowed him to obtain novel and illuminating quantization rules (the process of transitioning from a classical to a quantum understanding of physics), the so-called canonical quantization procedure. His rules incorporated the ideas of both Heisenberg’s matrix mechanics and Schrödinger’s wave mechanics and showed that they were in fact equivalent. As his admirer and fellow Lucasian Professor of Mathematics at Cambridge, Stephen Hawking would later write, “Of the three founders of modern quantum mechanics, Heisenberg and Schrödinger can claim to have caught the first glimpses of the theory. But it was Dirac who put them together and revealed the whole picture”.

A year after the Solvay conference, Dirac discovered, independently of Pauli, what is now known as the Dirac equation which describes all spin-½ massive particles such as electron and quarks for which parity is a symmetry. The discovery was the first to imply the existence of antimatter, which was experimentally confirmed only several years later. Dirac would go on to share the 1933 Nobel Prize in Physics with Schrödinger “for the discovery of new productive forms of atomic theory”.

Max Born

Finally, in the middle row, we also find the German physicist and mathematician Max Born (1882–1970) who although not as famous as Heisenberg, was highly instrumental in the his development of matrix mechanics and the formulation of the probability density function later used by Erwin Schrödinger in the Schrödinger equation.

It was Born who the year before the conference, in response to Heisenberg’s 1925 publication had proposed that quantum mechanics were best understood by probabilities. What is now known simply as the Born rule, gives the probability that a measurement on a quantum system will yield a given result. It was first introduced by Born in the 1926 paper Zur Quantenmechanik der Stoßvorgänge (“On the Quantum Mechanics of Collisions”). In the paper, Born solves the Schrödinger equation (postulated a year before) for a scattering problem. The rule is now considered a fundamental law of quantum mechanics.

Left: Max Born (1882–1970). Right: Born’s 1926 paper Zur Quantenmechanik der Stoßvorgänge (“On the Quantum Mechanics of Collisions”) where he defines what is now known as the Born rule.

By the time of the conference in October 1927, Born and Heisenberg were famously so confident in their results that they proclaimed that quantum mechanics was “complete and irrevocable”:

While we consider.. a quantum mechanical treatment of the electromagnetic field.. as not yet finished, we consider quantum mechanics to be a closed theory, whose fundamental physical and mathematical assumptions are no longer susceptible of any modification.. On the question of the 'validity of the law of causality' we have this opinion: as long as one takes into account only experiments that lie in the domain of our currently acquired physical and quantum mechanical experience, the assumption of indeterminism in principle, here taken as fundamental, agrees with experience. - Born & Heisenberg (1927). "Quantum Mechanics". Proceedings of the Fifth Solvay Congress

The Front Row