There were four reasons the early years of quantum mechanics were dominated by a brand of physics dubbed Knabenphysik, German for “boys’ physics”. They were Wolfgang Pauli, Paul A.M. Dirac, Werner Heisenberg and Enrico Fermi, all born at the turn of the century. Until about 1930, these four physicists, almost growing up together in various parts of Europe, extending Max Planck’s revolutionary idea of energy being transported in discrete packets to various areas of the natural sciences in parallel, laid the first robust conceptual foundations of theories that would come to rule the 21st century. One of those was the famous exclusion principle, formulated by Pauli in January 1925, ninety-two years ago this month.
In 1913, the Danish physicist Niels Bohr introduced a model of the atom resembling the Solar System, with electrons orbiting a nucleus at the centre. Each orbit denoted a fixed level of energy. Only an electron with that energy could occupy that orbit. The particles could also jump between orbits if they acquired or lost corresponding packets, or quanta, of energy. By the end of the decade, Bohr’s model was found to explain the case of the hydrogen atom – which had one electron orbiting the nucleus – very well. However, it struggled to account for the behaviour of larger atoms.
In the course of these developments, electrons came to be accorded a set of numbers called quantum numbers. Plugging these numbers into the Schrödinger equation yielded solutions that would reveal information about the electron. As a result, each electron could be described by a set of quantum numbers. It’s fascinating to note that the insights that would spring from analysing the quantum numbers would give rise to the machines that, in turn, would allow humans to image atoms and molecules for the first time. In other words, the insights of Knabenphysik were derived without anyone knowing the physical structure of what they were analysing, a position that would become evident with the Copenhagen Interpretation of quantum mechanics in 1927.
By the early 1920s, physicists had found that three quantum numbers could ‘explain’ an electron in a hydrogen atom. The principal quantum number (n) described the energy, or size, of the electron’s orbit; the azimuthal quantum number (l) described the shape of the orbit; and the magnetic quantum number (m) described the orientation of the orbit in the presence of an external magnetic field. Then, Pauli published a seminal paper in the German journal Zeitschrift für Physik in January 1925 (when he was 25). It was titled ‘On the Connexion between the Completion of Electron Groups in an Atom with the Complex Structure of Spectra’. In it, Pauli posited that no two electrons in an atom could have an identical set of quantum numbers.
(Neither Pauli nor anyone else has ever been able to answer why, however. Reflecting on his discovery in the 1940s, Pauli said, “The impression that the shadow of some incompleteness [falls] here on the bright light of success of the new quantum mechanics seems to me unavoidable.”)
It was a simple idea but it led to a cascade of significant discoveries that opened up quantum mechanics – notably in a way that reminded the world that other minds had been labouring on the problems of the day as well. One of the first such discoveries was a new quantum number. While the electron had been discovered in 1897, and the structure of an atom first elucidated in the Geiger-Marsden (a.k.a. Rutherford gold-foil) experiment in 1911, a discovery that predated both these efforts but strongly influenced their interpretation also impinged upon the exclusion principle. In the late 1800s, Pieter Zeeman performed an experiment in which he found that a magnetic field altered the behaviour of light waves.
The Bohr model couldn’t explain this so-called Zeeman effect because he couldn’t explain why the quanta emitted by electrons in the presence of a magnetic field seemed dissimilar to the emissions in the absence of a magnetic field. He as well as others were also at a loss as to why all the electrons in larger atoms didn’t simply occupy the lowest energy state.
But with Pauli’s exclusion principle in the picture, George Uhlenbeck and Samuel Goudsmit realised later in 1925 that the Zeeman effect could be explained if there was a fourth quantum number, called spin (s), that described electrons’ interactions with magnetic fields. And using n, l, m and s, physicists understood that electrons couldn’t crowd the lowest energy state around a nucleus but only the lowest available energy state – an outcome that made way for a more efficient arrangement of elements in the periodic table.
For his insight, Pauli won the Nobel Prize for physics in 1945.
The story doesn’t end here.
The significance of the exclusion principle lay in its historical context more than in its implicit individual importance. To be sure, the early 1900s was a time marked with upheavals, of discoveries and insights that were relentlessly, and far too rapidly for many, reshaping long-upheld theories. One cause of the conflict was a rising awareness that the thermodynamic equations powering the engines of industrialisation didn’t sit well with new experimental results involving light and heat. The upheavals’ epicentres were clustered in Europe, particularly in Germany, Austria, France, Italy and the Netherlands. Even if the exclusion principle was an important moment, it was not particularly more important than the findings shortly before and after.
For example, Fermi got his first breakthrough in 1926 (at age 25) by using the exclusion principle to understand the behaviour of larger assemblages of electrons, such as in electrical conductors. He came up with new statistical rules to determine how the properties of an object would change should they depend on particles obeying the exclusion principle. Interestingly, at the time he was writing this paper, his application to be a professor at the University of Cagliari was rejected because some of those who were evaluating his application didn’t think highly of quantum physics. From a biography of Fermi titled The Pope of Physics by Bettina Hoerlin and Gino Segrè:
[Vito] Volterra and [Tullio] Levi-Civita, two of the five professors on the Cagliari professorship selection committee, voted for him, but the other three were all physicists with little sympathy or interest in the field’s modern developments. The Cagliari position went to a man thirty years older than Fermi and undoubtedly less deserving. The committee’s three elderly members had felt obligated to reward their seasoned colleague rather than the young upstart. Their choice was even less defensible since while they were deliberating, Fermi was writing a seminal paper that would be considered a breakthrough in the world of physics.
Fermi’s calculations were later added on to by Paul Dirac (when he was 24), leading to the creation of Fermi-Dirac statistics. It applies to all particles that obey the exclusion principle, such particles since being called fermions.
Around the same time, Einstein and the Indian theoretical physicist Satyendra Nath Bose set the foundation for a complementary Bose-Einstein statistics. Unlike F-D statistics, B-E applies to all particles that don’t obey the exclusion principle. (One of its predictions, of the formation of a substance called Bose-Einstein condensate, also turns ninety-two this year.) In honour of Bose’s contribution, Dirac christened these particles bosons. Fermions and bosons are the only two kinds of fundamental particles known to this day.
A few months after the exclusion principle was published, Werner Heisenberg (only 23 at the time), Max Born and Pascual Jordan started developing matrix mechanics, which would replace the easily-visualised Bohr’s orbits with abstract and complex mathematical rules that did a better job of describing the properties of larger atoms. Referring to this, Heisenberg finished his 1932 physics Nobel Prize speech thus:
… the path so far traced by the quantum theory indicates that an understanding of those still unclarified features of atomic physics can only be acquired by foregoing visualization and objectification to an extent greater than that customary hitherto. We have probably no reason to regret this, because the thought of the great epistemological difficulties with which the visual atom concept of earlier physics had to contend gives us the hope that the abstracter atomic physics developing at present will one day fit more harmoniously into the great edifice of science.
Some six months later, the Austrian physicist Erwin Schrödinger discovered a less complex but equally agile way to interpret matrix mechanics, collected under a set of methods called wave mechanics. Heisenberg was discomfited by Planck, Einstein and Fermi all finding Schrödinger’s methods more accessible. The German moved to Copenhagen in 1926 to work more closely with Bohr to understand if he was missing something.
The result was 1927 becoming a very important year for quantum mechanics. That year, Bohr figured that all objects have pairs of complementary properties that can’t be measured simultaneously; Heisenberg came up with his eponymous uncertainty principle showing that position and momentum were complementary properties; and together they prompted Schrödinger to come up with his cat-in-a-box thought experiment to explain just how counterintuitive quantum mechanics was starting to seem. For one, it allowed particles to engage in faster-than-light communication with each other, a conclusion at complete odds with Einstein’s theories of relativity.
No matter the disputes and paradoxes that followed, the first thirty years of the 20th century were when the first principles of a modern conception of gravity, of the interactions between various subatomic particles and of the interactions between matter and radiation were first instituted. With this knowledge as substrate, semiconductors, superconductors, particle accelerators, solid-state physics, advanced medical diagnostics, supercomputers, quantum computers, digital storage devices, exotic forms of matter, and so on, were come upon over the next hundred years, setting the stage for the Atomic, Space and Information Ages.
However, quantum mechanics didn’t simply give. It also took. If its applications prevent it from being seen as a niche theory, the Knabenphysik should remind us that it wasn’t really of solitary origins either. All of Dirac, Pauli, Heisenberg and Fermi – and everyone before and since – benefited from their patrons, mentors and guides, too numerous and exceptional to recall in a few lines. And none of their achievements, not even their ideas, sprung from a vacuum devoid of the imagination or encouragement of others.
Then again, the same influence of social forces did also contribute to the suppression of women’s participation in research. It isn’t for nothing that Marie Curie was the sole female participant at the 1927 Solvay Conference (photo above).
PS: If you’re interested – an experiment kicked off in 2006 to check if particles ever violated the exclusion principle. The scientists involved haven’t been able to rule it out.
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