Science 1916: A Hundred-year Time Capsule

In one of my previous blog posts, as I was searching for Schwarzschild’s original papers on Einstein’s field equations and quantum theory, I obtained a copy of the January 1916 – June 1916 volume of the Proceedings of the Royal Prussian Academy of Sciences through interlibrary loan.  The extremely thick volume arrived at Purdue about a week after I ordered it online.  It arrived from Oberlin College in Ohio that had received it as a gift in 1928 from the library of Professor Friedrich Loofs of the University of Halle in Germany.  Loofs had been the Haskell Lecturer at Oberlin for the 1911-1912 semesters. 

As I browsed through the volume looking for Schwarzschild’s papers, I was amused to find a cornucopia of turn-of-the-century science topics recorded in its pages.  There were papers on the overbite and lips of marsupials.  There were papers on forgotten languages.  There were papers on ancient Greek texts.  On the origins of religion.  On the philosophy of abstraction.  Histories of Indian dramas.  Reflections on cancer.  But what I found most amazing was a snapshot of the field of physics and mathematics in 1916, with historic papers by historic scientists who changed how we view the world. Here is a snapshot in time and in space, a period of only six months from a single journal, containing papers from authors that reads like a who’s who of physics.

In 1916 there were three major centers of science in the world with leading science publications: London with the Philosophical Magazine and Proceedings of the Royal Society; Paris with the Comptes Rendus of the Académie des Sciences; and Berlin with the Proceedings of the Royal Prussian Academy of Sciences and Annalen der Physik. In Russia, there were the scientific Journals of St. Petersburg, but the Bolshevik Revolution was brewing that would overwhelm that country for decades.  And in 1916 the academic life of the United States was barely worth noticing except for a few points of light at Yale and Johns Hopkins. 

Berlin in 1916 was embroiled in war, but science proceeded relatively unmolested.  The six-month volume of the Proceedings of the Royal Prussian Academy of Sciences contains a number of gems.  Schwarzschild was one of the most prolific contributors, publishing three papers in just this half-year volume, plus his obituary written by Einstein.  But joining Schwarzschild in this volume were Einstein, Planck, Born, Warburg, Frobenious, and Rubens among others—a pantheon of German scientists mostly cut off from the rest of the world at that time, but single-mindedly following their individual threads woven deep into the fabric of the physical world.

Karl Schwarzschild (1873 – 1916)

Schwarzschild had the unenviable yet effective motivation of his impending death to spur him to complete several projects that he must have known would make his name immortal.  In this six-month volume he published his three most important papers.  The first (pg. 189) was on the exact solution to Einstein’s field equations to general relativity.  The solution was for the restricted case of a point mass, yet the derivation yielded the Schwarzschild radius that later became known as the event horizon of a non-roatating black hole.  The second paper (pg. 424) expanded the general relativity solutions to a spherically symmetric incompressible liquid mass. 

Schwarzschild’s solution to Einstein’s field equations for a point mass.

          

Schwarzschild’s extension of the field equation solutions to a finite incompressible fluid.

The subject, content and success of these two papers was wholly unexpected from this observational astronomer stationed on the Russian Front during WWI calculating trajectories for German bombardments.  He would not have been considered a theoretical physicist but for the importance of his results and the sophistication of his methods.  Within only a year after Einstein published his general theory, based as it was on the complicated tensor calculus of Levi-Civita, Christoffel and Ricci-Curbastro that had taken him years to master, Schwarzschild found a solution that evaded even Einstein.

Schwarzschild’s third and final paper (pg. 548) was on an entirely different topic, still not in his official field of astronomy, that positioned all future theoretical work in quantum physics to be phrased in the language of Hamiltonian dynamics and phase space.  He proved that action-angle coordinates were the only acceptable canonical coordinates to be used when quantizing dynamical systems.  This paper answered a central question that had been nagging Bohr and Einstein and Ehrenfest for years—how to quantize dynamical coordinates.  Despite the simple way that Bohr’s quantized hydrogen atom is taught in modern physics, there was an ambiguity in the quantization conditions even for this simple single-electron atom.  The ambiguity arose from the numerous possible canonical coordinate transformations that were admissible, yet which led to different forms of quantized motion. 

Schwarzschild’s proposal of action-angle variables for quantization of dynamical systems.

 Schwarzschild’s doctoral thesis had been a theoretical topic in astrophysics that applied the celestial mechanics theories of Henri Poincaré to binary star systems.  Within Poincaré’s theory were integral invariants that were conserved quantities of the motion.  When a dynamical system had as many constraints as degrees of freedom, then every coordinate had an integral invariant.  In this unexpected last paper from Schwarzschild, he showed how canonical transformation to action-angle coordinates produced a unique representation in terms of action variables (whose dimensions are the same as Planck’s constant).  These action coordinates, with their associated cyclical angle variables, are the only unambiguous representations that can be quantized.  The important points of this paper were amplified a few months later in a publication by Schwarzschild’s friend Paul Epstein (1871 – 1939), solidifying this approach to quantum mechanics.  Paul Ehrenfest (1880 – 1933) continued this work later in 1916 by defining adiabatic invariants whose quantum numbers remain unchanged under slowly varying conditions, and the program started by Schwarzschild was definitively completed by Paul Dirac (1902 – 1984) at the dawn of quantum mechanics in Göttingen in 1925.

Albert Einstein (1879 – 1955)

In 1916 Einstein was mopping up after publishing his definitive field equations of general relativity the year before.  His interests were still cast wide, not restricted only to this latest project.  In the 1916 Jan. to June volume of the Prussian Academy Einstein published two papers.  Each is remarkably short relative to the other papers in the volume, yet the importance of the papers may stand in inverse proportion to their length.

The first paper (pg. 184) is placed right before Schwarzschild’s first paper on February 3.  The subject of the paper is the expression of Maxwell’s equations in four-dimensional space time.  It is notable and ironic that Einstein mentions Hermann Minkowski (1864 – 1909) in the first sentence of the paper.  When Minkowski proposed his bold structure of spacetime in 1908, Einstein had been one of his harshest critics, writing letters to the editor about the absurdity of thinking of space and time as a single interchangeable coordinate system.  This is ironic, because Einstein today is perhaps best known for the special relativity properties of spacetime, yet he was slow to adopt the spacetime viewpoint. Einstein only came around to spacetime when he realized around 1910 that a general approach to relativity required the mathematical structure of tensor manifolds, and Minkowski had provided just such a manifold—the pseudo-Riemannian manifold of space time.  Einstein subsequently adopted spacetime with a passion and became its greatest champion, calling out Minkowski where possible to give him his due, although he had already died tragically of a burst appendix in 1909.

Relativistic energy density of electromagnetic fields.

The importance of Einstein’s paper hinges on his derivation of the electromagnetic field energy density using electromagnetic four vectors.  The energy density is part of the source term for his general relativity field equations.  Any form of energy density can warp spacetime, including electromagnetic field energy.  Furthermore, the Einstein field equations of general relativity are nonlinear as gravitational fields modify space and space modifies electromagnetic fields, producing a coupling between gravity and electromagnetism.  This coupling is implicit in the case of the bending of light by gravity, but Einstein’s paper from 1916 makes the connection explicit. 

Einstein’s second paper (pg. 688) is even shorter and hence one of the most daring publications of his career.  Because the field equations of general relativity are nonlinear, they are not easy to solve exactly, and Einstein was exploring approximate solutions under conditions of slow speeds and weak fields.  In this “non-relativistic” limit the metric tensor separates into a Minkowski metric as a background on which a small metric perturbation remains.  This small perturbation has the properties of a wave equation for a disturbance of the gravitational field that propagates at the speed of light.  Hence, in the June 22 issue of the Prussian Academy in 1916, Einstein predicts the existence and the properties of gravitational waves.  Exactly one hundred years later in 2016, the LIGO collaboration announced the detection of gravitational waves generated by the merger of two black holes.

Einstein’s weak-field low-velocity approximation solutions of his field equations.
Einstein’s prediction of gravitational waves.

Max Planck (1858 – 1947)

Max Planck was active as the secretary of the Prussian Academy in 1916 yet was still fully active in his research.  Although he had launched the quantum revolution with his quantum hypothesis of 1900, he was not a major proponent of quantum theory even as late as 1916.  His primary interests lay in thermodynamics and the origins of entropy, following the theoretical approaches of Ludwig Boltzmann (1844 – 1906).  In 1916 he was interested in how to best partition phase space as a way to count states and calculate entropy from first principles.  His paper in the 1916 volume (pg. 653) calculated the entropy for single-atom solids.

Counting microstates by Planck.

Max Born (1882 – 1970)

Max Born was to be one of the leading champions of the quantum mechanical revolution based at the University of Göttingen in the 1920’s. But in 1916 he was on leave from the University of Berlin working on ranging for artillery.  Yet he still pursued his academic interests, like Schwarzschild.  On pg. 614 in the Proceedings of the Prussian Academy, Born published a paper on anisotropic liquids, such as liquid crystals and the effect of electric fields on them.  It is astonishing to think that so many of the flat-panel displays we have today, whether on our watches or smart phones, are technological descendants of work by Born at the beginning of his career.

Born on liquid crystals.

Ferdinand Frobenius (1849 – 1917)

Like Schwarzschild, Frobenius was at the end of his career in 1916 and would pass away one year later, but unlike Schwarzschild, his career had been a long one, receiving his doctorate under Weierstrass and exploring elliptic functions, differential equations, number theory and group theory.  One of the papers that established him in group theory appears in the May 4th issue on page 542 where he explores the series expansion of a group.

Frobenious on groups.

Heinrich Rubens (1865 – 1922)

Max Planck owed his quantum breakthrough in part to the exquisitely accurate experimental measurements made by Heinrich Rubens on black body radiation.  It was only by the precise shape of what came to be called the Planck spectrum that Planck could say with such confidence that his theory of quantized radiation interactions fit Rubens spectrum so perfectly.  In 1916 Rubens was at the University of Berlin, having taken the position vacated by Paul Drude in 1906.  He was a specialist in infrared spectroscopy, and on page 167 of the Proceedings he describes the spectrum of steam and its consequences for the quantum theory.

Rubens and the infrared spectrum of steam.

Emil Warburg (1946 – 1931)

Emil Warburg’s fame is primarily as the father of Otto Warburg who won the 1931 Nobel prize in physiology.  On page 314 Warburg reports on photochemical processes in BrH gases.     In an obscure and very indirect way, I am an academic descendant of Emil Warburg.  One of his students was Robert Pohl who was a famous early researcher in solid state physics, sometimes called the “father of solid state physics”.  Pohl was at the physics department in Göttingen in the 1920’s along with Born and Franck during the golden age of quantum mechanics.  Robert Pohl’s son, Robert Otto Pohl, was my professor when I was a sophomore at Cornell University in 1978 for the course on introductory electromagnetism using a textbook by the Nobel laureate Edward Purcell, a quirky volume of the Berkeley Series of physics textbooks.  This makes Emil Warburg my professor’s father’s professor.

Warburg on photochemistry.

Papers in the 1916 Vol. 1 of the Prussian Academy of Sciences

Schulze,  Alt– und Neuindisches

Orth,  Zur Frage nach den Beziehungen des Alkoholismus zur Tuberkulose

Schulze,  Die Erhabunen auf der Lippin- und Wangenschleimhaut der Säugetiere

von Wilamwitz-Moellendorff, Die Samie des Menandros

Engler,  Bericht über das >>Pflanzenreich<<

von Harnack,  Bericht über die Ausgabe der griechischen Kirchenväter der dri ersten Jahrhunderte

Meinecke,  Germanischer und romanischer Geist im Wandel der deutschen Geschichtsauffassung

Rubens und Hettner,  Das langwellige Wasserdampfspektrum und seine Deutung durch die Quantentheorie

Einstein,  Eine neue formale Deutung der Maxwellschen Feldgleichungen der Electrodynamic

Schwarschild,  Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie

Helmreich,  Handschriftliche Verbesserungen zu dem Hippokratesglossar des Galen

Prager,  Über die Periode des veränderlichen Sterns RR Lyrae

Holl,  Die Zeitfolge des ersten origenistischen Streits

Lüders,  Zu den Upanisads. I. Die Samvargavidya

Warburg,  Über den Energieumsatz bei photochemischen Vorgängen in Gasen. VI.

Hellman,  Über die ägyptischen Witterungsangaben im Kalender von Claudius Ptolemaeus

Meyer-Lübke,  Die Diphthonge im Provenzaslischen

Diels,  Über die Schrift Antipocras des Nikolaus von Polen

Müller und Sieg,  Maitrisimit und >>Tocharisch<<

Meyer,  Ein altirischer Heilsegen

Schwarzschild,  Über das Gravitationasfeld einer Kugel aus inkompressibler Flüssigkeit nach der Einsteinschen Theorie

Brauer,  Die Verbreitung der Hyracoiden

Correns,  Untersuchungen über Geschlechtsbestimmung bei Distelarten

Brahn,  Weitere Untersuchungen über Fermente in der Lever von Krebskranken

Erdmann,  Methodologische Konsequenzen aus der Theorie der Abstraktion

Bang,  Studien zur vergleichenden Grammatik der Türksprachen. I.

Frobenius,  Über die  Kompositionsreihe einer Gruppe

Schwarzschild,  Zur Quantenhypothese

Fischer und Bergmann,  Über neue Galloylderivate des Traubenzuckers und ihren Vergleich mit der Chebulinsäure

Schuchhardt,  Der starke Wall und die breite, zuweilen erhöhte Berme bei frügeschichtlichen Burgen in Norddeutschland

Born,  Über anisotrope Flüssigkeiten

Planck,  Über die absolute Entropie einatomiger Körper

Haberlandt,  Blattepidermis und Lichtperzeption

Einstein,  Näherungsweise Integration der Feldgleichungen der Gravitation

Lüders,  Die Saubhikas.  Ein Beitrag zur Gecschichte des indischen Dramas

Dirac: From Quantum Field Theory to Antimatter

Paul Adrian Maurice Dirac (1902 – 1984) was given the moniker of “the strangest man” by Niels Bohr while he was reminiscing about the many great scientists with whom he had worked over the years [1].  It is a moniker that resonates with the innumerable “Dirac stories” that abound in the mythology of the hallways of physics departments around the world.  Dirac was awkward, shy, a loner, rarely said anything, was completely literal, had not the slightest comprehension of art or poetry, nor any clear understanding of human interpersonal interaction.  Dirac was also brilliant, providing the theoretical foundation for the central paradigm of modern physics—quantum field theory.  The discovery of the Higgs boson in 2012, a human achievement that capped nearly a century of scientific endeavor, rests solidly on the theory of quantum fields that permeate space.  The Higgs particle, when it pops into existence at the Large Hadron Collider in Geneva, is a singular quantum excitation of the Higgs field, a field that usually resides in a vacuum state, frothing with quantum fluctuations that imbue all particles—and you and me—with mass.  The Higgs field is Dirac’s legacy.

… all of a sudden he had a new equation with four-dimensional space-time symmetry.

Copenhagen and Bohr

Although Dirac as a young scientist was initially enthralled with relativity theory, he was working under Ralph Fowler (1889 – 1944) in the physics department at Cambridge in 1923 when he had the chance to read advanced proofs of Heisenberg’s matrix mechanics paper.  This chance event launched him on his own trajectory in quantum theory.  After Dirac was awarded his doctorate from Cambridge in 1926, he received a stipend that sent him to work with Niels Bohr (1885 – 1962) in Copenhagen—ground zero of the new physics. During his time there, Dirac became famous for taking long walks across Copenhagen as he played about with things in his mind, performing mental juggling of abstract symbols, envisioning how they would permute and act.  His attention was focused on the electromagnetic field and how it interacted with the quantized states of atoms.  Although the electromagnetic field was the classical field of light, it was also the quantum field of Einstein’s photon, and he wondered how the quantized harmonic oscillators of the electromagnetic field could be generated by quantum wavefunctions acting as operators.  But acting on what?  He decided that, to generate a photon, the wavefunction must operate on a state that had no photons—the ground state of the electromagnetic field known as the vacuum state.

            In late 1926, nearing the end of his stay in Copenhagen with Bohr, Dirac put these thoughts into their appropriate mathematical form and began work on two successive manuscripts.  The first manuscript contained the theoretical details of the non-commuting electromagnetic field operators.  He called the process of generating photons out of the vacuum “second quantization”.  This phrase is a bit of a misnomer, because there is no specific “first quantization” per se, although he was probably thinking of the quantized energy levels of Schrödinger and Heisenberg.  In second quantization, the classical field of electromagnetism is converted to an operator that generates quanta of the associated quantum field out of the vacuum (and also annihilates photons back into the vacuum).  The creation operators can be applied again and again to build up an N-photon state containing N photons that obey Bose-Einstein statistics, as they must, as required by their integer spin, agreeing with Planck’s blackbody radiation. 

            Dirac then went further to show how an interaction of the quantized electromagnetic field with quantized energy levels involved the annihilation and creation of photons as they promoted electrons to higher atomic energy levels, or demoted them through stimulated emission.  Very significantly, Dirac’s new theory explained the spontaneous emission of light from an excited electron level as a direct physical process that creates a photon carrying away the energy as the electron falls to a lower energy level.  Spontaneous emission had been explained first by Einstein more than ten years earlier when he derived the famous A and B coefficients, but Einstein’s arguments were based on the principle of detailed balance, which is a thermodynamic argument.  It is impressive that Einstein’s deep understanding of thermodynamics and statistical mechanics could allow him to derive the necessity of both spontaneous and stimulated emission, but the physical mechanism for these processes was inferred rather than derived. Dirac, in late 1926, had produced the first direct theory of photon exchange with matter.  This was the birth of quantum electrodynamics, known as QED, and the birth of quantum field theory [2].

Fig. 1 Paul Dirac in his early days.

Göttingen and Born

            Dirac’s next stop on his postodctoral fellowship was in Göttingen to work with Max Born (1882 – 1970) and the large group of theoreticians and mathematicians who were like electrons in a cloud orbiting around the nucleus represented by the new quantum theory.  Göttingen was second only to Copenhagen as the Mecca for quantum theorists.  Hilbert was there and von Neumann too, as well as the brash American J. Robert Oppenheimer (1904 – 1967) who was finishing his PhD with Born.  Dirac and Oppenheimer struck up an awkward friendship.  Oppenheimer was considered arrogant by many others in the group, but he was in awe of Dirac who arrived with his manuscript on quantum electrodynamics ready for submission.  Oppenheimer struggled at first to understand Dirac’s new approach to quantizing fields, but he quickly grasped the importance, as did Pascual Jordan (1902 – 1980), who was also in Göttingen.

            Jordan had already worked on ideas very close to Dirac’s on the quantization of fields.  He and Dirac seemed to be going down the same path, independently arriving at very similar conclusions around the same time.  In fact, Jordan was often a step ahead of Dirac, tending to publish just before Dirac, as with non-commuting matrices, transformation theory and the relationship of canonical transformations to second quantization.  However, Dirac’s paper on quantum electrodynamics was a masterpiece in clarity and comprehensiveness, launching a new field in a way that Jordan had not yet achieved with his own work.  But because of the closeness of Jordan’s thinking to Dirac’s, he was able to see immediately how to extend Dirac’s approach.  Within the year, he published a series of papers that established the formalism of quantum electrodynamics as well as quantum field theory.  With Pauli, he systematized the operators for creation and annihilation of photons [3].  With Wigner, he developed second quantization for de Broglie matter waves, defining creation and annihilation operators that obeyed the Pauli exclusion principle of electrons[4].  Jordan was on a roll, forging ahead of Dirac on extensions of quantum electrodynamics and field theory, but Dirac was about to eclipse Jordan once and for all.

St. John’s at Cambridge

            At the end of the Spring semester in 1927, Dirac was offered a position as a fellow of St. John’s College at Cambridge, which he accepted, returning to England to begin his life as a college professor.  During the summer and into the Fall, Dirac returned to his first passion in physics, relativity, which had yet to be successfully incorporated into quantum physics.  Oskar Klein and Walter Gordon had made initial attempts at formulating relativistic quantum theory, but they could not correctly incorporate the spin properties of the electron, and their wave equation had the bad habit of producing negative probabilities.  Probabilities went negative because the Klein-Gordon equation had two time derivatives instead of one.  The reason it had two (while the non-relativistic Schrödinger equation has only one) is because space-time symmetry required the double space derivative of the Schrödinger equation to be paired with a double time derivative.  Dirac, with creative insight, realized that the problem could be flipped by requiring the single time derivative to be paired with a single space derivative.  The problem was that a single space derivative did not seem to make any sense [5].

St. John’s College at Cambridge

            As Dirac puzzled how to get an equation with only single derivatives, he was playing around with Pauli spin matrices and hit on a simple identity that related the spin matrices to the electron momentum.  At first he could not get the identity to apply to four-dimensional relativistic momenta using the usual 2×2 spin matrices.  Then he realized that four-dimensional space-time could be captured if he expanded Pauli’s 2×2 spin matrices to 4×4 spin matrices, and all of a sudden he had a new equation with four-dimensional space-time symmetry with single derivatives on space and time.  As a test of his new equation, he calculated fine details of the experimentally-measured hydrogen spectrum, known as the fine structure, which had resisted theoretical explanation, and he derived answers in close agreement with experiment.  He also showed that the electron had spin-1/2, and he calculated its magnetic moment.  He finished his manuscript at the end of the Fall semester in 1927, and the paper was published in early 1928[6].  His relativistic quantum wave equation was an instant sensation, becoming known for all time as “the Dirac Equation”.  He had succeeded at finding a correct and long-sought relativistic quantum theory where many before had failed.  It was a crowning achievment, placing Dirac firmly in the firmament of the quantum theorists.

Fig. 1 The relativistic Dirac equation. The wavefunction is a four-component spinor. The gamma-del product is a 4×4 matrix operator. The time and space derivatives are both first-order operators.

Antimatter

            In the process of ridding the Klein-Gordon equation of negative probability, which Dirac found abhorent, his new equation created an infinite number of negative energy states, which he did not find abhorent.  It is perhaps a matter of taste what one theoriest is willing to accept over another, and for Dirac, negative energies were better than negative probabilities.  Even so, one needed to deal with an infinite number of negative energy states in quantum theory, because they are available to quantum transitions.  In 1929 and 1930, as Dirac was writing his famous textbook on quantum theory, he became intrigued by the similarity between the positive and negative electron states of the vacuum and the energy levels of valence electrons on atoms.  An electron in a state outside a filled electron shell behaves very much like a single-electron atom, like sodium and lithium with their single valence electrons.  Conversely, an atomic shell that has one electron less than a full complement can be described as having a “hole” that behaves “as if” it were a positive particle.  It is like a bubble in water.  As water sinks, the bubble rises to the top of the water level.  For electrons, if all the electrons go one way in an electric field, then the hole goes the opposite direction, like a positive charge. 

            Dirac took this analogy of nearly-filled atomic shells and applied it to the vacuum states of the electron, viewing the filled negative energy states like the filled electron shells of atoms.  If there is a missing electron, a hole in this infinite sea, then it would behave as if it had positive charge.  Initially, Dirac speculated that the “hole” was the proton, and he even wrote a paper on that possibility.  But Oppenheimer pointed out that the idea was inconsistent with observations, especially the inability of the electron and proton to annihilate, and that the ground state of the infinite electron sea must be completely filled. Hermann Weyl further pointed out that the electron-proton theory did not have the correct symmetry, and Dirac had to rethink.  In early 1931 he hit on an audacious solution to the puzzle.  What if the hole in the infinite negative energy sea did not just behave like a positive particle, but actually was a positive particle, a new particle that Dirac dubbed the “anti-electron”?  The anti-electron would have the same mass as the electron, but would have positive charge. He suggested that such particles might be generated in high-energy collisions in vacuum, and he finished his paper with the suggestion that there also could be an anti-proton with the mass of the proton but with negative charge.  In this singular paper, titled “Quantized Singularities of the Electromagnetic Field” published in 1931, Dirac predicted the existence of antimatter.  A year later the positron was discovered by Carl David Anderson at Cal Tech.  Anderson had originally called the particle the positive electron, but a journal editor of the Physical Review changed it to positron, and the new name stuck.

Fig. 3 An electron-positron pair is created by the absorption of a photon (gamma ray). Positrons have negative energy and can be viewed as a hole in a sea of filled electron states. (Momentum conservation is satisfied if a near-by heavy particle takes up the recoil momentum.)

            The prediction and subsequent experimental validation of antmatter stands out in the history of physics in the 20th Century.  In previous centuries, theory was performed mainly in the service of experiment, explaining interesting new observed phenomena either as consequences of known physics, or creating new physics to explain the observations.  Quantum theory, revolutionary as a way of understanding nature, was developed to explain spectroscopic observations of atoms and molecules and gases.  Similarly, the precession of the perihelion of Mercury was a well-known phenomenon when Einstein used his newly developed general relativity to explain it.  As a counter example, Einstein’s prediction of the deflection of light by the Sun was something new that emerged from theory.  This is one reason why Einstein became so famous after Eddington’s expedition to observe the deflection of apparent star locations during the total eclipse.  Einstein had predicted something that had never been seen before.  Dirac’s prediction of the existence of antimatter similarly is a triumph of rational thought, following the mathematical representation of reality to an inevitable conclusion that cannot be ignored, no matter how wild and initially unimaginable it is.  Dirac went on to receive the Nobel prize in Physics in 1933, sharing the prize that year with Schrödinger (Heisenberg won it the previous year in 1932).


[1] Framelo, “The Strangest Man: The Hidden Life of Paul Dirac” (Basic Books, 2011)

[2] Dirac, P. A. M. (1927). “The quantum theory of the emission and absorption of radiation.” Proceedings of the Royal Society of London Series A114(767): 243-265.;  Dirac, P. A. M. (1927). “The quantum theory of dispersion.” Proceedings of the Royal Society of London Series A114(769): 710-728.

[3] Jordan, P. and W. Pauli, Jr. (1928). “To quantum electrodynamics of free charge fields.” Zeitschrift Fur Physik 47(3-4): 151-173.

[4] Jordan, P. and E. Wigner (1928). “About the Pauli’s equivalence prohibited.” Zeitschrift Fur Physik 47(9-10): 631-651.

[5] This is because two space derivatives measure the curvative of the wavefunction which is related to the kinetic energy of the electron.

[6] Dirac, P. A. M. (1928). “The quantum theory of the electron.” Proceedings of the Royal Society of London Series A 117(778): 610-624.;  Dirac, P. A. M. (1928). “The quantum theory of the electron – Part II.” Proceedings of the Royal Society of London Series A118(779): 351-361.