# Modern Physics: An Historical Overview of the Development of Quantum Mechanics, Quantum Field Theory, Relativity, and Cosmology

This timeline is is a greatly expanded version of that presented in Wikipedia’s article on the history of quantum mechanics, with milestones in the development of Relativity, cosmology, and particle physics also included due to their overlap in attempts to construct a Theory of Everything (TOE). Where possible, I’ve included references to the original founding documents related to each development, along with links to online copies of the original articles (or English translations thereof) where available. Please note that some of these documents are accessible by subscription only. In such cases, the articles should be viewable from the networks of institutions with site license access, such as universities or larger libraries.

## The Era of Classical Physics, and Cracks in its Foundations (Antiquity-1899)

c. 624 BCE – c. 546 BCE – Thales of Miletus (Θαλῆς ὁ Μιλήσιος), considered by many to be the “Father of Science,” predicted a solar eclipse which halted the Battle of Halys between the Lydians and Medes. Thales’ rejection of mythological explanations for natural phenomena marked the birth of the Greek tradition of Western philosophy.

c. 570 BCE – c. 495 BCE – Pythagoras of Samos (Ὁ Πυθαγόρας ὁ Σάμιος), Ionian philosopher and mathematician, was credited with many advancements in mathematics and philosophy, including the Pythagorean theorem and the Pythagorean tuning system of music (which produces purer harmonies than modern twelve tone equal temperament tuning, but without the ability to span octaves without introducing discordance).

c. 510 BCE – 428 BCE – Anaxagoras (Ἀναξαγόρας) brought philosophy to Athens, and considered matter as consisting of indestructible primary elements. He held that matter could neither be created nor destroyed, but merely modified by rearrangement of these primary elements.  This view constituted an early conservation law.

c. 490 BCE – 430 BCE – Empedocles (Ἐμπεδοκλῆς) elaborated on the ideas of Anaxagoras and originated the theory of the four Classical Elements.

c. 460 BCE – c. 370 BCE – Democritus (Δημόκριτος) espoused an early version of atomic theory.

c. 384 BCE – c 322 BCE – Aristotle (Ἀριστοτέλης) formulated an early system of physics. Although deeply flawed, Aristotelian physics held sway until the era of Galileo and Newton.

c. 310 BCE – c. 230 BCE – Aristarchus (Ἀρίσταρχος) of Samos formulated a heliocentric model of the solar system. No copies of his work on the subject survive, but there are references to it in Archimedes’ The Sand Reckoner (Archimedis Syracusani Arenarius & Dimensio Circuli)

c. 300 BCE – Euclid (Εὐκλείδης) of Alexandria developed the axiomatic principles of what is now known as Euclidean geometry, described in his book, Elements, which is widely regarded as being the most influential textbook ever written.

c. 297 BCE – c. 212 BCE – Archimedes (Ἀρχιμήδης) of Syracuse, Greek mathematician, physicist, engineer, inventor, and astronomer, made many advances in the fields of hydrostatics, statics, and mechanics, as well as inventing the “method of exhaustion,” a mechanism for calculating the area under a parabolic arc, presaging the later development of integral calculus.

c. 276 BCE – c. 195 BCE – Eratosthenes (Ἐρατοσθένης) of Cyrene was the father of geography, inventing the first system of latitude and longitude. He is also credited with having performed a remarkably accurate measurement of the circumference of the Earth (yielding a value within 2% of modern measured values). When Columbus set sail in 1492 AD, he was relying upon a later and far less accurate measurement for his navigation.

c. 10 CE – 70 CE – Heron of Alexandria (Ἥρων ὁ Ἀλεξανδρεύς), Hellenistic Egyption engineer and mathematician, came to be widely known for numerous hydraulic and steam-powered inventions, including a crude precursor to the steam engine.

c. 90 CE – c. 168 CE – Claudius Ptolemy (Κλαύδιος Πτολεμαῖος) of Alexandria, Greco-Roman Egyptian mathematician, astronomer, astrologer, and geographer, was noted for three main written works: The Almagest, the Geographia, and the Tetrabiblos. His formulation of the ancient geocentric cosmological model was widely accepted until the rise of the geocentric Copernican model.

c. 201 CE – 298 CE – Diophantus of Alexandria (Διόφαντος ὁ Ἀλεξανδρεύς) developed an early form of algebra known as Diophantine analysis, published in a series of books known as Arithmetica. (An English translation of Arithmetica is included in the book Diophantus of Alexandria; a study in the history of Greek algebra by Sir Thomas Little Heath, 1910.)

c. 370 CE – 415 CE – Hypatia (Ὑπατία) of Alexandria, a Neoplatonist philosopher, mathematician, and astronomer, was tortured and murdered by a mob of Christian monks as part of a political power struggle over the control of Alexandria. Her death is widely regarded as marking the end of the Classical era of science and philosophy.

c. 780 CE – 850 CE, Abū ʿAbdallāh Muḥammad ibn Mūsā al-Khwārizmī  (محمد بن موسى الخوارزميّ المجوسـيّ القطربّـليّ), a Persian astronomer, mathematician, and geographer, elaborated on earlier development of algebra with his tome, Al-Kitāb al-mukhtaṣar fī hīsāb al-ğabr wa’l-muqābala or الكتاب المختصر في حساب الجبر والمقابلة (The Compendious Book on Calculation by Completion and Balancing). It is from the word “al-ğabr” that we obtain the word algebra.

965 CE – c. 1040 CE, Abū ʿAlī al-Ḥasan ibn al-Ḥasan ibn al-Haytham ( أبو علي، الحسن بن الحسن بن الهيثم), the Muslim scientist also known as Alhazen, developed concepts regarding motion, gravity, and optics which would later be rediscovered by Galileo and Newton.

c. 1214 – 1294 – Roger Bacon, an English philosopher and Fransiscan friar, emphasized what is now called the scientific method, the development of deductive theories based upon observational evidence from the natural world.

1543 – Nicolaus Copernicus published De revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres), in which he argued for a heliocentric model of the solar system.

1573 – Tycho Brahe (Tyge Ottesen Brahe), a Danish nobleman, published De nova stella et nullius ævi memoria prius visa stella, which chronicled his observations of supernova in 1573 (in the process, coining the term “nova” for such “new stars”).  He was able to establish that the nova lacked parallax, and thus could not be as near the Earth. Over the course of his career, he conducted extensive and detailed observations of the stars and planets without the aid of a telescope.

1588 – Tycho Braha published the first volume of  Astronomiæ Instauratæ Progymnasmata (“Introduction to the New Astronomy”), focucing mainly on his observations of the 1572 supernova. The remaining two volumes were not published until after his death.

1600 – Giordano Bruno, Italian Dominican friar, philosopher, astronomer, and mathematician, was burned at the stake after being found guilty of heresy by the Inquisition for advocating the notion that the Sun is merely a star, and that there might be other inhabited worlds orbiting other stars.

1609 – Johannes Kepler, a German astronomer and mathematician, published Astronomia nova, in which he laid out two of his three laws of planetary motion, derived from Tycho Brahe’s observations of the orbit of Mars.

1619 – Kepler published Harmonices Mundi (excerpts in English here), which included a section describing his third law of planetary motion.

Kepler’s Laws of Planetary Motion

1. The Law of Orbits: Planets orbit the sun in elliptical orbits, with the Sun at one of the two foci of the ellipse.

2. The Law of Areas: An imaginary line from the sun to the planet sweeps out equal areas in equal times.

3. The Law of Periods: The square of the period of a planet’s orbit is proportional to the cube of the semi-major axis of the the orbit.

1632 – Galileo Galilei published Dialogo sopra i due massimi sistemi del mondo (Dialogue Concerning the Two Chief World Systems). It was this work, a discourse comparing Ptolemaic and Copernican views of the solar system, which resulted in Galileo being convicted of “grave suspicion of heresy.”

1685 – Sir Isaac Newton wrote a precursor to the Principia, published in English posthumously under the title A Treatise of the System of the World.

1687 – Sir Isaac Newton published Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy). (online: Book 1, Books 2 & 3)

1704 – Sir Isaac Newton published Opticks: or, a Treatise of the Reflexions, Refractions, Inflexions and Colours of Light.

1736 – Sir Isaac Newton published The Method of Fluxions and Infinite Series; with its Application to the Geometry of Curve-Lines, his book on differential calculus. (He referred to integral calculus as “fluents.”)

1785-1789 – Charles-Augustin de Coulomb published a series of papers on his observations of electrodynamics, the first and second of which laid out what is now known as Coulomb’s Law.

Coulomb (1785) “Premier mémoire sur l’électricité et le magnétisme,” Histoire de l’Académie Royale des Sciences, pages 569-577.

Coulomb (1785) “Second mémoire sur l’électricité et le magnétisme,” Histoire de l’Académie Royale des Sciences, pages 578-611.

Coulomb (1785) “Troisième mémoire sur l’électricité et le magnétisme,” Histoire de l’Académie Royale des Sciences, pages 612-638.

Coulomb (1786) “Quatrième mémoire sur l’électricité,” Histoire de l’Académie Royale des Sciences, pages 67-77.

Coulomb (1787) “Cinquième mémoire sur l’électricité,” Histoire de l’Académie Royale des Sciences, pages 421-467.

Coulomb (1788) “Sixième mémoire sur l’électricité,” Histoire de l’Académie Royale des Sciences, pages 617-705.

Coulomb (1789) “Septième mémoire sur l’électricité et le magnétisme,” Histoire de l’Académie Royale des Sciences, pages 455-505.

Thomas Young’s sketch of two-slit diffraction of light. Narrow slits at A and B act as sources, and waves interfering in various phases are shown at C, D, E, and F. Young presented the results of this experiment to the Royal Society in 1803. (Image courtesy of Wikimedia Commons.)

1801-1804 – Thomas Young performed the double-slit experiment, demonstrating the wavelike nature of light. An excellent article on accurately reproducing the experiment can be found here.

T. Young, “Experimental Demonstration of the General Law of the Interference of Light”, Philosophical Transactions of the Royal Society of London, vol 94 (1804)

1812 – Michael Faraday constructed a voltaic pile (a simple battery) from seven halfpence coins stacked with interleaved sheets of zinc and pieces of paper soaked in salt water.

1820 – Hans Christian Ørsted discovered that an electric current produces a magnetic field.

1821 – Michael Faraday, inspired by Ørsted’s discovery,  constructed the first crude electric motor.

1826 – André-Marie Ampère published Mémoire sur la théorie mathématique des phénomènes électrodynamiques uniquement déduite de l’experience (“Memoir on the Mathematical Theory of Electrodynamic Phenomena, Uniquely Deduced from Experience”) in which he introduced the mathematical formulation of Ørsted’s discovery, known as Ampère’s Law.

1831 – Faraday began a series of experiments in which he discovered electromagnetic induction.

1831-1835 – Joseph Henry conducted a series of experiments in which he discovered electromagnetic induction (concurrently with and independently of Faraday) and self-induction, as well as perfecting the electromagnet and inventing the electric relay. He also worked on early electric motor designs.

1831, 1844 – Faraday published two volumes on his experiments with electricity, Experimental Researches in Electricity, vols. i. and ii.

1835 – Johann Carl Friedrich Gauss, one of the most prolific mathematicians and physicists of his day, formulated what we now know as Gauss’s Law, which relates electric charge distribution to the resulting electric field.

1855-56 – James Clerk Maxwell delivered a two-part paper providing a mathematical analysis of Faraday’s work.

James C. Maxwell, “On Faraday’s Lines of Force“, Transactions of the Cambridge Philosophical Society, Vol. X Part I (Dec. 10, 1855)

James C. Maxwell, “On Faraday’s Lines of Force, Part II: On Faraday’s ‘Electro-tonic State’“, Transactions of the Cambridge Philosophical Society, Vol. X, Part II (Feb. 11, 1856)

1861-1862 – James Clerk Maxwell consolidated the work of Gauss, Faraday, and Ampère in a four part paper, “On Physical Lines of Force,” in which he presents what are now known as Maxwell’s Equations. In retrospect, Maxwellian electrodynamics represents the first (and simplest) gauge field theory, as well as the first step towards grand unification of the fundamental forces of nature.

### Maxwell’s Equations:

Gauss’s Law: $\nabla \cdot \mathbf{D} = \rho_f$

Gauss’s Law for Magnetism: $\nabla \cdot \mathbf{B} = 0$

Faraday’s Law of Induction: $\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}$

Ampère’s Law: $\nabla \times \mathbf{H} = \mathbf{J}_f + \frac{\partial \mathbf{D}}{\partial t}$

James C. Maxwell (1861). “On Physical Lines of Force“. Philosophical Magazine. Vol. 21 & 23 Series 4, Part I-IV. (Also here.)

1865 – James Clerk Maxwell published “A Dynamical Theory of the Electromagnetic Field,” in which he demonstrated that light is an electromagnetic phenomenon.

Maxwell, James Clerk (1865). “A dynamical theory of the electromagnetic field” (PDF). Philosophical Transactions of the Royal Society of London 155: 459–512. doi:10.1098/rstl.1865.0008 (Also here.)

1873 – Maxwell published A Treatise on Electricity and Magnetism, a two-volume textbook encompassing his earlier work on the subject.

James C. Maxwell, A Treatise on Electricity and MagnetismOxford: Clarendon Press (1873).

1874 – George Johnstone Stoney postulated the existence of the electron has a fundamental quantity of electricity.  He introduced the word “electron” itself in 1891.  See  Stoney, G.J. (1894). “Of the “Electron,” or Atom of Electricity”. Philosophical Magazine 38 (5): 418-420.  doi:10.1080/14786449408620653

1877 – Ludwig Boltzmann suggested that the energy states of a physical system could be discrete. He used this primarily as a mathematical tool, subdividing the energy continuum into cells or elements in order to construct a probabilistic derivation in his calculations of entropy and velocity distribution in a gas.

L. Boltzmann, “Über die Beziehung eines allgemeine mechanischen Satzes zum zweiten Hauptsatze der Warmetheorie” (“On the Relation of a General Mechanical Theorem to the Second Law of Thermodynamics”), Sitzungsberichte Akad. Wiss., Vienna, part II, 75, 67–73 (1877); reprinted in Boltzmann’s Wissenschaftliche Abhandlungen, Vol. 2, Leipzig, J. A. Barth, 1909, pp. 116–22].

(English translation in Kinetic Theory, Vol. 2, by S.G. Brush, New York: Pergamon Press (1966), pp. 362-367.)

1885 – Johann Jakob Balmer discovered the Balmer series, visible light (with some ultraviolet) spectral lines of hydrogen corresponding to transitions to the n’=2 state. Balmer used this spectroscopic data to construct the Balmer formula:

$\lambda = B\left(\frac{m^2}{m^2-n^2}\right) = B\left(\frac{m^2}{m^2-2^2}\right)$

Balmer, J. J. (1885), “Notiz uber die Spectrallinien des Wasserstoffs“, Annalen der Physik 261 (5): 80–87, Bibcode: 1885AnP…261…80B, doi: 10.1002/andp.18852610506

1887 – By bending cathode rays in a vacuum tube with magnetic fields, J. J. Thomson measured the charge/mass ratio of the electron, establishing the corpuscular nature of electricity.

J.J. Thomson “Cathode rays”, Philosophical Magazine, 44, 293 (1897)

J.J. Thomson “On bodies smaller than atoms”, The Popular Science Monthly (Bonnier Corp.): pp.323–335 (August 1901)

1888 – Johannes Rydberg generalized the Balmer formula for all spectroscopic transitions in hydrogen by introducing the Rydberg formula:

$\frac{1}{\lambda_{vac}} = R \left(\frac{1}{n^2_1} - \frac{1}{n^2_2} \right)$

Rydberg, J. “Recherches sur la constitution des spectres d’émission des éléments chimiques,” in Kungliga Svenska vetenskapsakademiens handlingar, n.s. 23. no. 11 (1890)

1895 – Wilhelm Conrad Röntgen discovered X-rays.

1896-1897 – Pieter Zeeman observed the splitting of spectral lines in the presence of a static magnetic field (“The Zeeman effect“).

P. Zeeman. “On the influence of Magnetism on the Nature of the Light emitted by a Substance”. Phil. Mag. 43: 226. (1897). (Reprinted in The Effects of a Magnetic Field on Radiation: Memoirs by Faraday, Kerr, and Zeeman, edited by E.P. Lewis, American Book Company, NY (1900), pp.65-82)

P. Zeeman, “On the Influence of Magnetism on the Nature of the Light Emitted by a Substance”. Astrophysical Journal, 5:332 (1897)

P. Zeeman. “Doubles and triplets in the spectrum produced by external magnetic forces”. Phil. Mag. 44: 55. (1897). (Reprinted in The Effects of a Magnetic Field on Radiation: Memoirs by Faraday, Kerr, and Zeeman, edited by E.P. Lewis, American Book Company, NY (1900), pp. 83-97)

1896 – Henri Becquerel discovered radioactivity. His work was subsequently expanded upon by Pierre and Marie Curie.

Henri Becquerel. Sur les radiations émises par phosphorescence” (“On the rays emitted by phosphorescence”)Comptes Rendus 122: 420–421 (1896). (English translation by Carmen Giunta)

Henri Becquerel. “Sur les radiations invisibles émises par les corps phosphorescents” (“On the invisible rays emitted by phosphorescent bodies”). Comptes Rendus 122: 501 (1896). (English translation by Carmen Giunta)

## “Old quantum theory” (1900-1924)

Built on the work of Planck, Einstein, Bohr, and Sommerfeld, and others, “old quantum theory” was never fleshed-out as a fully complete or self-consistent theory, but provided a mechanism for performing calculations involving simple systems such as the hydrogen atom. This era also witnessed the birth of the Special and General Theory of Relativity.

1900-1901 – Max Planck introduced the concept of  energy “quanta” to avoid the “Ultraviolet Catastrophe” in the black body radiation problem, suggesting that electromagnetic energy could only be emitted in energies which are integer multiples of E = hν, where h is Planck’s constant, and ν is the frequency.

M. Planck, Ann. d. Phys. 1, p. 99 (1900)

Planck, Max. (1900). “Entropy and Temperature of Radiant Heat.” Annalen der Physik, 1, no 4. April, pg. 719–37.

M. Planck, “Über das Gesetz der Energieverteilung im Normalspektrum” (“On the Law of Distribution of Energy in the Normal Spectrum”). Annalen der Physik, 4, p. 553 ff (1901)

1900 – Poincaré defined what came to be known as the Poincaré Group of symmetry transformations, of which Lorentz transformations are a subset.

Henri Poincaré, (1900) “La theorie de Lorentz et la Principe de Reaction” (“The Theory of Lorentz and the Principle of Reaction“), Archives NeerlandaisesV, 253–78.

1901 – Frederick Soddy and Ernest Rutherford discovered nuclear transmutation when they observe the decay of thorium into radium.

E. Rutherford and F. Soddy. “The Cause and Nature of Radioactivity.” Philosophical Magazine, Sixth Series 4:370-396 (1902).

Albert Einstein c. 1904 (Image courtesy of Wikipedia.)

1905 – Albert Einstein publishes his four annus mirabilis papers:

Einstein, Albert (1905). “Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen” (“Investigations on the theory of Brownian Movement”). Annalen der Physik 17: 549–560. (in which Einstein used an analysis of Brownian Motion to prove John Dalton’s Atomic Theory of Matter)

Einstein, Albert (1905). “Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig?” (“Does the Inertia of a Body Depend Upon Its Energy Content?”). Annalen der Physik 18: 639–641 (Mass-energy equivalence in Special Relativity)*

* Interestingly enough, Einstein’s famous equation $E = mc^2$ appears nowhere in this paper. Instead, he expressed it in a different form. But, alas, $m = \frac{L}{c^2}$ does not roll off the tongue as smoothly.

1905-1906 – Henri Poincaré pointed out that Lorentz transformations are equivalent to rotations through 4-dimensional space-time with the time component being an imaginary quantity.

H. Poincaré, “Sur la dynamique de l’électron” (“On the Dynamics of the Electron”), Rendicontri del Circolo matematico di Palermo 21: 129-176 (1905,1906)

1906-1914 – Theodore Lyman discovered the Lyman series, ultraviolet spectral lines in hydrogen corresponding to transitions to the n’=1 state.

Lyman, Theodore (1906), “The Spectrum of Hydrogen in the Region of Extremely Short Wave-Length”, Memoirs of the American Academy of Arts and Sciences, New Series 13 (3): 125–146, ISSN 0096-6134, JSTOR 25058084

Lyman, Theodore (1914), “An Extension of the Spectrum in the Extreme Ultra-Violet”, Nature 93: 241, Bibcode 1914Natur..93..241L, doi:10.1038/093241a0

1907 – Einstein’s initial paper on General Relativity, in which he introduced the Correspondence Principle, the bending of light paths by gravity, and the extension of the equivalence of mass and energy to include gravitational mass as well as inertial mass.

A. Einstein, “On the relativity principle and the conclusions drawn from it”, Jahrbuch der Radioaktivitaet und Elektronik 4  [English translation in The Collected Papers of Albert Einstein, vol. 2 (tr. by Anna Beck and consultant Peter Havas), Princeton University Press, 1989.]

1907-1909 – Herman Minkowski expanded upon Poincaré’s work and constructed his famous Minkowski space-time geometry. This proved to be the appropriate space-time metric for Special Relativity. Later, with the development of General Relativity, the Minkowski metric came to be seen as an approximation of the locally-flat Reimann metric for an object in free-fall.

1907-1911 – Ernest Rutherford (assisted by Hans Geiger and Ernest Marsden) performed his scattering experiments, resulting in the nuclear model of the atom, disproving the “plum pudding model.” For an excellent informal account of this discovery, see “A Little Nut.”

H. Geiger. “On the Scattering of the alpha-particles by Matter.” Proceedings of the Royal Society, Series A 81:174 (1908)

H. Geiger and E. Marsden. “On a Diffuse Reflection of the alpha-particles.” Proceedings of the Royal Society, Series A 82:495 (1909)

E. Rutherford, “The Scattering of alpha and beta Particles by Matter and the Structure of the Atom”, Phil. Mag. 21, pp. 669-688 (1911)

1908 – Friedrich Pacshen discovered the Pacshen series, infrared spectroscopic lines in hydrogen corresponding to transitions to the n’=3 state.

Paschen, Friedrich (1908), “Zur Kenntnis ultraroter Linienspektra. I. (Normalwellenlängen bis 27000 Å.-E.)“, Annalen der Physik 332 (13): 537–570, Bibcode 1908AnP…332..537P, doi: 10.1002/andp.19083321303

1909 – Geoffrey Ingram Taylor demonstrated that interference patterns of light are present in Young’s slit diffraction experiment even when light passes through the apparatus one photon at a time, laying the foundations for the concept of wave-particle duality.

1911 – Einstein’s second paper laying the foundations of General Relativity, containing a specific prediction of the deflection of light rays by the sun and time dilation in a gravitational field.

A. Einstein, “Ueber den Einfluss der Schwerkraft auf die Ausbreitung des Lichtes”, Annalen der Physik 35, 1911, 898-908.

1911-1912 – Henri Poincaré published a groundbreaking (from the standpoint of the philosophy of science) analysis of the evolution of Natural Law, as well as a mathematical proof of Planck’s quanta. (Thus far, I have found little of his work translated into English, but much of his work in the original French is available herehere, and here.) An overview of Poincaré’s study of quantum phenomena is given by F.E. Irons, “Poincaré’s 1911-12 proof of quantum discontinuity interpreted as applying to atoms”, American Journal of Physics, Vol. 69, No. 8, pp. 879-884 (August 2001).

H. Poincaré, “L’evolution des lois” (“The Evolution of Laws”), Scientia, v. IX , pp. 275-292 (1911), (This essay on the evolution of our understanding of natural law was based upon a speech given at the Congresso di Filosofia di Bologna on 8 April 1911. It later was made into the first chapter of  his book, Dernières Pensées (Last Essays), published in Paris in 1913. Digital scans of this book can also be seen here.)

H. Poincaré, “Sur la theorie des quanta” (“On the Theory of Quanta”), Comptes Rendus de l’Academie des Sciences, 153:pp. 1103-1108 (1912)

H. Poincaré, “Sur la theorie des quanta” (“On the Theory of Quanta”), Journal de Physique theorique et appliquee, 2: pp. 5-34 (1912)

H. Poincaré, “L’hypothese des quanta” (“The Quanta Hypothesis”), Revue Scienti que, 50: pp. 225-232 (1912)

H. Poincaré, “Les rapports de la matiere et l’ether” (“Reports of Matter and Ether”), Journal de physique theorique et appliquee, ser 5, 2, pp. 347-360 (1912)

1912 – Victor Hess discovered cosmic radiation by sending aloft sensitive radiation detectors aboard high-altitude balloons, both manned and unmanned (the former at great risk to himself).

Nobel Prize in Physics 1936 – Presentation Speech

1912 – Einstein begins to realize that the relativistic theory of gravity he is developing cannot allow time to warp while keeping space flat.

A. Einstein, “Lichtgeschwindigkeit und Statik des Gravitationsfeldes”, Annalen der Physik (ser. 4)38, 355–369, link

A. Einstein “Theorie des statischen Gravitationsfeldes”, Annalen der Physik (ser. 4)38, 443–458, link

1913 – Einstein enlisted the help of his old ETH friend Marcel Grossmann to incorporate Riemannian geometry into his nascent theory of General Relativity.

A. Einstein & M. Grossmann, “Entwurf einer verallgemeinerten Relativitaetstheorie und einer Theorie der Gravitation”, Zeitschrift fuer Mathematik und Physik 62, 1913, 225-261.

1913 – Robert Millikan published the results of his famed oil drop experiment, in which he measured the charge of the electron. This measurement made it possible to calculate Avogadro’s number, thus enabling the determination of atomic weights.

Millikan, R. A. “On the Elementary Electric charge and the Avogadro Constant”. Phys. Rev. 2(2): 109–143 (1913)

1913 – Johannes Stark and Antonino Lo Surdo discovered the shifting and splitting of atomic spectra in the presence of an external electric field (the “Stark effect“).

J. Stark, “Beobachtungen über den Effekt des elektrischen Feldes auf Spektrallinien I. Quereffekt” (“Observations of the effect of the electric field on spectral lines I. Transverse effect”), Annalen der Physik, vol. 43, pp. 965-983 (1914). Published earlier (1913) in Sitzungsberichten der Kgl. Preuss. Akad. d. Wiss.

1913-1914 – Niels Bohr proposed his “shell” model of the atom, which explained, at a basic level at least, the spectral lines of the hydrogen atom consistent with the Rydberg formula. Long-supplanted by the quantum probability cloud model, this image of the atom persists in the minds of the general public to this day.

N. Bohr, “On the Constitution of Atoms and Molecules”, Philosophical Magazine, Sixth Series 26:1 (July 1913)

1914 – Einstein presented the “Hole Argument” to explain why he felt it would be impossible to construct gravitational field equations in his theory which satisfy general covariance.

“Die formale Grundlage der allgemeinen Relativitaetstheorie”, Preussische Akademie der Wissenschaften, Sitzungsberichte (1914), 1030-1085.

1915 – Einstein presented four iterations of his General Theory of Relativity to the Prussian Academy of Science (with the third containing an explanation for the precession of the perihelion of Mercury, and the last containing the final form of his field equations), which physicist to this day are still attempting to reconcile with QM.

### The Einstein Field Equations:

$R_{\mu\nu}\ -\ \frac{1}{2}\,R\,g_{\mu\nu}\ =\ 8\pi\,T_{\mu\nu}$

where $R_{\mu\nu}$ is the Ricci curvature tensor and $T_{\mu\nu}$ is stress-energy tensor.

A. Einstein, “Zur allgemeinen Relativitaetstheorie”, Preussische Akademie der Wissenschaften, Sizungsberichte (1915), 778-786.

A. Einstein, “Zur allgemeinen Relativitaetstheorie (Nachtrag)”, Preussische Akademie der Wissenschaften, Sizungsberichte (1915), 799-801.

A. Einstein, “Erklaerung der Perihelbewegung des Merkur aus der allgemeinen Relativitaetstheorie”, Preussische Akademie der Wissenschaften, Sizungsberichte (1915), 831-839.

A. Einstein, “Die Feldgleichung der Gravitation”, Preussische Akademie der Wissenschaften, Sizungsberichte (1915), 844-847.

1916 – Einstein published the final form of his paper on the General Theory of Relativity.

A. Einstein, “Die Grundlage der allgemeinen Relativitätstheorie” (“The Foundation of the General Theory of Relativity”), Annalen der Physik, Vol. 354, Issue 7, pp. 769-822 (1916)

1916 – The Schwarzschild metric for General Relativity was introduced.

K. Schwarzschild, “Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie” (”On the gravitational field of a mass point according to Einstein’s theory“, Sitzungsber. K. Preuss. Akad. Wiss., Phys.-Math. Kl. 189-196 (1916).

1918-1923 – N. Bohr formulated the Correspondence Principle, which states that quantum mechanics should reproduce classical physics in the limit of large quantum numbers (or, equivalently, as h → 0).

N. Bohr, “On The Quantum Theory of Line-Spectra”, D. KGL. Danske Vidensk. Selsk. Skrifter, naturvidensk. og mathem. Afd. 8. Raekke, IV.1, 1-3 1 (1918).

N. Bohr, “Über die Serienspektra der Elemente”, Zeitschrift für Physik 2 (5): 423–478 (1920)

N. Bohr, “Über die Anwendung der Quantentheorie auf den Atombau I. Die Grundpostulate der Quantentheorie.” Zeitschrift für Physik Volume 13, Number 1: 117-165.

1919 – Ernest Rutherford experimentally verified the existence of protons.

1921 – Chadwick and Bieler determine that the force holding nuclei together must be strong compared to the electromagnetic force.

J. Chadwick, E.S. Bieler, “Collisions of α Particles with Hydrogen Nuclei“, Phil. Mag. 42 (1921) 923

1921 – The introduction of Kaluza-Klein theory, an early attempt to unify gravitation with electromagnetism.

Kaluza, Theodor (1921). “Zum Unitätsproblem in der Physik”. Sitzungsber. Preuss. Akad. Wiss. Berlin. (Math. Phys.) 1921: 966–972.

Klein, Oskar (1926). “Quantentheorie und fünfdimensionale Relativitätstheorie”. Zeitschrift für Physik a Hadrons and Nuclei 37 (12): 895–906. doi:10.1007/BF01397481

[English translations of both articles can be found in Modern Kaluza-Klein Theories by Applequist, Chodos, and Freund, (Addison-Wesley, 1987). Many thanks to Prof. Matt Strassler for pointing this out.]

The Stern-Gerlack experiement (Image courtesy of Wikimedia Commons.)

1922 – Otto Stern and Walther Gerlach performed the Stern-Gerlack experiment, demonstrating that particle spin is quantized. (See the 2003 Physics Today article, “Stern and Gerlach: How a Bad Cigar Helped Reorient Atomic Physics.”)

Gerlach, W.; Stern, O. (1922). “Das magnetische Moment des Silberatoms”. Zeitschrift für Physik 9: 353–355. doi:10.1007/BF01326984

Stern, O. (1921). “Ein Weg zur experimentellen Pruefung der Richtungsquantelung im Magnetfeld”. Zeitschrift für Physik 7: 249–253. doi:10.1007/BF01332793

1922-1924 – Friedmann Cosmology – Alexander Freidman found a solution to Einstein’s general relativity field equations for an expanding universe, predating the theoretical work of Lemaître and the observations of Edwin Hubble.

A. A. Friedman, “Uber die Krümmung des Raumes”, Zeitschrift fur Physik, 10:377-387 (1922).

Friedman, A. (1924). “Über die Möglichkeit einer Welt mit konstanter negativer Krümmung des Raumes”. Zeitschrift für Physik 21 (1): 326–332. doi:10.1007/BF01328280.

1922-1923 – Using X-ray scattering experiments, Arthur Compton discovered what is now known as the “Compton effect,” an inelastic scattering of photons in matter.

1923-24 – Louis de Broglie posited his theory of matter waves, paving the way for the birth of modern quantum mechanics. de Broglie suggested that an electron possesses a wavelike aspect with a wavelength equal to Planck’s constant divided by the electron’s momentum.

L. de Broglie, “Ondes et Quanta” (”Waves and Quanta“), Compt. Ren. 177:507 (1923)

## The Birth of Modern Quantum Mechanics (1924-1941)

In this period, quantum theory was mathematically formalized.

1924-1927 – The Copenhagen interpretation of QM began to form. Much of the consensus regarding the Copenhagen interpretation arose from discussions held in 1927 at the Fifth Solvay International Conference on Electrons and Photons and the accompanying Bohr-Einstein debates.

### Principles of the Copenhagen Interpretation

1. A wave function ψ completely describes a system and represents an observer’s knowledge of the system. (Heisenberg)
2. Rather than being deterministic (as was the case in Newtonian mechanics, quantum descriptions of nature are probabilistic. The probability of an event is given by the square of the amplitude of the wave function related to it. (Born rule, due to Max Born)
3. Heisenberg’s uncertainty principle states that it is not possible to know the values of all of the properties of the system simultaneously with arbitrary precision.
4. Complementarity principle: matter exhibits a wave-particle duality. Matter can exhibit particle-like properties or wave-like properties (depending upon how it is observed), but not both at the same time. (Niels Bohr)
5. Measuring devices should be treated as classical devices. They measure classical properties such as position and momentum, which represent probabilistic expectation values of the corresponding quantum properties.
6. The correspondence principle of Bohr and Heisenberg: the quantum mechanical description of large systems should converge upon the classical description when taken to the classical limit (as h → 0).

1924 – Satyendra Nath Bose derived Planck’s quantum radiation law without making any reference to classical physics. His approach paved the way for Bose-Einstein statistics, the theoretical description of Bose-Einstein condensates. Bosons, the class of particles obeying Bose-Einstein statistics, are named in his honor. Initially, journals refused to publish his work since he was interpreting what appeared to be an error as an indication of new physics, but a letter from Einstein to Zeitschrift für Physik persuaded them to publish Bose’s paper.

S. N. Bose. “Plancks Gesetz und Lichtquantenhypothese” (Planck’s Law and Light Quantum Hypothesis”), Zeitschrift für Physik 26:178-181 (1924)

A. Einstein, “Quantentheorie des einatomigen idealen Gases”, Sitzungsber. Kgl. Preuss. Akad. Wiss., 261 (1924), 3 (1925).

1924 – Max Born coined the term “quantum mechanics.”

M. Born, “Über Quantenmechanik,” Z. Phys26, 379–395 (1924).

1924-1925 – Walther Bothe and Hans Geiger performed Compton scattering experiments with X-rays and coincidence detection to show that the X-rays were truly discrete particles.

W. Bothe and H. Geiger, Z.Physik 32 (1925) 639-663.

1925 – Wolfgang Pauli formulated his exclusion principle, which holds that no two identical fermions may simultaneously occupy the same quantum state. This principle forms the foundation of chemistry, dictating the chemical interactions of the various elements.

W. Pauli, “Über den Zusammenhang des Abschlusses der Elektronengruppen im Atom mit der Komplexstruktur der Spektren” (”On the Connexion between the Completion of Electron Groups in an Atom with the Complex Structure of Spectra“), Z. Phys. 31:765 (1925).

1925-1926 – Werner Heisenberg, Max Born, and Pascual Jordan formulated the matrix formalism of quantum mechanics, and Erwin Schrödinger invented wave mechanics and constructed the non-relativistic Schrödinger equation (built upon de Broglie’s theory). Schrödinger later showed that matrix mechanics and wave mechanics are equivalent.

Schrödinger’s equation: $i\hbar\frac{\partial}{\partial t}\Psi = \hat{H}\Psi$

W. Heisenberg, “Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen” (”Quantum-Theoretical Re-Interpretation of Kinematic and Mechanical Relations”), Z. Phys. 33:879 (1925).

M. Born, and P. Jordan, “Zur Quantenmechanik” (“On Quantum Mechanics”), Z. f. Phys. 34, 858-888 (1925).

M. Born, W. Heisenberg, and P. Jordan, “Zur Quantenmechanik II” (“On Quantum Mechanics II“), Z. f. Phys. 35, 557-615 (1926).  (This paper is frequently referred to as the Dreimännerarbeit, or “Three-Man Paper,” and marks the birth of quantum matrix mechanics.)

M. Born, “Zur Quantenmechanik der Stoßvorgänge” (”Quantum Mechanics of Collision”), Z. Phys. 37:863 (1926).
(It is in this paper that Born put forth the Born Rule.)

E. Schrödinger, “Quantizierung als Eigenwertproblem (Erste Mitteilung)” (”Quantization as an Eigenvalue Problem. Part I.”), Annalen der Physik., 79:361-76 (1926).

E. Schrödinger, “Quantizierung als Eigenwertproblem (Zweite Mitteilung)” (”Quantization as an Eigenvalue Problem. Part II.”), Ann. Phys. 79: 489-527 (1926).

E. Schrödinger, “Der stetige Übergang von der Mikro-zur Makromechanik, Die Naturwissenschaften” (“The Science of the Continuous Transition from Micro- to Macro-mechanics), 14. Jahrg. Heft 28:664-666 (1926).

E. Schrödinger, “Über das Verhältnis der Heisenberg-Born-Jordanschen Quantenmechanik zu der meinen” (”On the Relation Between the Quantum Mechanics of Heisenberg, Born, and Jordan, and that of Schrödinger”), Ann. Phys. 79:734-56 (1926).

E. Schrödinger, “Quantisierung als Eigenwertproblem (Dritte Mitteilung)” (“Quantization as an Eigenvalue Problem. Part III.”), Ann. Phys. 80:437-90 (1926).

E. Schrödinger, Quantisierung als Eigenwertproblem (Vierte Mitteilung) (“Quantization as an Eigenvalue Problem. Part IV.”), Ann. Phys. 81:109-39 (1926).

1926 – Enrico Fermi and P.A.M. Dirac developed Fermi-Dirac statistics, which govern the behavior of fermions (particles with fractional spin).

E. Fermi, “Zur Quantelung des Idealen Einatomigen Gases” (”On Quantizating an Ideal Monatomic Gas“), Z. Phys. 36, 902 (1926).

P.A.M. Dirac, “On the Theory of Quantum Mechanics“, Proc. Roy. Soc. A 112, 661 (1926).

1926 – Gilbert N. Lewis coined the term “photon.”

Lewis, G.N. (1926). “The conservation of photons”. Nature 118: 874–875. doi:10.1038/118874a0

1927 – Clinton Davisson and Lester Germer performed the Electron diffraction experiment, an analog to Young’s double slit experiment, demonstrating the wavelike nature of electrons.

1927 – Monsignor George Lemaître, a Belgian astronomer and Roman Catholic priest, proposed that the universe is in a state of expansion.

Lemaître, G. (1927). “Un univers homogène de masse constante et de rayon croissant rendant compte de la vitesse radiale des nébuleuses extragalactiques”. Annals of the Scientific Society of Brussels 47A: 41.(French)

1927 – Heisenberg formulated the Uncertainty Principle$\Delta x \Delta p \geq \frac{\hbar}{2}$

W. Heisenberg, “Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik” (”The Actual Content of Quantum Theoretical Kinematics and Mechanics“), Z. Phys. 43:172 (1927).

1927 – Publication of Ehrenfest’s Theorem (represented below in the later Dirac bra-ket notation), which demonstrates computation of the time derivative of the expectation value for a quantum operator by taking the commutator of that operator with the Hamiltonian of the system.

$\frac{d}{dt}\langle A\rangle = \frac{1}{i\hbar}\langle [A, H]\rangle + \langle\frac{\partial A}{\partial t}\rangle$

P. Ehrenfest, “Bemerkung über die angenaherte Gultigkeit der klassischen Mechanik innerhalb der Quantenmechanik” (“Remarks on the approximate validity of classical mechanics in quantum mechanics”). Z. Phys. 45:455 (1927).

1927 – Wolfgang Pauli modified Schrödinger’s equation to include spin, resulting in the Pauli Equation.

Wolfgang Pauli (1927) Zur Quantenmechanik des magnetischen Elektrons Zeitschrift für Physik (43) 601-623

1927-1930 – Dirac constructed a relativistic version of Schrödinger’s equation now known as the Dirac Equation, thus unifying QM with Special Relativity. This provided a description of spin-1/2 particles and predicted the existence of the positron. Dirac’s 1930 textbook also made extensive use of operator theory.

The Dirac equation:

$\left( \beta m c^2 + \displaystyle\sum_{k=1}^3 \alpha_k p_k c \right) \psi (\mathbf{x},t) = i \hbar \frac{\partial \psi (\mathbf{x},t )}{\partial t}$

P. A. M. Dirac, “The Quantum Theory of Dispersion“, Proc. Roy. Soc. A 114:710-728 (1927).

P.A.M. Dirac (1927). “The Quantum Theory of the Emission and Absorption of Radiation”.Proceedings of the Royal Society of London A 114 (767): 243–265. Bibcode1927RSPSA.114..243Ddoi:10.1098/rspa.1927.0039 (which marks the origin of the theory of quantum electrodynamics, or QED, which at this point is plagued with divergences, a problem later solved by Feynman, Schwinger, and Tomonaga.)

P.A.M. Dirac, “The Quantum Theory of the Electron”, Proc. Roy. Soc. A, Vol. 117, No. 778, pp. 610-624 (1928)

P.A.M. Dirac, “The Quantum Theory of the Electron. Part II”, Proc. Roy. Soc. A, Vol. 118, No. 779, pp. 351-361 (1928)

P.A.M. Dirac, “A theory of Electrons and Protons”, Proc. Roy. Soc. A, Vol 126, No. 801 ,p.360-365 (1930)

P.A.M. Dirac, Principles of Quantum Mechanics, Oxford: Clarendon Press (1930)

1929 – Edwin Hubble put forth his analysis of the redshift of distant celestial objects, laying the foundations for the Big Bang Theory.

E. Hubble, “A Relation between Distance and Radial Velocity among Extra-Galactic Nebulae“, Proceedings of the National Academy of Sciences, 15:168-173 (1929).

1930 – Wolfgang Pauli postulated the existence of neutrinos in order to preserve conservation of energy, momentum, and angular momentum in beta decay reactions. He originally called this particle a neutron, but that name was appropriated in 1932 by James Chadwick when he discovered the more massive particle now known by that name. Enrico Fermi coined the name neutrino in 1934 in the course of developing his theory of beta decay.

1931 – In light of Hubble’s work, Lemaître expanded upon his earlier work and posited the Big Bang Theory. (That appellation was later coined by Fred Hoyle as a pejorative. Hoyle advocated a steady state cosmology.)

G. Lemaître. “The Evolution of the Universe: Discussion”. Nature 128: 699–701. (1931) doi:10.1038/128704a0

1931 – Dirac proposed the existence of magnetic monopoles as a way of explaining charge quantization. To date, no magnetic monopoles have been detected experimentally. In the same paper, he predicted (based upon interpretation of his eponymous equation) the existence of positrons.

P.A.M. Dirac, “Quantized Singularities in the Electromagnetic Field”. Proceedings of the Royal Society A 133;pp. 60-72 (1931)

1932 – James Chadwick discovered the neutron.

Chadwick, J., “Possible Existence of a Neutron“. Nature 129 (1932) 312.

Chadwick, J., “The Existence of a Neutron”. Proc. Roy. Soc A136 (1932) 692.

1933 – Carl Anderson publishes confirmation of the experimental detection of the positron predicted from the Dirac Equation.

Carl D. Anderson, “The positive electron”, Physical Review 13 March 1933, vol. 43, p491.

1932-1949 – John von Neumann formulated the mathematical basis for QM in terms of operator algebras.

P. Jordan, J. von Neumann & E. Wigner: On an algebraic generalization of the quantum mechanical
formalism. Ann. Math. 35, 29-64 (1934)

Neumann, J. von, 1937, “Quantum Mechanics of Infinite Systems”, first published in (Rédei and Stöltzner 2001, 249-268). [A mimeographed version of a lecture given at Pauli’s seminar held at the Institute for Advanced Study in 1937, John von Neumann Archive, Library of Congress, Washington, D.C.]

Ibid., 1955, Mathematical Foundations of Quantum Mechanics, Princeton, NJ: Princeton University Press. [First published in German in 1932: Mathematische Grundlagen der Quantenmechank, Berlin: Springer.]

F.J. Murray & J. von Neumann: On rings of operators i, ii, iv. Ann. Math. 37, 116-229 (1936),
Trans. Amer. Math. Soc. 41, 208-248 (1937), Ann. Math. 44, 716-808 (1943)

J. von Neumann: On rings of operators iii, v. Ann. Math. 41, 94-161 (1940), ibid. 50, 401-485
(1949)

1934 – Enrico Fermi published his theory of beta decay.

Fermi, E. (1934). “Versuch einer Theorie der β-Strahlen. I”. Zeitschrift für Physik 88 (3–4): 161-177. Bibcode1934ZPhy…88..161Fdoi:10.1007/BF01351864 (English translation: “Attempt at a Theory of β Rays”)

1935 – Chandrasekhar presented his analysis of the dynamics of white dwarfs and black holes.

S. Chandrasekhar, “The highly collapsed configurations of a stellar mass“, Monthly Notices of the Royal Astronomical Society, 95, 207-225 (1935).

1935 – A quantum field theory for nuclear interactions associated with the strong nuclear force was proposed by Hideki Yukawa, specifically including a mechanism for beta decay. The Yukawa interaction was later also used to describe coupling with the Higgs field. The Yukawa interaction forms the foundation for later work in Gauge Theory, such as Yang-Mills Theory and Electroweak Theory, ultimately culminating in the Standard Model.

H. Yukawa, “On the Interaction of Elementary Particles“, Proc. Phys. Math. Soc. Jap. 17:48 (1935).

1935 – Einstein, Podolsky, and Rosen pointed out the EPR paradox, which implies the nonlocality of quantum interactions.

A. Einstein, B. Podolsky, N. Rosen, “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?“, Phys. Rev. 47: 777–780 (May 15, 1935).

1935 – Erwin Schrödinger, in a response to the EPR paradox, giving us the Schrödinger’s cat paradox.

Schrödinger, Erwin (November 1935). “Die gegenwärtige Situation in der Quantenmechanik (The present situation in quantum mechanics)”. Naturwissenschaften. 23: pp.807-812; 823-828; 844-849 (English translation)

1935 – Euler and Heisenberg published a famous analysis of Dirac’s theories.

W. Heisenberg and H. Euler, “Folgerungen aus der Diracshen Theorie des Positrons” (“Consequences of Dirac’s Theory of the Positron”)

1937-1947 – The muon was discovered in cosmic rays, but initially mistaken for Yukawa’s predicted “meson.” It was not until the 1947 that this mistake was recognized, prompting I.I. Rabi’s famous comment, “Who ordered that?”

Neddermeyer, S.H.; Anderson, C.D.;
Note on the Nature of Cosmic-Ray Particles”
Phys. Rev. 51 (1937) 884

Street, J.C.; Stevenson, E.G.;
Penetrating Corpuscular Component of the Cosmic Radiation”
Phys. Rev. 51 (1937) 1005

Street, J.C.; Stevenson, E.G.;
New Evidence for the Existence of a Particle of Mass Intermediate Between the Proton and Electron”
Phys. Rev. 52 (1937) 1003;

Nishina, Y.; Takeuchi, M.; Ichimiya, T.;
On the Nature of Cosmic-Ray Particles”
Phys. Rev. 52 (1937) 1198;

Rossi, B.; Van Norman Hilbery, H.; Hoag, J.B.;
The Disintegration of Mesotrons”
Phys. Rev. 56 (1939) 837;

Williams, E.J.; Roberts, G.E.;
Evidence for Transformation of Mesotrons into Electrons
Nature 145 (1940) 102;

Rasetti, F.;
Mean Life of Slow Mesotrons
Phys. Rev. 59 (1941) 613;

Rasetti, F.;
Disintegration of Slow Mesotrons
Phys. Rev. 60 (1941) 198;

Rossi, B.; Nereson, N.;
Experimental Determination of the Disintegration Curve of Mesotrons
Phys. Rev. 62 (1942) 417;

Nereson, N.; Rossi, B.;
Further Measurements on Disintegration Curve of Mesotrons
Phys. Rev. 64 (1942) 199;

Conversi, M.; Pancini, E.; Piccioni, O.;
On the Disintegration of Negative Mesons
Phys. Rev. 71 (1947) 209;

1939 – Weisskopf demonstrated ultraviolet divergences in the higher-order terms of Dirac’s QED theory.

V. F. Weisskopf (1939). “On the Self-Energy and the Electromagnetic Field of the Electron”. Physical Review 56: 72–85. Bibcode 1939PhRv…56…72W.doi:10.1103/PhysRev.56.72

1939 – Dirac introduced “bra-ket” notation, which was subsequently incorporated into the 3rd edition of his 1930 textbook.

P.A.M. Dirac, “A New Notation for Quantum Mechanics”. Proceedings of the Cambridge Philosophical Society 35: pp. 416-418 (1939)

## Towards a Theory of Everything (1942-present)

Feynman Diagram by Dmitri Fedorov (Image use granted under the GNU Free Documentation License and the Creative Commons Attribution-ShareAlike 3.0 License.)

This period witnessed the growth and development of modern quantum field theory, and its offshoots quantum electrodynamics (QED) and quantum chromodynamics (QCD), electroweak theory, the Standard Model, and efforts at unification with the goal of creating a “theory of everything.” Much of this development was driven by the embrace of the path integral picture of quantum mechanics, gauge theory, and group theory.

1942 – Feynman’s PhD dissertation, The Principle of Least Action in Quantum Mechanics laid the groundwork for overcoming earlier issues with divergence in Dirac’s QED theory.

1943 – Gelfand and Naimark reformulated quantum mechanics in terms of C*-algebras.

I.M. Gelfand & M.A. Naimark: On the imbedding of normed rings into the ring of operators in
Hilbert space. Mat. Sbornik 12, 197-213 (1943)

1946-1948 – Japanese physicist Sin-Itiro Tomonaga published a series of papers on a formulation of QED which was relativistically invariant and eliminated ultraviolet divergences via renormalization. A few weeks after Feynman and Schwinger reported their own efforts in this area at the Pocono conference in March 1948, Robert Oppenheimer received a letter from Tomonaga describing his work and immediately recognized the overlap in their efforts.

S. Tomonaga (1946). “On a Relativistically Invariant Formulation of the Quantum Theory of Wave Fields”. Progress of Theoretical Physics 1 (2): 27–42. doi:10.1143/PTP.1.27

Z. Koba, S. Tati & S. Tomonaga (1947). “On a relativistically invariant formulation of the quantum theory of wave fields II”.  Progress of Theoretical Physics 2 (3): pp. 101-116. doi10.1143/PTP.2.101

Z. Koba, S. Tati & S. Tomonaga (1947). “On a relativistically invariant formulation of the quantum theory of wave fields III”. Progress of Theoretical Physics 2 (4): pp. 198-208. doi10.1143/PTP.2.198

D. Ito, Z. Koba & S. Tomonaga (1947). “Correction due to the reaction of ‘cohesive force field’ for the elastic scattering of an electron”. Progress of Theoretical Physics 2 (4): pp. 216-217. doi: 10.1143/PTP.2.216

Z. Koba & S. Tomonaga (1947). “Application of the ‘self-consistent’ subtraction method to the elastic scattering of an electron”. Progress of Theoretical Physics 2 (4): p. 218. doi10.1143/PTP.2.218

S. Kanesawa & S. Tomonaga (1948). “On a relativistically invariant formulation of the quantum theory of wave fields V [i.e. IV]”. Progress of Theoretical Physics 3 (1): pp. 1-13. doi10.1143/PTP.3.1

S. Kanesawa & S. Tomonaga (1948). “On a relativistically invariant formulation of the quantum theory of wave fields V”.  Progress of Theoretical Physics 3 (2): pp. 101-113. doi10.1143/PTP.3.101

T. Tati & S. Tomonaga (1948). “A self-consistent subtraction method in the quantum field theory, I”. Progress of Theoretical Physics 3  (4): pp. 391-406. doi10.1143/PTP.3.391

S. Tomonaga & J.R. Oppenheimer (1948). “On infinite field reactions in quantum field theory”.  Physical Review 74 (2): pp. 224-225. doi10.1103/PhysRev.74.224

1947 – Lamb and Retherford experimentally demonstrated a shifting in the spectra of hydrogen atoms which was inconsistent with the Dirac-Heisenberg-Pauli theory. On the train ride home from the Shelter Island conference where these results were announced, Hans Bethe performed a quick calculation of appropriate radiative corrections to account for the shift, an early form of renormalization. More info here and here.

W. E. LambR. C. Retherford (1947). “Fine Structure of the Hydrogen Atom by a Microwave Method,”. Physical Review 72 (3): 241-243.  Bibcode 1947PhRv…72..241L.doi:10.1103/PhysRev.72.241

H. Bethe (1947). “The Electromagnetic Shift of Energy Levels”. Physical Review 72 (4): 339–341. Bibcode 1947PhRv…72..339Bdoi:10.1103/PhysRev.72.339

1948 – Foley and Kusch experimentally measured anomalous values for the magnetic moment of the electron. Schwinger then used a renormalization technique similar to Bethe’s to perform new calculations for the value of the magnetic moment, and found the results to be in good agreement with the experimental results.

P. KuschH. M. Foley (1948). “On the Intrinsic Moment of the Electron,”. Physical Review73 (3): 412. Bibcode 1948PhRv…74..250Kdoi:10.1103/PhysRev.74.250

J. Schwinger (1948). “On Quantum-Electrodynamics and the Magnetic Moment of the Electron”. Physical Review 73 (4): 416–417. Bibcode 1948PhRv…73..416S.doi:10.1103/PhysRev.73.416

1948-1949 – Julian Schwinger published a series of articles describing his formulation of QED.

J. Schwinger (1948). “Quantum Electrodynamics. I. A Covariant Formulation”. Physical Review 74 (10): 1439–1461. Bibcode 1948PhRv…74.1439S.doi:10.1103/PhysRev.74.1439

J. Schwinger (1949).  “Quantum electrodynamics II. Vacuum polarization and self-energy”,  Physical Review 75 (4): pp. 651-672. doi:10.1103/PhysRev.75.651

J. Schwinger (1949). “On radiative corrections to electron scattering”,  Physical Review 75 (5): pp. 898-899.  doi10.1103/PhysRev.75.898

J. Schwinger (1949). “Quantum electrodynamics III: the electromagnetic properties of the electron – radiative corrections to scattering”, Physical Review 76 (6): pp. 790-817.  doi10.1103/PhysRev.76.790

1948-1950 – Richard Feynman published a series of articles describing his formulation of Quantum Electrodynamics (QED), a subset of quantum field theory describing interactions between photons and electrically-charged particles based upon the path integral formulation of quantum mechanics. Notable features of QED include the use of Feynman diagrams to assist in constructing the calculations, and the use of renormalization to avoid divergences in the calculations.

R. P. Feynman, “Relativistic Cut-Off for Quantum Electrodynamics“, Phys. Rev. 74: 1430 (1948).

P. Feynman, “Space-Time Approach to Non-Relativistic Quantum Mechanics“, Rev. of Mod. Phys. 20:367 (1948). (This was essentially a published version of Feynman’s dissertation.)

R.P. Feynman, “The Theory of Positrons” Phys. Rev. 76, pp. 749-759 (1949)

R.P. Feynman, “Space-Time Approach to Quantum Electrodynamics” Phys. Rev. 76, pp. 769-789 (1949)

R.P. Feynman, “Mathematical Formulation of the Quantum Theory of Electromagnetic Interaction” Phys. Rev. 80, pp. 440-457 (1950)  (This paper constituted an attempt by Feynman to provide his approach with mathematical rigor and to explain why it worked.)

1948 – The Big Bang nucleosynthesis theory was proposed to describe the formation of bulk of existing hydrogen and helium in the universe during the Big Bang.

R. A. Alpher, G. Gamow, “The Origin of Chemical Elements“, Physical Review, 73:803 (1948).

1949 – Freeman Dyson demonstrated that Tomonaga, Schwinger, and Feynman’s approaches to QED were equivalent (despite Feynman’s diagrammatic approach being qualitatively different). Dyson then went on to show that the only quantities needing to be renormalized were mass, change, and the wave function.

F. Dyson (1949). “The Radiation Theories of Tomonaga, Schwinger, and Feynman”.Physical Review 75 (3): 486–502. Bibcode 1949PhRv…75..486D.doi:10.1103/PhysRev.75.486

F. Dyson (1949). “The S Matrix in Quantum Electrodynamics”. Physical Review 75 (11): 1736–1755. Bibcode 1949PhRv…75.1736Ddoi:10.1103/PhysRev.75.1736

1949 – Victor Weisskopf  published an overview of developments in quantum theory.

V.F. Weisskopf, “Ueber die Elektrodynamik des Vakuums auf Grund der Quantentheorie des Elektrons” (“Recent Developments in the Theory of the Electron”). Reviews of Modern Physics 21:2 pp. 305-315.

1950 – John Clive Ward demonstrated that all ultraviolet divergences in QED are eliminated by renormalization.

WARD, J. C. An Identity in quantum electrodynamics, Physical Review, Vol. 78, No. 2 (1950), p. 182. DOI: 10.1103/PhysRev.78.182

1954 – Locally gauge invariant Yang-Mills Theory was introduced, based in part upon Pauli’s unpublished efforts to apply Kaluza-Klein theory to QED and strong interactions. Initial versions of Yang-Mills failed to properly describe strong interactions since all bosons predicted by the theory were massless. This, however, was later corrected by the introduction of symmetry breaking concepts to the theory.

C. N. Yang, R. L. Mills, “Conservation of Isotopic Spin and Isotopic Gauge Invariance“, Phys. Rev. 96:191 (1954).

1955 – Clyde L. Cowan and Frederick Reines provided experimental confirmation of the existence  of the neutrino.

1957 – Everett introduced the “Many worlds” interpretation of QM.

H. Everett, “Relative state formulation of quantum mechanics“, Rev. Mod. Phys. 29: 454-462 (1957).

The Eightfold Way: J=1/2 bottom Baryons (Image courtesy of FermiLab.)

1961 – Murray Gell-Mann proposed “The Eightfold Way,” a system of organizing baryons and mesons.

M. Gell-Mann, The Eightfold Way: A Theory of Strong Interaction Symmetry, DOE Technical Report, March 15, 1961

1960-1962 Nambu-Goldstone bosons were postulated initially in the context of BCS superconductivity theory, then later generalized to quantum field theory. These bosons arise in models involving the spontaneous breakdown of continuous symmetries.

Nambu, Y (1960). “Quasiparticles and Gauge Invariance in the Theory of Superconductivity”. Physical Review 117: 648 – 663. doi:10.1103/PhysRev.117.648

Goldstone, J (1961). “Field Theories with Superconductor Solutions”. Nuovo Cimento 19: 154 – 164. doi:10.1007/BF02812722

Goldstone, J; Salam, Abdus; Weinberg, Steven (1962). “Broken Symmetries”. Physical Review 127: 965 – 970. doi:10.1103/PhysRev.127.965

1961 – Clauss Jönsson performed the double-slit experiment with electrons, re-affirming the results of the Davisson-Germer experiment.

Jönsson C,(1961) Zeitschrift für Physik, 161:454–474

Jönsson C (1974). Electron diffraction at multiple slits. American Journal of Physics, 4:4–11.

1963 – The Kerr metric, which describes the geometry of spacetime near a massive spinning body, was introduced.

R. P. Kerr, “Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics“, Physical Review Letters, 11:237–238 (1963).

1964 – Murray Gell-Mann and George Zweig both proposed the Quark model.

G. Zweig, “An SU3 model for strong interaction symmetry and its breaking“, Developments in the Quark Theory of Hadrons, pp. 22-101.

1964 – Higgs proposed a mechanism for boson mass generation via spontaneous symmetry breaking.

P. W. Higgs, “Broken Symmetries and Masses of Gauge Bosons“, Phys. Rev. Lett. 13, 508 (1964).

1964 – The introduction of Bell’s Theorem essentially eliminated local hidden variable theories from quantum mechanics.

Bell, J. S., “On the Einstein-Podolsky-Rosen paradox“, Physics 1: 195–200 (1964).

1965 – Penzias and Wilson detected the Cosmic Microwave Background radiation field, the “afterglow” of the Big Bang.

Penzias, A.A.; Wilson, R. W. (1965). “A Measurement of Excess Antenna Temperature at 4080 Mc/s”. Astrophysical Journal 142: 419.doi:10.1086/148307

1967 – Andrei Sakharov demonstrated that the baryon/antibaryon asymmetry of the universe can be explained by a CP symmetry violation.

Sakharov, A.D. (1967). “Violation of CP Invariance, C Asymmetry and Baryon Asymmetry of the Universe”. Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, Pisma 5: 32. (Russian)

1967 – DeWitt made an early attempting at constructing a quantum gravity theory, introducing in the process the Wheeler-DeWitt equation, an analogue of Schrödinger’s equation .

1967 – Steven Weinberg introduced Electroweak Theory, unifying the electromagnetic and weak nuclear forces.

S. Weinberg, “A model of leptons“, Phys. Rev. Lett. 19: 1264-1266 (1967).

1968-1970 – String Theory was proposed.

G. Veneziano, “Construction of a crossing-symmetric, Regge-behaved amplitude for linearly rising trajectories”, Nuovo Cimento, 57A: 190 (1968).

L. Susskind, “Dual symmetric theory of hadrons. – I”, Nuovo Cimento, 69A: 457 (1970).

G. Frye, C.W. Lee and L. Susskind, “Dual-symmetric theory of hadrons II. – Baryons”, Nuovo Cimento, 69A:pp. 497-507 (1970)

1970 – Quantum Decoherence was introduced as a potential description of the emergence of classical behavior out of quantum systems, yielding the appearance of wave function collapse.

H. D. Zeh, “On the interpretation of measurement in quantum theory“, Found. Phys. 1: 69-76 (1970).

1971 – Gerard t’ Hooft analyzed the issue of determining the renormalizability of gauge fields using massless Yang-Mills fields as an example.

G. ‘t Hooft, “Renormalization of Massless Yang-Mills Fields“, Nucl. Phys. B 33:173 (1971).

1973 – Asymptotic freedom in quark interactions (and in non-Abelian gauge theories in general) was described.

D. J. Gross, F. Wilczek, “Ultraviolet Behaviour of Non-Abelian Gauge Theory“, Phys. Rev. Lett. 30:1343 (1973).

1973 – Thermodynamics and information theory, specifically the concept of entropy, was applied to Black holes, leading to extensive study of black hole thermodynamics.

J. D. Bekenstein, “Black Holes and Entropy“, Phys. Rev. D 7:2333-2346 (1973).

1974 – String theory was applied to quantum gravity.

J. Scherk, J. H. Schwarz, “Dual models for non-hadrons“, Nucl. Phys. B 81:118 (1974).

1974 – The Standard Model of Physics fell into place: all fundamental forces of nature, except for gravity, were shown to be describable via quantum field theory (Electro-weak theory and QCD), with the hope of eventually unifying them in a Grand Unified Theory describing them as manifestations of the same fundamental interaction.

H. Georgi, S. L. Glashow, “Unity of All Elementary-Particle Forces“, Phys. Rev. Lett. 32:438-441 (1974).

1975 – Stephen Hawking proposed a model for the emission of radiation from black holes, now commonly referred to as Hawking radiation.

S. W. Hawking, “Particle creation by black holes“, Comm. Math. Phys., 43:3, 199-220 (1975).

1980 – Klaus von Klitzing discovered the Quantum Hall effect.

1981 – Alan Guth proposed Inflation Theory to resolve several problems associated with Big Bang cosmology.

A. Guth, “Inflationary universe: A possible solution to the horizon and flatness problems“, Physical Review D (Particles and Fields), 23:2, 347-356 (1981).

1981 – Superstring theory (supersymmetric string theory) was introduced

M. B. Green, J. H. Schwarz, “Supersymmetrical dual string theory“, Nuclear Physics B 181:3, 502-530 (1981).

1982 – Linde proposed what is known as chaotic inflation theory.

A. D. Linde, “A new inflationary universe scenario: A possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems“, Physics Letters B, 108:6, 389-393 (1982).

1982 – Alain Aspect experimentally verified quantum entanglement.

A. Aspect, P. Grangier, and G. Roger (1982). “Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: A New Violation of Bell’s Inequalities”. Physical Review Letters 49 (2): 91–94.doi:10.1103/PhysRevLett.49.91

1986 – Ashtekar created a formulation of general relativity meant to simplify its integration with quantum theory.

A. Ashtekar, “New variables for classical and quantum gravity“, Phys. Rev. Lett., 57 (18), 2244-2247 (1986).

1990 – A competitor to string theory appeared on the scene with the introduction of Loop Quantum Gravity.

C. Rovelli, L. Smolin, “Loop space representation of quantum general relativity“, Nucl. Phys., B 331 (1), 80-152, (1990).

1993 – ‘t Hooft introduced the Holographic Principle, an outgrowth of black hole thermodynamics.

G. ‘t Hooft, “Dimensional Reduction in Quantum Gravity“, arXiv:gr-qc/9310026 (1993).

1993 – Quantum teleportation via quantum entanglement was predicted.

C. H. Bennett, G. Brassard, et al., “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels“, Phys. Rev. Lett. 70: 1895-1899 (1993).

(Subsequent experimental confirmations:)

Bouwmeester, D. et al. (1997). “Experimental quantum teleportation”. Nature. pp. 575–579.

Xian-Min Jin (16 May 2010). “Quantum teleportation achieved over 16 km”. Nature.

D. Boschi; S. Branca, F. De Martini, L. Hardy, and S. Popescu (1998). “Experimental Realization of Teleporting an Unknown Pure Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels”. Phys. Rev. Lett.. pp. 80, 1121.

R. Ursin, et. al. “Quantum teleportation across the Danube”. Nature. 430: 849 (19 August 2004)

1995 – Formulation of M-theory, an extension of string theory utilizing 11 dimensions.

E. Witten, “String Theory Dynamics In Various Dimensions“, Nucl. Phys. B 443:85-126 (1995).

### 2 Responses to Modern Physics: An Historical Overview of the Development of Quantum Mechanics, Quantum Field Theory, Relativity, and Cosmology

1. Nathan Reed says:

Nice timeline! Enjoyed reading it. Just one quibble: you say “The Standard Model of Physics fell into place: all fundamental forces of nature, except for gravity, were shown to be manifestations of the same fundamental interaction,” but that is not the Standard Model – in the SM, the electroweak and strong interactions are still separate. The Georgi-Glashow paper you cite is an example of a so-called Grand Unified Theory (GUT), which attempts to unify electroweak and strong interactions – but no GUT to date has become widely accepted and some, including the Georgi-Glashow one, have been experimentally falsified.

• glenmartin says:

You are quite right. I was rather sloppy with my phrasing.

Correcting now