An Act of Desperation

Essay · physics · September 2026

Quantum mechanics was not discovered. It was assembled, over twenty-seven years, by two dozen people who mostly disagreed with one another and several of whom disliked what they had made. It began with a formula fitted to a furnace in Berlin, passed through a young man’s hay fever on a North Sea island, and was finished in a hotel in Brussels where its founders argued about what it meant and did not settle the argument. The argument was reopened in 1964 by a Belfast engineer working in his spare time, and closed, insofar as it can be, by three experiments that won the Nobel prize in 2022. This is that history.

Reading time ≈ 23 min Berlin 1900 → Brussels 1927 → Vienna 2015 A standalone essay

Berlin, 1900

Max Planck did not want to start a revolution. He was forty-two, a professor in Berlin, a conservative in physics as in everything else, and the problem he was working on was, by the standards of 1900, an engineering problem: what colour is a hot object? The German state had built an institute in Charlottenburg to answer such questions for industry, and its experimenters, Otto Lummer, Ernst Pringsheim, Heinrich Rubens and Ferdinand Kurlbaum, had spent five years measuring the light from a heated cavity, the closest thing that can be built to Kirchhoff’s ideal black body, across a widening range of wavelengths.[1] Wilhelm Wien had a formula from 1896 that fitted the short wavelengths and that Planck believed he had derived from thermodynamics. In the autumn of 1900 Rubens and Kurlbaum pushed the measurements out to 50 micrometres, deep in the infrared, and the formula failed.

Rubens told Planck on a Sunday in October, over lunch. By that evening Planck had a new formula, found by interpolating between Wien’s at short wavelengths and the classical proportionality to temperature that the long-wavelength data obeyed, and he presented it to the Berlin Physical Society on 19 October as a guess.[2] It fitted everything, at every temperature, to the precision of the measurements. Figure 1 shows what it had to do: Wien’s law drops away too fast beyond the peak, the classical law that Lord Rayleigh had written down four months earlier rises without limit at short wavelengths, and Planck’s curve joins the two with a single expression that neither of them could have produced.

Figure 1. The black-body spectrum at 1600 kelvin, the temperature range Rubens and Kurlbaum measured in October 1900. Wien’s 1896 law (dashed) fits the short-wavelength side and falls too fast past the peak; at 50 micrometres it is a sixth of the measured value. Rayleigh’s classical law (teal) fits the long-wavelength tail and rises without limit toward short wavelengths, nine hundred times too high at one micrometre. Planck’s formula (magenta) is the single curve that does both.

Then he had to explain it, and the explanation is the revolution. In the eight weeks that followed he tried to derive the formula from the thermodynamics of oscillators in the cavity walls and could not, until he used a method of Boltzmann’s that he had spent his career resisting: count the ways the energy can be distributed among the oscillators, and take the entropy to be the logarithm of the count. To count, the energy has to come in pieces, and for the count to give his formula the piece for an oscillator of frequency ν had to be hν, with h a new constant of nature. He presented the derivation on 14 December 1900, which is the conventional birthday of quantum theory, and he did not believe that the pieces were real.[3] Boltzmann had used the same trick and let the piece size go to zero at the end. Planck could not, because the constant was in the formula that fitted the data. He wrote thirty years later that it had been an act of desperation, that he had been prepared to sacrifice any of his previous convictions except the two laws of thermodynamics, and that he had spent years afterward trying to fit h into classical physics and failing.[4]

The name for the classical failure, the ultraviolet catastrophe, was coined by Paul Ehrenfest in 1911, and it has given generations of students the impression that Planck was rescuing physics from a crisis. He was not. In 1900 almost no one thought the classical law was compulsory, and Planck had never used it. He was fitting a furnace, and the constant he found in the fit turned out to be the size of the grain in everything.

1905 to 1916

Light itself

For four years nobody took the pieces seriously, including Planck. Then in March 1905, in the first of the four papers of his miraculous year, a patent examiner in Bern proposed that the pieces were not a property of the oscillators but of the light. Einstein called the paper “very revolutionary” in a letter to a friend, and it was the only one of his papers he ever described that way.[5] Its argument was thermodynamic, showing that the entropy of radiation in Wien’s regime behaves like the entropy of a gas of independent particles of energy hν. Its consequences were a set of predictions, and the sharpest was for an effect Philipp Lenard had measured in 1902 and could not explain: light falling on a metal knocks out electrons, and the energy of the electrons depends on the colour of the light, not its brightness. If light comes in quanta of hν, an electron absorbs one quantum, pays the metal’s binding energy, and leaves with the rest. The energy of the fastest electron should then rise in a straight line with the frequency, with slope h, the same for every metal, and below a threshold frequency no electrons should come out however bright the light.

Figure 2. Einstein’s 1905 prediction for the photoelectric effect: the voltage needed to stop the fastest electrons against the frequency of the light, for three metals. Each line starts at the metal’s threshold, below which no light of any brightness ejects electrons, and all three have the same slope, Planck’s constant divided by the electron’s charge. Millikan measured the sodium line in 1916, obtained h from its slope to half a per cent, and reported the result as evidence against the theory that predicted it.

The physicist who tested this was Robert Millikan at Chicago, who spent a decade on it because he was sure it was wrong. Maxwell’s theory of light as a wave had been confirmed in every detail, and a particle theory of light seemed to him, as he wrote, reckless. He built an apparatus that shaved the surface of a sodium sample under vacuum with a rotating knife, to keep it clean, and measured the stopping voltage against frequency. In 1916 he published a straight line of the predicted slope, from which he extracted h to half a per cent, and wrote in the same paper that the theory it confirmed was untenable.[6] Einstein received the Nobel prize for the equation in 1922 and Millikan for measuring it in 1923. Arthur Compton settled the matter for most physicists in 1923 by scattering X-rays from electrons and finding that they bounced like particles, with the momentum of a quantum.

1913

The atom that should not exist

The second front was the atom, and there the classical theory was not incomplete but absurd. Ernest Rutherford had found in 1911, by firing alpha particles at gold foil and seeing a few come straight back, that the atom was mostly empty, with its positive charge and almost all its mass in a nucleus a hundred thousand times smaller than the whole. The electrons had to be in orbit, and an orbiting electron, being an accelerating charge, radiates; by Maxwell’s equations it should spiral into the nucleus in about a hundredth of a microsecond. Atoms exist, so something was wrong.

Niels Bohr arrived in Manchester to work with Rutherford in 1912, aged twenty-six, and in 1913 published three papers that did not so much solve the problem as forbid it.[7] The electron, he postulated, can occupy only certain orbits, those in which its angular momentum is a whole number of units of h/2π, and in those orbits it does not radiate. It radiates only when it jumps from one orbit to another, and the light it emits then carries the energy difference as a single quantum, at the frequency given by Planck’s relation. The postulates contradicted electrodynamics and were justified by one thing: they gave the spectrum of hydrogen. Johann Balmer, a schoolteacher in Basel, had noticed in 1885 that the four visible lines of hydrogen obeyed a formula involving the squares of small integers, and Johannes Rydberg had generalised it. Bohr’s orbits gave Balmer’s formula with the constant in it computed from h, the electron’s mass and charge, and the speed of light, to within the accuracy of the measurements. Figure 3 is what the postulates predict: the Balmer lines in the visible, a series in the ultraviolet that Theodore Lyman had just found, and one in the infrared that Friedrich Paschen found in 1908, each series converging to a limit where the integers run out.

Figure 3. The hydrogen spectrum as Bohr’s 1913 postulates give it, from the Rydberg formula with the constant computed from h, the electron’s charge and mass, and the speed of light. Each series is the set of jumps down to one orbit: the Balmer series to the second orbit, with its red line at 656 nanometres, was known from 1885; the Lyman series in the ultraviolet was being found as Bohr wrote; the Paschen series in the infrared had been found in 1908. Each converges to a limit where the integers run out.

Bohr’s atom worked for hydrogen and for nothing else. Arnold Sommerfeld in Munich extended it to elliptical orbits and to relativistic corrections and recovered the fine structure of the lines, and for a decade a school of physicists developed what is now called the old quantum theory, a set of rules for which classical orbits were allowed, applied to one problem after another. Helium, with two electrons, defeated every attempt. The theory was, in Bohr’s own words, a way of using classical mechanics to compute things that classical mechanics forbade, and by 1924 the people using it knew it was a scaffold and not a building. That year Bohr, Hendrik Kramers and John Slater proposed giving up energy conservation in individual atomic events to save the wave picture of light, and within months Walther Bothe and Hans Geiger showed by coincidence counting that energy was conserved event by event.[8] The old theory had run out of moves.

Two ideas from outside the Copenhagen and Munich schools set up the endgame. In 1924 Louis de Broglie, in a doctoral thesis in Paris that his examiners could not evaluate and sent to Einstein, proposed that if light waves were particles then particles were waves, with a wavelength h over the momentum, and that Bohr’s allowed orbits were the ones into which a whole number of waves fitted.[9] Einstein said the thesis had lifted a corner of the great veil. And Wolfgang Pauli in January 1925 stated the exclusion principle, that no two electrons can share the same set of quantum numbers, which explained the periodic table and required a fourth number for the electron that George Uhlenbeck and Samuel Goudsmit identified that autumn as spin.[10]

1925 to 1927

Twenty-four months

Werner Heisenberg was twenty-three, an assistant to Max Born in Göttingen, when in June 1925 a bout of hay fever sent him to Heligoland, a bare rock in the North Sea with no pollen. He had decided that the trouble with the old theory was that it talked about orbits, which nobody could observe, and he set out to build a mechanics from the things spectroscopy actually measured: the frequencies and intensities of the lines, each labelled by the two states it connected. Those form a square array, and in trying to make the arrays obey the equations of motion he found that his rule for multiplying them did not commute: the product of position and momentum was not the product of momentum and position. He nearly abandoned the idea for that reason. Instead, on the island, he checked that energy was conserved in his scheme and, by his own account, was so excited that he could not sleep and climbed a rock to wait for the sunrise.[11]

What followed is the densest two years in the history of any science, and it is easiest to give as a list.

July 1925 · Heisenberg

The paper is received on 29 July. Born recognises the arrays as matrices, a branch of mathematics physicists did not then learn, and with Pascual Jordan writes the theory out properly in September; the three of them publish the full “three-man paper” in November. In Cambridge, Paul Dirac, aged twenty-three, reads the proofs of Heisenberg’s paper and in November produces his own formulation, in which the non-commutation is the whole content and the classical theory is recovered as a limit.[12]

January 1926 · Schrödinger

Erwin Schrödinger, thirty-eight, professor in Zurich and by temperament a classical physicist, takes de Broglie’s waves to an Alpine resort over Christmas and comes back with a wave equation whose standing-wave solutions in the hydrogen atom are Bohr’s energy levels. Four papers between January and June cover everything the matrix theory could do, in mathematics physicists already knew.[13] In March he proves that the two theories are the same theory in different clothes. Heisenberg finds the wave theory disgusting; Schrödinger finds the jumps repellent; both are right about the other’s formalism and wrong about the physics.

June 1926 · Born

In a paper on scattering, Born proposes what the wave is. It is not the electron smeared out, as Schrödinger hoped. Its square is the probability of finding the electron at that place. The proposal is in a footnote added in proof, correcting the main text, which had left out the square.[14] It is the point at which the theory stops being deterministic, and it earned Born the Nobel prize in 1954, twenty-two years after Heisenberg’s.

March 1927 · Heisenberg again

The uncertainty relations: position and momentum cannot both be known to better than a product of order h, and the same for energy and time. Heisenberg presents it with a thought experiment about a microscope that Bohr immediately shows to be wrong in detail and right in conclusion, and the two argue so bitterly that Heisenberg is reduced to tears.[15]

1927 · the waves are seen

Clinton Davisson and Lester Germer at Bell Labs, and George Thomson in Aberdeen, diffract electrons from crystals and find de Broglie’s wavelength. Thomson’s father had won the Nobel prize for showing the electron was a particle; the son won it for showing it was a wave.[16]

October 1927 · Brussels

The fifth Solvay conference brings the founders together in one room for a week, twenty-nine people of whom seventeen had or would receive the Nobel prize. Bohr presents complementarity, the doctrine that wave and particle descriptions are each complete in their own experimental context and never needed together. Einstein, at breakfast each morning, presents a thought experiment designed to beat the uncertainty relation, and Bohr, by dinner, finds the flaw. The exchanges are remembered from Bohr’s account, written twenty years later; Einstein left no account and remained unconvinced.[17]

January 1928 · Dirac

The relativistic equation for the electron, which produces spin without assuming it and has solutions of negative energy that Dirac, after two years of trying to make them go away, interprets in 1931 as a new particle with the electron’s mass and opposite charge. Carl Anderson photographs one in a cloud chamber in 1932.[18] It is the first time a particle was predicted by an equation before it was seen, and the moment the theory stopped describing the world and began to enlarge it.

By the end of 1927 the theory was complete in the sense that it has not changed since. Every calculation in chemistry and solid-state physics, every transistor and laser, uses the equations that existed in the spring of that year. John von Neumann put the mathematics on a rigorous footing in 1932 and in doing so stated the problem that the equations left open: the theory has one rule for how a state evolves when nobody looks, smooth and reversible, and another for what happens when someone does, sudden and random, and it does not say what a look is.[19]

1935

Two objections that would not go away

Einstein had lost every round in Brussels and did not accept the verdict, and in May 1935, now at Princeton, he published with Boris Podolsky and Nathan Rosen the objection he had been circling for eight years.[20] Take two particles that have interacted and flown apart. The theory says their state is a single joint state, and that measuring the position of one fixes the position of the other, while measuring the momentum of one fixes the momentum of the other. The second particle can be arbitrarily far away. Since a measurement here cannot disturb a particle there, the second particle must have had both a definite position and a definite momentum all along, which the theory denies. Either the theory is incomplete, there being facts about the second particle it does not contain, or it allows what Einstein called, in a later letter, spooky action at a distance. He was sure it was the former.

Bohr replied within months, and the reply is widely agreed to be obscure. Schrödinger replied in November with a paper containing the cat, a creature whose life or death is tied to a radioactive atom that the theory says is both decayed and not, so that the theory, taken literally, says the cat is both dead and alive until the box is opened.[21] He meant it as a reductio; it has become the theory’s mascot. The same paper introduced the word entanglement for the joint state Einstein had objected to, and called it not one but the characteristic trait of quantum mechanics, the thing that separates it entirely from classical thought.

Then the subject went quiet, for a reason that has nothing to do with physics: the theory worked, the war came, and after the war the people who had built it were building bombs, accelerators and the quantum theory of fields, which between 1947 and 1949 produced the most precise predictions in science. Asking what the equations meant became a career-ending hobby. David Bohm, who asked in 1952 and produced a consistent theory in which the particles have definite positions and are guided by the wave, was by then in exile in Brazil after refusing to testify to the House Un-American Activities Committee, and his theory was ignored for thirty years.[22] Hugh Everett, who asked in 1957 and answered that every outcome happens in its own branch of the universe, left physics for defence contracting after Bohr received the idea coldly.[23]

1964 to 2022

The argument becomes an experiment

John Bell was an accelerator physicist at CERN who had been troubled by von Neumann’s proof, and by Bohm’s counterexample to it, since his student days in Belfast, and who worked on the foundations of quantum mechanics, as he said, on Sundays. In 1964, on sabbatical in the United States, he did what nobody in the thirty years since Einstein’s paper had done: he turned the objection into an inequality.[24] Suppose Einstein was right, and each particle carries its own definite properties, fixed at the source, with nothing passing between them afterward. Then the correlations between measurements on the two particles, at detectors set to various angles, are constrained. Bell derived the constraint. Quantum mechanics predicts correlations that violate it. So the question Einstein and Bohr had argued about over breakfast was not philosophy. It was a number, and the number could be measured.

The paper appeared in a new journal that folded after four issues, and it took five years for anyone to notice. In 1969 John Clauser, Michael Horne, Abner Shimony and Richard Holt put the inequality into a form an experiment could use, a combination S of four correlations that no local theory can push beyond 2 and that quantum mechanics takes to 2√2, and in 1972 Clauser and Stuart Freedman at Berkeley measured it, with photon pairs from calcium atoms and detectors that took hours to accumulate a count, and found the quantum value.[25] Clauser had expected the opposite. Alain Aspect in Orsay in 1982 closed the most obvious loophole by switching the detector settings while the photons were in flight, too fast for any signal between the detectors to matter, and measured S = 2.70 ± 0.02.[26] Figure 4 is what he measured against what the two theories predict.

Figure 4. The quantity S that Clauser, Horne, Shimony and Holt built from four correlation measurements, against the angle between the polarisation analysers. Any theory in which the photons carry their properties from the source, and nothing passes between the detectors, keeps S between −2 and 2. Quantum mechanics predicts the curve, reaching 2√2 at 22.5 degrees. Aspect’s 1982 value and Weihs’s 1998 value at that angle are shown; both are inside the region no local theory can reach.

Anton Zeilinger’s group in Innsbruck repeated it in 1998 with the detectors 400 metres apart and the settings chosen by a quantum random number generator, and got 2.73 ± 0.02; and in 2015 three groups, in Delft, Vienna and Boulder, closed the remaining loopholes at once, with detection efficient enough that no sample of undetected pairs could account for the result.[27] Clauser, Aspect and Zeilinger were given the Nobel prize in 2022. The citation did not say that Einstein was wrong, and physicists argue about exactly what the experiments rule out. What they rule out at minimum is the world Einstein wanted: one in which things have their properties before anyone looks and nothing travels faster than light. One of those has to go.

The question Einstein and Bohr argued about over breakfast turned out not to be philosophy. It was a number, and the number could be measured.bell, 1964

The last chapter is one this blog has covered elsewhere and can be given in a paragraph. In 1981 Richard Feynman observed that simulating a quantum system on an ordinary computer takes resources that grow exponentially with its size, and asked whether a computer built of quantum parts would do better. David Deutsch made the question precise in 1985; Peter Shor showed in 1994 that such a machine could factor large numbers efficiently, which no ordinary computer is believed able to do, and which is the foundation of the encryption on which the internet runs.[28] The technology that has followed is the industrial exploitation of the very features that troubled the founders: superposition, entanglement, and the interference of amplitudes. What Schrödinger called the characteristic trait, and Einstein called spooky, is now a resource with a price.

Coda

What the history says about the theory

Set this story beside the companion essay on general relativity and the contrast is the point. That theory was made by one man from one idea over eight years, and every prediction it made came from the mathematics and was checked afterward. This one was made by twenty people over twenty-seven years, and every step was forced by a measurement: a furnace, a metal plate, a spectral line, a scattered electron. Nobody wanted it. Planck did not believe in the quanta, Einstein did not believe in the dice, Schrödinger did not believe in the jumps, and Bohr, who believed in all of it, built a philosophy to explain why it could not be asked what any of it meant.

The second thing is that the theory was complete before anyone understood it, and it is not clear that anyone understands it now. The equations of 1927 have made every prediction asked of them for a century, to a precision no other theory approaches, and the question Einstein put in 1935 was answered by experiment in his disfavour without being answered in the sense he meant. The founders’ argument about what the wave is, and what happens when it is looked at, is still open, and is now the subject of a small industry of interpretations that agree on every number and disagree on everything else.

The third is that the argument itself became useful. Bell’s theorem was a Sunday hobby of a man who thought the theory he tested was probably wrong, and it became the foundation of a technology. The features the founders found most objectionable are the ones that turned out to be exploitable. That is, if one wanted a moral, a better one than the usual: a theory does not have to be understood to be right, and does not have to be liked to be used.

On method and tools

This piece was written collaboratively with Claude Fable 5.1 (Anthropic): human specification, editorial direction and critical review; machine synthesis, drafting, computation and figure generation.

The figures are computed, not traced. The script scripts/physics_history.py evaluates Planck’s, Wien’s and the Rayleigh–Jeans formulas at 1600 kelvin, the temperature range of the Rubens–Kurlbaum measurements; the photoelectric line eV = hν − φ for three metals from their tabulated work functions; the hydrogen series from the Rydberg formula; and the CHSH combination 3 cos 2θ − cos 6θ for a polarisation-entangled pair, with the two measured values transcribed from the papers cited. Its numerical output is in docs/physics-history-results.json. Dates and quotations are from the sources below, chiefly Mehra and Rechenberg and Kumar; where a story survives only in one participant’s later recollection, the text says so.

Authored by: Luis Matos Ferreira — Physicist, Developer, Writer

Related essays on this blog

1. The Happiest Thought — the companion history: how general relativity was made, by one person, in the same years.
2. The Smooth and the Grainy — where this theory and general relativity contradict each other, and the attempts to join them.
3. The Interference Machine — what a quantum computer does with the features the founders disliked.

Sources

1. Kirchhoff, Annalen der Physik 109, 275 (1860); Wien, Annalen der Physik 58, 662 (1896); Lummer & Pringsheim, Verhandlungen der Deutschen Physikalischen Gesellschaft 1, 23 (1899); Rubens & Kurlbaum, Sitzungsberichte der Preussischen Akademie, 25 October 1900, p. 929.
2. Planck, “Über eine Verbesserung der Wienschen Spektralgleichung”, Verhandlungen der Deutschen Physikalischen Gesellschaft 2, 202 (1900), presented 19 October; Rayleigh, Philosophical Magazine 49, 539 (June 1900), with the numerical factor corrected by Jeans in 1905.
3. Planck, “Zur Theorie des Gesetzes der Energieverteilung im Normalspectrum”, Verhandlungen der Deutschen Physikalischen Gesellschaft 2, 237 (1900), presented 14 December; Kuhn, Black-Body Theory and the Quantum Discontinuity, 1894–1912, Oxford, 1978, on what Planck did and did not believe.
4. Planck to Robert Williams Wood, 7 October 1931, in Hermann, The Genesis of Quantum Theory, MIT, 1971, p. 23; Ehrenfest, Annalen der Physik 36, 91 (1911), for the “catastrophe”.
5. Einstein, “Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt”, Annalen der Physik 17, 132 (1905); Einstein to Habicht, May 1905, CPAE vol. 5, doc. 27; Lenard, Annalen der Physik 8, 149 (1902).
6. Millikan, “A Direct Photoelectric Determination of Planck’s h”, Physical Review 7, 355 (1916); Compton, Physical Review 21, 483 (1923).
7. Rutherford, Philosophical Magazine 21, 669 (1911); Bohr, “On the Constitution of Atoms and Molecules”, parts I–III, Philosophical Magazine 26, 1, 476, 857 (1913); Balmer, Annalen der Physik 25, 80 (1885); Rydberg, Kungliga Svenska Vetenskapsakademiens Handlingar 23, no. 11 (1889).
8. Sommerfeld, Annalen der Physik 51, 1 (1916); Bohr, Kramers & Slater, Philosophical Magazine 47, 785 (1924); Bothe & Geiger, Zeitschrift für Physik 32, 639 (1925).
9. de Broglie, Recherches sur la théorie des quanta, thesis, Paris, November 1924; Annales de Physique 3, 22 (1925). Einstein’s remark is in a letter to Langevin, December 1924.
10. Pauli, Zeitschrift für Physik 31, 765 (1925); Uhlenbeck & Goudsmit, Naturwissenschaften 13, 953 (1925).
11. Heisenberg, Der Teil und das Ganze, Piper, 1969, ch. 5, for the Heligoland account, written forty years later; Heisenberg, “Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen”, Zeitschrift für Physik 33, 879 (1925), received 29 July.
12. Born & Jordan, Zeitschrift für Physik 34, 858 (1925); Born, Heisenberg & Jordan, Zeitschrift für Physik 35, 557 (1926); Dirac, “The Fundamental Equations of Quantum Mechanics”, Proceedings of the Royal Society A 109, 642 (1925).
13. Schrödinger, “Quantisierung als Eigenwertproblem”, parts I–IV, Annalen der Physik 79, 361 and 489; 80, 437; 81, 109 (1926); “Über das Verhältnis der Heisenberg-Born-Jordanschen Quantenmechanik zu der meinen”, Annalen der Physik 79, 734 (1926). Moore, Schrödinger: Life and Thought, Cambridge, 1989, on Arosa.
14. Born, “Zur Quantenmechanik der Stossvorgänge”, Zeitschrift für Physik 37, 863 (1926), footnote added in proof; and 38, 803 (1926).
15. Heisenberg, “Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik”, Zeitschrift für Physik 43, 172 (1927); the tears are Heisenberg’s own recollection, in the 1963 interviews with Kuhn, Archive for the History of Quantum Physics.
16. Davisson & Germer, Physical Review 30, 705 (1927); Thomson & Reid, Nature 119, 890 (1927).
17. Électrons et Photons: Rapports et Discussions du Cinquième Conseil de Physique Solvay, Gauthier-Villars, 1928; Bohr, “Discussion with Einstein on Epistemological Problems in Atomic Physics”, in Schilpp (ed.), Albert Einstein: Philosopher-Scientist, 1949; Bacciagaluppi & Valentini, Quantum Theory at the Crossroads, Cambridge, 2009, for the full proceedings and a corrective reading.
18. Dirac, “The Quantum Theory of the Electron”, Proceedings of the Royal Society A 117, 610 (1928); “Quantised Singularities in the Electromagnetic Field”, Proceedings of the Royal Society A 133, 60 (1931); Anderson, Physical Review 43, 491 (1933).
19. von Neumann, Mathematische Grundlagen der Quantenmechanik, Springer, 1932, ch. VI.
20. Einstein, Podolsky & Rosen, “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?”, Physical Review 47, 777 (1935); “spukhafte Fernwirkung” is from Einstein to Born, 3 March 1947, in The Born–Einstein Letters, Macmillan, 1971.
21. Bohr, Physical Review 48, 696 (1935); Schrödinger, “Die gegenwärtige Situation in der Quantenmechanik”, Naturwissenschaften 23, 807, 823, 844 (1935); “Discussion of Probability Relations between Separated Systems”, Proceedings of the Cambridge Philosophical Society 31, 555 (1935), for “entanglement”.
22. Bohm, “A Suggested Interpretation of the Quantum Theory in Terms of ‘Hidden’ Variables”, I and II, Physical Review 85, 166 and 180 (1952); Peat, Infinite Potential, Addison-Wesley, 1997.
23. Everett, “‘Relative State’ Formulation of Quantum Mechanics”, Reviews of Modern Physics 29, 454 (1957); Byrne, The Many Worlds of Hugh Everett III, Oxford, 2010.
24. Bell, “On the Einstein Podolsky Rosen Paradox”, Physics 1, 195 (1964); “On the Problem of Hidden Variables in Quantum Mechanics”, Reviews of Modern Physics 38, 447 (1966); the “Sundays” remark is in Bernstein, Quantum Profiles, Princeton, 1991.
25. Clauser, Horne, Shimony & Holt, Physical Review Letters 23, 880 (1969); Freedman & Clauser, Physical Review Letters 28, 938 (1972).
26. Aspect, Dalibard & Roger, “Experimental Test of Bell’s Inequalities Using Time-Varying Analyzers”, Physical Review Letters 49, 1804 (1982); Aspect, Grangier & Roger, Physical Review Letters 49, 91 (1982), S = 2.697 ± 0.015.
27. Weihs et al., Physical Review Letters 81, 5039 (1998); Hensen et al., Nature 526, 682 (2015); Giustina et al., Physical Review Letters 115, 250401 (2015); Shalm et al., Physical Review Letters 115, 250402 (2015); Nobel Prize in Physics 2022.
28. Feynman, “Simulating Physics with Computers”, International Journal of Theoretical Physics 21, 467 (1982), from the May 1981 lecture; Deutsch, Proceedings of the Royal Society A 400, 97 (1985); Shor, in Proceedings of the 35th Annual Symposium on Foundations of Computer Science, 1994.