Einstein and the Quantum
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Moore, Walter. Schrödinger: Life and Thought. Cambridge: University of Cambridge Press, 1989.
Nagel, Bengt. “The Discussion Concerning the Nobel Prize for Max Planck.” In Science, Technology and Society in the Time of Alfred Nobel: Nobel Symposium 52. Edited by C. G. Bernhard, E. Crawford, and P. Sorbom. New York: Pergamon Press, 1982.
Pais, Abraham. Subtle Is the Lord. Oxford: Oxford University Press, 2005.
Planck, Max. Scientific Biography and Other Papers, 1949. Translated by Frank Gaynor. New York: Philosophical Library, 1949.
Schrödinger, Erwin. What Is Life? The Physical Aspect of the Living Cell with Mind and Matter & Autobiographical Sketches. Cambridge: Cambridge University Press, 1958.
Scott, William T. Erwin Schrödinger: An Introduction to His Writings. Amherst: University of Massachusetts Press, 1967.
Stachel, John. “Einstein and Bose.” In Einstein from B to Z, vol. 9, pp. 519–538. Edited by John Stachel and Don Howard. Boston: Birkhauser, 2002.
Strutt, Robert John. The Life of Lord Rayleigh. Madison: University of Wisconsin Press, 1968.
Tolstoy, Ivan. James Clerk Maxwell. Edinburgh: Canongate, 1981.
Wali, K. “The Man behind Bose Statistics.” Physics Today, October 2006, p. 46.
ORIGINAL SCIENTIFIC RESEARCH ARTICLES (CHRONOLOGICAL)
1. Max Planck, “On an Improvement of Wien’s Equation for the Spectrum,” Proceedings of the German Physical Society, vol. 2, p. 202 (1900); reprinted in translation in Haar, The Old Quantum Theory, 79–81.
2. Max Planck, “On the Theory of the Energy Distribution Law of the Normal Spectrum,” Proceedings of the German Physical Society, vol. 2, p. 237 (1900); reprinted in translation in Haar, The Old Quantum Theory, 82–90.
3. Lord Rayleigh, “Remarks upon the Law of Complete Radiation,” Philosophical Magazine, vol. 49, pp. 539–40 (1900); reprinted in Scientific Papers by Lord Rayleigh, vol. 6, doc. 260, pp. 483–485, Dover, New York (1964).
4. Lord Rayleigh, “The Law of Partition of Kinetic Energy,” Philosophical Magazine, vol. 49, pp. 98–118 (1900); reprinted in Scientific Papers by Lord Rayleigh, vol. 6, doc. 253, pp. 433–451, Dover, New York (1964).
5. Albert Einstein, “On the General Molecular Theory of Heat,” Annalen der Physik, vol. 14, pp. 354–362 (1904); reprinted in CPAE, vol. 2, doc. 5, pp. 68–77.
6. Albert Einstein, “On a Heuristic Point of View concerning the Production and Transformation of Light,” Annalen der Physik, vol. 17, pp. 132–148 (1905); reprinted in CPAE, vol. 2, doc. 14, pp. 86–103.
7. Albert Einstein, “On the Electrodynamics of Moving Bodies,” Annalen der Physik, vol. 17, pp. 891–921 (1905); reprinted in CPAE, vol. 2, doc. 23, pp. 140–171.
8. Albert Einstein, “On the Theory of Light Production and Light Absorption,” Annalen der Physik, vol. 20, p. 199 (1906); reprinted in CPAE, vol. 2, doc. 34, pp. 192–199.
9. Albert Einstein, “Planck’s Theory of Radiation and the Theory of Specific Heat,” Annalen der Physik, vol. 22, pp. 180–190 (1907); reprinted in CPAE, vol. 2, doc. 38, pp. 214–224.
10. Albert Einstein, “On the Present Status of the Radiation Problem,” Physikalische Zeitschrift, vol. 10, pp. 185–193 (1909); reprinted in CPAE, vol. 2, doc. 56, pp. 357–375.
11. Albert Einstein, “On the Development of Our Views concerning the Nature and Constitution of Radiation,” Physikalische Zeitschrift, vol. 10, pp. 817–826 (1909), presented at the 81st Meeting of the German Scientists and Physicians, Salzburg, September 21, 1909; reprinted in CPAE, vol. 2, doc. 60, pp. 379–394.
12. “Discussion Following the Lecture: On the Development of Our Views concerning the Nature and Constitution of Radiation,” Physikalische Zeitschrift, vol. 10, pp. 825–826 (1909), presented at the 81st Meeting of the German Scientists and Physicians, September 21, 1909; reprinted in CPAE, vol. 2, doc. 61, pp. 395–398.
13. Albert Einstein, “On the Present State of the Problem of Specific Heats,” Proceedings of the Solvay Conference, October 30–November 3, 1911; reprinted in CPAE, vol. 2, doc. 26, pp. 419–420.
14. Niels Bohr, “On the Constitution of Atoms and Molecules,” Philosophical Magazine, vol. 26, p. 1 (1913); reprinted in The Old Quantum Theory, by D. Ter Haar, pp. 132–159.
15. Albert Einstein, “Emission and Absorption of Radiation in Quantum Theory,” Proceedings of the German Physical Society, vol. 18, pp. 318–323 (1916); reprinted in CPAE, vol. 6, doc. 34, pp. 212–216.
16. Albert Einstein, “On the Quantum Theory of Radiation,” Physikalische Gesellschaft Zurich, Mitteilungen, vol. 18 (1916); reprinted in CPAE, vol. 6, doc. 38, pp. 220–233.
17. Albert Einstein, “On the Quantum Theorem of Sommerfeld and Epstein,” Proceedings of the German Physical Society, vol. 19 (1917); reprinted in CPAE, vol. 6, doc. 45, pp. 434–443.
18. S. N. Bose, “Planck’s Law and the Light Quantum Hypothesis,” Zeitschrift für Physik, vol. 26, p. 178 (1924); reprinted in O. Theimer and B. Ram, “The Beginning of Quantum Statistics,” American. Journal of Physics, vol. 44, pp. 1056–1057 (1976).
19. S. N. Bose, “Thermal Equilibrium in the Radiation Field in the Presence of Matter,” Zeitschrift für Physik, vol. 27, p. 384 (1924); reprinted in O. Theimer and B. Ram, “Bose’s Second Paper: A Conflict with Einstein,” American Journal of Physics, vol. 45, pp. 242–246 (1976).
20. Albert Einstein, “Quantum Theory of the Monatomic Ideal Gas,” Proceedings of the Prussian Academy of Sciences, vol. 22, p. 261 (1924); reprinted in translation in I. Duck and E.C.G. Sudarshan, eds., Pauli and the Spin-Statistics Theorem, World Scientific, Singapore (1997), 82–87.
21. Albert Einstein, “Quantum Theory of the Monatomic Ideal Gas, Part Two,” Proceedings of the Prussian Academy of Sciences, vol. 1, p. 3 (1925); reprinted in translation in I. Duck and E.C.G. Sudarshan, eds., Pauli and the Spin-Statistics Theorem, World Scientific, Singapore (1997), 89–99.
22. Albert Einstein, “On the Quantum Theory of the Ideal Gas,” Proceedings of the Prussian Academy of Sciences, vol. 3, p. 18 (1925); reprinted in translation in I. Duck and E.C.G. Sudarshan, eds., Pauli and the Spin-Statistics Theorem, World Scientific, Singapore (1997), 100–107.
23. Louis de Broglie, “Black Radiation and Light Quanta,” Journal de Physique et le Radium, vol. 3, p. 422 (1922); reprinted in Selected Papers on Wave Mechanics by Louis de Broglie and Leon Brillouin, vols. 1–7, Blackie and Sons, London (1928).
24. Louis de Broglie, “A Tentative Theory of Light Quanta,” excerpt from Philosophical Magazine, vol. 47, p. 446 (1924); reprinted in I. Duck and E.C.G. Sudarshan, eds., 100 Years of Planck’s Quanta, chapter 4, World Scientific, Singapore (2000), 128–141.
25. Louis de Broglie, “Studies on the Theory of Quanta,” PhD thesis, originally published in Annales de Physique, vol. 3, p. 22 (1925).
26. Erwin Schrödinger collected nine of his seminal papers on the wave equation into a volume titled Abhandlungen der Wellenmechanik (Treatise on Wave Mechanics), which was originally published in 1927. These papers are available in English translation in E. Schrödinger, Collected Papers on Wave Mechanics, Chelsea Publishing, New York (1978). The nine papers are titled “Quantisation as a Problem of Proper Values, Parts I, II, III, IV,” “The Continuous Transition from Micro-to Macro-Mechanics,” “On the Relation between the Quantum Mechanics of Heisenberg, Born and Jordan, and That of Schrödinger,” “The Compton Effect,” “The Energy-Momentum Theorem for Material Waves,” and “The Exchange of Energy According to Wave Mechanics.” Note that the term “proper value” was the chosen translation for the German term Eigenvalue, which has become standard mathematical terminology in English as well.
INDEX
Note: page numbers in italics refer to images.
Absolute units, 116
Absorption: energy, 185–186; light, 75–77, 270–271
Academic appointments of Einstein, 122–125, 130, 150–152, 165–167
Action, 88, 199–201; principle of least, 88, 200; quantum of, 80, 89, 99, 115, 132, 15
5, 177, 281
Adler, Friedrich, 124
Angström, Knut, 117, 120
Annalen der Physik, 4, 26, 44, 46, 80, 88, 106, 266
Anschütz, Hermann, 212
Anti-Semitism, 151, 169, 206, 207–209, 211–212
Arrhenius, Svante Augustus, 111–117, 142, 212
Atomic theory, 37–38, 45–46, 113–114; Bohr’s, 172–179, 181–182; First Solvay Congress and, 150. See also Quantum theory
Atomic vibration, 104, 106–110, 178
Atoms, 81, 107–108, 112; energy absorption, 185–186, 270–271; light absorption, 75–77, 270–271; random behavior by, 232–234, 284; vibration, 108–110, 145, 178, 248–250
Autobiographical notes of Einstein, 279–280, 285
Avogadro’s number, 39, 87, 113–114, 115
Bertel, Annemarie, 258
Besso, Michele, 48, 65–66, 73; correspondence with Einstein, 130, 156, 163, 182–183, 188, 194–196, 201, 271–273
Blackbody radiation, 56–58, 70–74, 91, 108, 138; Einstein’s quantum theory of, 184–185; frequency and, 97–98, 293; Kirchoff’s law and, 291. See also Laws of thermal radiation; Thermal radiation
Bohr, Niels, 156, 170–174, 181, 199, 220, 274, 280, 283–284; atomic theory, 172–179, 181–182; de Broglie and, 245; Einstein on, 179–180, 283; Heisenberg and, 268, 269–270; Schrödinger and, 255, 258, 263, 268, 274; theory of spectra and, 184–186
Bohr-Sommerfeld theory, 170–174, 183–184, 199–201, 249, 256, 259–260, 266, 270
Boltzmann, Ludwig, 6, 14, 17, 33, 44, 45, 55, 73, 125, 223; death of, 259; Einstein on, 36, 38, 46, 47; equation for entropy, 51–52, 56, 58, 68, 91, 115, 154, 288; Newtonian mechanics and, 42; Third Law of thermodynamics and, 144–145; tomb of, 51, 52
Boltzmann’s constant, 51, 68, 91, 115, 154, 293
Born, Max, 20, 49, 136, 141, 162, 211, 255, 280–281, 285; ghost fields and, 198–199; Heisenberg and, 269, 271; interpretation of the wave function, 198, 274–277; Pauli and, 269; reverence for Einstein, 269; Schrödinger and, 274, 277
Bose, Satyendra Nath, 215, 228, 245, 253, 274; academic appointments of, 218; correspondence with Einstein, 215–216; derivation of Planck’s law, 219–224; education of, 217–218; Einstein’s critique of second paper by, 225; Einstein’s endorsement of first paper by, 216, 229–230; influence on Einstein, 229–232; influence on physics, 217; on new quantum mechanics, 272; second paper of, 224; visit to Europe, 225–227;
Bose-Einstein condensation, 233–238, 249, 256, 260, 261, 279, 282
Boson, 217; Higgs boson, 217
Bothe, Walter, 211; experiment with Geiger on Compton Effect, 283–284
Boyle’s Law, 38, 221
Brillouin, Leon, 244
Brownian motion, 39, 259
Bucherer, Alfred, 141
Calculus, 28
Caltech, 197
Cartan, Elie, 250
Children of Albert Einstein, 86, 87, 152, 167
Classical physics, 27–30, 171
Clausius, Rudolph, 42, 51, 113
Cleve, Per Theodor, 112
Compton, Arthur Holly, 283
Compton effect, 283–284
Coulomb, Charles Augustin de, 30
Curie, Marie, 149, 157, 226
De Broglie, Louis, 240, 241, 264, 280; Einstein on, 241–242, 251; family of, 242–243; Nobel prize, 252; Solvay Congress of 1911 and, 244; theoretical physics and, 244–245; theory on light quanta, 245–247; wave-particle duality, 247–250
De Broglie, Maurice, 242, 243–244, 245, 250
De Broglie, Pauline, 243
De Broglie wavelength, 252
Debye, Peter, 103, 229
Degenhart, Joseph, 17
De Haas, Wander J., 162
Determinism in quantum mechanics, 277
Diamond, 104–105
Dice, 232–234, 284–285
Diffusion, 39
Dirac, Paul, 162, 256
Doppler effect, 190–191, 210–211
Drude, Paul, 44–45, 71, 73, 108
Dulong, Pierre, 103–104
Dulong-Petit law, 103–108
Dynamical Theory of Gases, 99
Dyson, Frank, 205
Eddington, Arthur Stanley, 204–205
Edison, Thomas, 143–144
Ehrat, Jakob, 22
Ehrenfest, Paul, 72, 167, 194, 195, 197, 211, 224, 231, 271, 273; Bose statistics and, 238; ultraviolet catastrophe and, 72
Einstein, Albert, 14, 153; academic appointments of, 122–125, 130, 150–151; accomplishments of, 279–282; anti-Semitism and, 151, 169, 206, 207–209, 211–212; autobiographical notes by, 279–280, 285; in Berlin, Germany, 165–167; in Bern, Switzerland, 46–48, 62–66, 122–123; on blackbody radiation, 70–74, 184–187, 284–285; on Bohr, 180, 283; on Boltzmann, 36, 38, 46; Born and, 285; Bose and, 215–227, 229–230, 281–282; on Brownian motion, 39, 259; children of, 86, 87, 152, 167; correspondence with Besso, 130, 156, 163, 182–183, 188, 194–196, 201, 271–273; on de Broglie, 241–242, 251; dislike of quantum theory, 1–2, 277; divorce from Mileva Maric, 194–196; on Drude, 44; early work in theoretical physics, 26–27; early work on relativity theory, 3–4, 151, 161; Elsa Einstein and, 164–165, 193, 210; on energy quantization using Planck’s resonators, 91–92; on ether, 83–85; fame of, 205–207, 216; first published work on atomic theory, 45–46; formal education of, 15–20, 46–47; “fusion” theory of light, 137–138; on Gibbs, 50; health of, 193–196; heuristic point of view on light, 70–79; on idea gas law, 230–238; influence of Maxwell on, 34–35, 50, 84–85, 153; influence of Nernst on, 146–148, 154, 163–164, 228; influence of Newton on, 29, 35; interest in quantum theory, 3, 125–128, 183–184; Jewish identity of, 208–209; Lorentz and, 50, 130–135, 153–154, 167, 194, 197; on matrix mechanics, 271–3; Mileva Maric and, 48, 62, 63, 129–130, 152, 164–165; Anna Meyer-Schmid and, 129–130; Nobel prize won by, 282; Olympia Academy and, 63–66, 212; papers on First and Second Laws of thermodynamics, 48–49; parents of, 24–25; peers and friends in Bern, 63–66; PhD thesis, 46–47; on Planck, 26–27, 73–74, 285; Planck’s response to theory of light quanta, 80–81; Planck’s support for special theory of relativity and, 88–89; in Prague, Bohemia, Austro-Hungarian Empire, 152; probabilistic interpretation of wavefunction and, 276, 282; as a prodigy, 15–16; quantum ideal gas and, 230–232, 235–238; on radioactive decay, 182–183; reputation among his peers, 21–23; rise in stature of, 150–152; Rubens on, 208; Schrödinger and, 238–240, 254–267; sliding mirror thought experiment, 138–139, 189; Ernest Solvay and, 149–150, 156–158; Sommerfeld and, 125–126, 184; A. Douglas Stone’s interest in, 2–3; teaching career of, 44–45, 47, 63, 122; time dilation and, 248; travel around the world, 209–210, 212–213; on wave function in q-space, 275–276; Heinrich Weber and, 15–20, 26, 35, 103, 152; during World War I, 168–170, 193–194, 204. See also Quantum theory; Theory of relativity
Einstein, Eduard, 152
Einstein, Elsa, 164–165, 193, 194–196, 210
Einstein, Hans Albert, 86
Einstein, Mileva Maric, 4, 16, 20, 22, 167; children of, 86, 87, 152, 167; divorce from Einstein, 194–196; early relationship with Einstein, 23–25; Einsteins’ correspondence with, 26–27, 36, 44, 46, 47, 106; marriage to Einstein, 48, 62, 63, 129–130, 152, 164–165; move to Berlin, 167
Electromagnetic (EM) radiation, 7–8, 42; blackbody, 56–60, 70–74, 78–79, 91, 97–98, 108, 138, 184–185, 291; Boltzmann’s principle and, 56–58; conservation of energy and, 74–75; Einstein’s struggles with quantum theory of, 153–156; frequency and, 97–98; gas molecules’ interaction with, 189–190; Maxwell’s work on, 33–34, 83; Planck’s constant and, 154–155; Rayleigh-Jeans law and, 100–102, 119–120, 292; thermal radiation law, 291, 293–294; visible, 11–12, 113–119; wavelengths, 72–73; waves, 81–85; Wien law and, 94–99, 292. See also Maxwell’s equations; Planck’s law
Electrons, 45, 81; orbital frequencies, 174–178, 183–184; orbits, 200–202; photoelectric effect and, 78–79; wavefunction, 265–267, 275–276
Elementary Principles of Statistical Mechanics, 49
Elsasser, Walter, 252
“Emission and Absorption of Radiation in Quantum Theory,” 184–185
Emission of light: directed, 192; Einstein’s flawed experiment on, 210–211; spontaneous, 186, 224–225; stimulated 187, 224–225
Emission theory of light, 137
Energy: Dulong-Petit law, 103–108; emission and, 137, 186–187; fluctuations, 250–251; free, 49; frequency and, 68–69, 72; ground state, 185–186, 229; linear oscillator and, 174–175; orbital, 174–178; peak frequency and, 95–96; photoelectric effect and, 78–79; potential, 68–69, 265–266; quantization of, 97–98, 106–110, 131–132, 219–224, 264–265; Rayleigh-Jeans law, 100–102, 119–120; temperature and, 38, 96; thermal, 67–68; ultraviolet catastrophe and, 72, 98–102, 99–100, 102; Wien law and, 94–99
Entropy, 42, 51–55, 67, 238; additivity of, 238; blackbody radiation and, 56–60, 74; Boltzmann’s equation for, 51–2, 56, 58, 68, 91, 115, 154, 288; Bose on, 220–222; calculations using Planck’s resonators, 91–92; chance and, 232–233; Second Law of thermodynamics and, 10, 41, 54, 56, 57; thermal equilibrium and, 7, 100–102, 140, 185–186, 189, 224, 250, 291; Third Law of thermodynamics and, 144, 238
Epstein, Paul, 136, 140, 201, 275
Equilibrium, thermal, 185–186
Ether, the, 83–85, 99–100, 132
Failure of Planck-Wien Law, 9–11
Fan waves, 81–82
Faraday, Michael, 26, 30–31, 34–35
Faraday’s Law, 30–31, 32
Fermi, Enrico, 269
Feynman, Richard, 5, 34
First Law of thermodynamics, 41, 48–49
Fischer, Emil, 143–144, 151
Fluctuations, energy, 250–251
Force, fluctuating, 191
Force-carrying particle. See Photons
Formal education of Einstein, 15–20, 46–47
Franck, James, 276
Frank, Philipp, 159, 166–167
Fredholm, Ivar, 114, 121
Free energy, 49
Freezing, quantum, 144–145
Frequency, 68–69, 72, 75–76, 293; electron orbital, 174–178, 183–184; low, 98–99; peak, 95–96; rest, 248; transition, 270–271