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Adler, Gottlieb, 122
Alchemy, 12–13
Arrhenius, Svante, 67, 68, 95, 128, 197, 215, 230
Atheism, 5, 7, 8, 12, 110–11, 131
Atom(s)
billard ball model of, 25
direct proof of existence of, 207
distinction between molecules and, 13
distribution of velocity, 24–26.
See also Maxwell’s velocity distribution
estimates of size, 21–22, 23, 27–28, 51, 72
origin of word, 3
pigeonhole model for energy distribution of, 89–92
Boltzmann as “last pillar” of, 145, 146
debate on in America, 201
energeticism rejection of. See Energeticism
Gibbs’ work and, 156, 158–60, 161
historical perspective on, 1–14
Mach on, vii, ix–xi, 124, 132–34, 136–37, 168–69, 199, 218–19
Planck’s view of, 174–75
Bacon, Francis, 169
Ballot, Christopher Buys, 24
Bell, Alexander Graham, 148
Bell curve of probability theory, 39
Bernoulli, Daniel, 3, 13, 16, 17, 19, 20, 21, 109
Boltzmann, Albert (Boltzmann’s brother), 34
Boltzmann, Arthur (Boltzmann’s son), 66, 148, 191, 200, 217
Boltzmann, Elsa (Boltzmann’s daughter), 66, 114, 217
Boltzmann, Hedwig (Boltzmann’s sister), 34, 57, 66, 107
Boltzmann, Henriette (Boltzmann’s daughter), 66, 198
Boltzmann, Henriette (Boltzmann’s wife), 44, 57–60, 61–62, 64–65, 66, 68, 94, 98, 103–4, 105, 113–14, 149, 180, 198, 216–17, 218, 231
Boltzmann, Ida (Boltzmann’s daughter), 66, 198, 200
Boltzmann, Katharina (Boltzmann’s mother), 32, 66, 97–98
Boltzmann, Ludwig (Boltzmann’s son), 66, 107
Boltzmann, Ludwig Eduard. See also specific theories of
background of, 32–35
Berlin position and, 98–107
birth of, 33
burial site of, 231
departure from Graz, 107–8
early publications of, 38–39
emotional problems of, 185–87, 192, 214–15, 224
at Graz, 46–47, 63–68, 94–95, 99–103
health problems of, 94, 120, 163, 214
honorary degree from Oxford, 112–13, 120
at Institute of Physics, 120–22
intellectual awakening of, 34
inventions of, 148
at Leipzig, 179–80, 183–87, 190, 191–93
as mathematics professor, 57–58, 60–63
at Munich, 107–8, 113–14, 120, 121–22
as a philosophy professor, 166–74, 198–200, 201–2
piano played by, 22–23, 32, 191, 222
poetry of, 188–89
poor eyesight of, 34, 64, 94, 102, 103, 148, 163, 191, 214, 222
proposed for Nobel Prize, 200
return to Vienna, 191–94
social awkwardness of, 102, 197–98
stay at sanatorium, 185–87
student nationalism and, 99–100
suicide attempt of, 192
as an undergraduate, 21–23, 29–32
unhappiness in Vienna, 179–82
vindication of theories, 219–22
visits to America, 149, 180, 200–201, 202–5
Boltzmann, Ludwig Georg (Boltzmann’s father), 32, 34
Boltzmann’s constant, 91
Boltzmann’s formula, 88–93, 95
Boltzmann’s transport equation, 54, 75
Branes, 10
Brentano, Franz, 199, 202, 211, 214–15
British Association for the Advancement of Science, 112–13, 117, 160
Brown, Robert, 210
Brownian motion, 210–11, 212–13
Bruckner, Anton, 32
Brunel, Isambard Kingdom, 147
Burbury, S. H., 109–10, 117, 118, 119
Café Elefant, 136
Caloric theory of heat, 14–16, 17
Carnot, Sadi, 72–73
Cathode rays, 166
Cavendish, Henry (Duke of Devonshire), 80
Cavendish Laboratory, 80
Christian Socialist movement, 181–82
Clark University, 149
Clausius, Rudolf, 17–18, 19, 21, 23, 26, 27, 71–75, 109, 114, 115, 140, 155, 213, 227
Boltzmann’s elaboration of kinetic theory and, 56
death of, 145
on entropy, 73–74, 91, 144, 230
estimates of atomic velocity, 24–25
Coffeehouses of Vienna, 136
Conservation of Energy, The, 137, 138–39, 174
Culverwell, Edward P., 112, 117, 118, 119
Curie, Marie, 165–66
Darwin, Charles, 110, 141, 225–26
Democritus, 7–8, 9, 10, 11–12, 13, 16, 21, 169
Disraeli, Benjamin, 35
Doppler, Christian, 29
Edinburgh Royal Society, 79
Ehrenfest, Paul, 194, 220, 223, 230
Ehrenfest, Tatiana, 220
Einstein, Albert, 61, 173, 177, 190, 206–13, 219
Electrical Engineering Society of Vienna, 148
Electromagnetic fields, 29, 228
Electromagnetic radiation. See Radiation spectrum Electromagnetism, 21, 29, 30–31, 41, 62, 67, 81, 140, 208–9, 227, 228
Elementary Principles in Statistical Mechanics (Gibbs), 161, 195–97, 207
Energeticism, 124–29, 156, 160, 170, 173–74, 179, 192, 197, 218
Energy conservation, principle of, 49, 72, 73, 125, 227
Entropy, 73–78, 84, 142–44, 219, 220, 230. See also Boltzmann’s formula;
H-theorem; Reversibility objection
Clausius’ work on, 73–75, 91, 144, 230
Gibbs’ work on, 152, 157, 158, 159, 160, 195–96
Equal opportunity rule, 92, 96
Evolutionary theory, 225–26
Exner, Franz (father), 22, 194
Experimental physics, 28
Ferdinand, Emperor, 37
First law of thermodynamics. See Energy conservation, principle of
Fitzgerald, George, 170
Flamm, Ludwig, 215
Fluorescence, 165
Franco-Prussian War, 47–49
Franz I, Emperor, 36
Franz Ferdinand, Archduke, 223
Franz-Josef, Emperor, 37–38, 47–48, 99, 100, 104, 130, 182, 193, 200, 223, 231
Fuchs, Ernst, 185–86
“Further Studies of the Thermal Equilibrium of Gas Molecules” (Boltzmann), 54
Galileo, 69
Gases
Bernoulli’s theories of, 3
Boscovich’s theories of, 14
kinetic models of. See Kinetic theory
Maxwell’s research on, 70–71
Waterson’s theories of, 2–3
German Physical Society, 50
German Society of Natural Scientists, 115–16, 123
Gibbs, Josiah Willard, 149–62, 170, 195–97, 207, 227
background of, 149–51
Boltzmann and, 155, 156–57, 158–62, 190–91
death of, 195
Gibbs’ paradox, 157–58
Gödel, Kurt, 229
Hall, G. Stanley, 149
Hamilton, Sir William, 80
Hearst, Mrs., 203
Heat
Herapath’s theories of, 3
kinetic theory of. See Kinetic theory
Mach’s theories of, 132
second law of thermodynamics on, 72–73
Heat death, 144
Hegel, Georg Wilhelm Friedrich, 199, 201
Heisenberg, Werner, 228
Helmholtz, Frau von, 102
Helmholtz, Hermann von, 49–50, 63, 99, 102, 105, 106, 115, 136, 145, 155, 174, 182
background of, 49
on energy conservation principle, 49, 72, 227
Heraclitus, 11
Hertz, Heinrich, 29
Hofmannsthal, Hugo von, 178–79
H-theorem, 75–77, 83–85, 88, 91, 92, 93, 96, 111–12, 158, 163
Boltzmann’s confusion over meaning of, 219, 220
energeticism versus, 126
Maxwell’s analysis of, 96
philosophical defense of, 170
reception of in Britain, 117–19
recurrence theorem versus, 142, 143, 144, 221
significance of, 75
Hummel, Karl, 46
Huygens, Christiaan, 69–70
Institute of Physics, 29–32, 46, 60, 120–22, 129–30, 194
Irresistible analogy, 172–74
Irreversible changes, 73
Jaffé, George, 192
Jäger, Gustav, 218
Jerome, St., 6
“Journey of a German Professor to Eldorado” (Boltzmann), 203
Karl, Emperor, 231
Kelvin, Lord. See Thomson, William
Kienzl, Wilhelm, 64–65, 68, 114
Kind of Motion We Call Heat, The (Clausius), 17, 24–25
Kinetic theory, 20, 21, 24, 25–28, 29, 71, 169, 194, 214
apparent paradoxes in, 84–87
Boltzmann’s early work on, 39–42
Brownian motion and, 212–13
early development of, 16–19
elaboration of, 50–56
energeticism versus, 126–29
entropy and. See Entropy exploration of diffusion and viscosity in, 95–96
Gibbs’ work and, 155–56, 160–61
increasing attention paid to, 66
Maxwell-Boltzmann distribution in. See Maxwell-Boltzmann distribution mean free path in, 25, 26, 27
persistence of arguments over, 228
Planck’s opinion of, 114–17, 174–77
reception of in Britain, 109–13, 117–19
renewed attacks on, 141–46
significance of Boltzmann’s contribution to, 18–19
Zermelo on, 142–43, 144–45, 212, 213, 220
Kirchhoff, Gustav, 44–46, 47, 98, 103, 115, 116
Klein, Felix, 126, 127, 163, 214, 220
Koenigsberger, Leo, 43–44, 47, 180
Krafft-Ebing, Richard, 103
Laplace, Pierre Simon de, 110–11
Lectures on Gas Theory (Boltzmann), 119, 160, 163, 197, 207, 222
Lenin, V. I., 37
Leucippus, 7–8
Lick, James, 204
Lick Observatory, 204
Locke, John, 169
Logical positivism, 229
Loschmidt, Josef, 30, 36, 41–42, 68, 71, 94, 120, 145, 180, 194, 196
background of, 22
Boltzmann’s obituary notice for, 224–25
death of, 141
early relationship with Boltzmann, 22–23
estimates of atomic size, 27–28, 51, 72
innovations on chemical compound structure, 23
objections to Boltzmann’s theories, 84, 88, 93, 111, 116, 118, 141, 142, 158
Lübeck debate, 126–29, 163, 179–80
Lucretius (Titus Lucretius Carus), 3–7, 9, 11, 13, 16, 110, 168
Lueger, Karl, 181–82
Mach, Ernst, vii, ix–xi, 30, 46, 86–87, 145, 156, 160, 174, 195, 198, 199, 201, 211, 218–19, 223, 224, 228–29, 230
Boltzmann’s death and, 217–18
Boltzmann’s growing animosity toward, 177–78
as candidate for Graz position, 64–65
as candidate for Institute of Physics position, 30, 120–21
death of, 219
education of, 134–35
philosophy of, 129–41, 166–69, 170, 171–74, 177–79
scientific achievements of, 136–37
stroke of, 178
Mach, Heinrich, 131
Maric, Mileva, 207
Mathematical Encyclopedia, 213, 220
Mathematical physics, 137
Mathematical Theory of Electricity and Magnetism, The (Watson and Burbury), 110
Mathematics, 60–61. See also Statistics
Maxwell, James Clerk, 23, 28–29, 39–42, 56, 69–72, 76–83, 86, 88, 96–97, 109, 110, 111, 118, 141, 145, 196, 220, 221
background of, 78–80
differences in style between Boltzmann and, 81–83
early work on kinetic theory, 18
electromagnetic theory of, 29, 30–31, 41, 62, 67, 81–82, 140, 166, 175, 208–9, 227–28
Gibbs’ work and, 152, 155, 156, 161–62
poetry of, 188–90
pragmatic approach of, 170
research on Saturn’s rings, 69–71, 81
on viscosity of gases, 26–27
Maxwell-Boltzmann distribution, 18, 60, 62, 90
applied to Brownian motion, 210
establishing correctness of, 50–56
formulation of, 40–41
Maxwell’s analysis of, 96–97
Maxwell’s atomic velocity distribution, 25–26, 50, 56, 71, 96
Boltzmann’s demonstration of, 39–41
thermal equilibrium and, 75
Maxwell’s demon, 76–77, 83, 84, 196
Meyer, Stefan, 197, 214, 215, 218, 222
Millikan, Robert A., 201
Minimum theorem. See H-theorem
Nature, 110, 117, 119, 144, 170
Nernst, Walther, 67, 68, 95, 148, 230
Newton’s laws of mechanics, 9, 13, 52, 55, 84, 85, 88, 110, 138, 168, 211, 227
Nuclear fission, 194
“On a Thesis of Schopenhauer’s” (Boltzmann), 201
“On the Develoopment of the Methods of Theoretical Physics in Recent Times (Boltzmann), 163
“On the Dynamical Theory of Gases” (Maxwell), 71
On the Nature of Things (Lucretius), 3–5, 168
Ostwald, Wilhelm, 123–27, 128, 170, 174, 190, 191, 192, 195, 197, 201, 224. See also Energeticism
acceptance of atomism, 218
approaches Boltzmann for Lepizig position, 179–81, 183–84
Gibbs’ work and, 155–56, 159, 160
Outline of General Chemistry (Ostwald), 218
Oxford University, 112–13, 120
Pascal, Blaise, 53
Perrin, Jean, 211
Phenomenology, 171–72
Philosophical Magazine, 112, 113
Philosophical Transactions, 1, 20
Photoelectric effect, 209
Physical chemistry, 123–24, 155
Physics
experimental, 28
mathematical, 137
quantum. See Quantum theory theoretical, 28, 60, 137, 140, 228
Planck, Max, 114–17, 140, 142, 145, 174–78, 190, 200
work on quantum theory, 176–77, 190, 212, 227
work on radiation spectrum, 175–77, 206, 208–10, 227
Poincaré, Henri, 141–42, 143, 144, 220–21. See also Recurrence theorem
Polytechnic Institute, 62
Popular Writings (Boltzmann), 214
Probability, ix, 69, 86, 88, 156–57, 195–96, 207
Proceedings of the Cambridge Philosophical Society, 155
Proceedings of the Viennese Academy of Sciences, 39, 45, 101
“Proof that Schopenhauer is a stupid, ignorant philosophaster . . .” (Boltzmann), 201
Proust, Marcel, 186
Pupin, Michael, 49–50, 105, 182–83
Quantum theory, 176–77, 190, 208–10, 211–12, 222, 227, 228, 230
Quarks, viii, 10
Quetelet, Lambert A., 69
Radiation spectrum, 96, 166, 175–77, 206, 208–10, 227
Radioactivity, 165–66
Radio waves, 29
Rankine, William, 73
Recurrence theorem, 141–42, 143, 220–21
Relativity, special theory of, 206, 211–12, 219
Reversibility objection, 84, 116, 117, 118–19, 126, 141–42, 219
Reversible changes, 73
Rohling, August, 131
Röntgen, Wilhelm, 165
Royal Society, 1, 2–3, 16, 19, 20
Rudolf, Prince, 223
Rumford, Count. See Thompson, Benjamin
Schopenhauer, Arthur, 201–2
Schratt, Katharina, 193
Schrödinger, Erwin, 230
Schulze, Franz, 103–4, 105, 120
Science of Mechanics, The (Mach), 137
Scientific Autobiography (Planck), 175
Second law of thermodynamics, 72–73, 85–86, 144–45, 212, 219, 227, 228, 230
energeticism and, 127
Watson on, 109
Sommerfeld, Arnold, 128
Statistic(s), 69–71, 88–89, 156–57, 195–96, 207
Statistical ensembles, 196
Statistical mechanics, 195–97, 227
Stefan, Josef, 30–31, 36, 41, 42, 45–46, 47, 50, 61, 67, 71, 94, 95, 131, 135, 145, 182
background of, 31
Boltzmann as assistant to, 38
Boltzmann’s obituary notice for, 224–25
as head of Institute of Physics, 30, 120, 121, 129
Stefan-Boltzmann law, 67, 96, 209
Strauss, Richard, 179
Streintz, Heinrich, 100–101
Superstring theory, 10–11, 132–33, 228
Tait, P. G., 71, 76, 77, 79, 82, 83, 97, 111, 161
Tennyson, Alfred Lord, 6
Theoretical physics, 28, 60, 137, 140, 228
Theoria Philosphiae Naturalis (Boscovich), 14
Theory of Energy, The (Helm), 125
Theory of Heat (Maxwell), 83
Thermal equilibrium, 67, 91–92, 196
Boltzmann’s early work on, 54–56
Boltzmann’s revised analysis of, 90
Clausius’ work on, 73
Thermodynamics, 73, 85–87. See also Energy conservation, principle of; Second law of thermodynamics
Gibbs’ work on, 151–60
Planck’s views of, 174–75, 209
Thermodynamic stability, 152–53
Thermodynamic surface, 152
Thompson, Benjamin (Count Rumford), 14–15, 49
Thomson, J. J., 166
Thomson, William (Lord Kelvin), 42, 56, 73, 79, 84, 86, 111, 145, 148, 204
Toepler, August, 47, 57, 61, 63, 68, 94, 129
Transactions of the Connecticut Academy of Sciences, 151, 155
Treatise on the Kinetic Theory of Gases, A (Watson), 109–10
Trinity College, 112
Uncertainty principle, 228
“Unity of the Physical World Picture, The” (Planck), 177
University of California at Berkeley, 202–5
University of Cambridge, 80, 110, 111, 166
University of Edinburgh, 79, 80, 82
University of Freiburg, 62
University of Giessen, 183
University of Graz, 30, 46–47, 57, 61, 63–68, 94–95, 99–103, 107–8, 129
University of Heidelberg, 43, 180
University of Leipzig, 124, 179–80, 183–87, 190, 191–93
University of Munich, 107–8, 113–14, 120, 121–22
University of Prague, vii, 22
University of Riga, 124
University of Vienna, 21, 31, 41, 120, 131–32, 135, 191–94. See also Institute of Physics
Uranium, 165–66
van Hartel, Wilhelm 185, 186, 191, 192, 193
Vienna Philosophical Society, 201
Viennese Academy of Sciences, 44, 58, 68, 74, 84, 148, 169
Von Ettingshausen, Albert, 95, 100, 107
Von Ettingshausen, Andreas, 29–30, 95, 135
Von Lang, Viktor, 46
Von Stremayr, Karl, 64
Von Taaffe, Count Edward, 130, 182
Waterston, John James, 1–3, 16, 17, 19–20, 21, 25, 213
Watson, Henry William, 109–10, 111
Wittgenstein, Ludwig, 230
X rays, 165–66
Yale University, 151, 161, 190–91
Young Vienna, 178
Zeitschrift für physikalische Chemie, 124