A Brief Guide to the Great Equations
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Catherine I, Empress of Russia, 94
Catherine II ‘the Great,’ Empress of Russia, 97
Catholic Church, books prohibited by, 66–67
Cavendish, Henry, 143
celestial sphere, 24, 72–77, 78, 79–80, 82
circular motions observed in, 49, 58, 63, 70, 74, 281n
earthly realm vs., 49, 51, 53, 55, 56, 63, 70, 71
God-given impetus of, 54–55, 282n
see also astronomy
Chadwick, James, 172, 174
Chandrasekhar, Subrahmanyan, 19–20
changing acceleration, 56
Chaucer, Geoffrey, 55
Chicago, University of, 175
China, 14
Pythagorean theorem known by, 25–26, 28, 29
Christina, Grand Duchess of Tuscany, 66–67
Christofilos, Nicholas, 182–83
circular arguments, 29
Cité des Sciences et de l’Industrie, 42
Civil War, U.S., 133, 145
Classical Electrodynamics (Jackson), 151
Clausius, Rudolf, 111, 112, 118, 119, 120, 124
clockwork universe, 61, 84
Cockcroft, John, 172
Cohen, I. Bernard, 60, 62, 69, 70, 90, 283n
Columbia University, 24, 25, 174
comets, 77, 79
commutative law, 242–43, 244, 251–52, 297n
compensation factor, 163–64, 170
complementarity, doctrine of, 263, 298n
complex numbers, 104, 224
Compton, Arthur H., 218
Compton effect, 218–19, 250, 256
Comte, Auguste, 75
configuration space, 224, 225, 227, 246, 247
congeners, 177–78
continuous force, 58, 59, 60
Copenhagen (Frayn), 211, 235, 262–63
Copenhagen interpretation, 249, 259–60
Copernicus, Nicolaus, 66, 67, 72, 73–74, 239, 284n
correspondence principle, 239
cosine function, 97, 101–2
cosines, law of, 32
Cosmicomics (Calvino), 110, 209
‘Cosmological Considerations in the General Theory of Relativity’ (Einstein), 293n–94n
Cotes, Roger, 16–17
Cottingham, E. T., 204
Cottrell, William, 92
covariance, 159, 189, 192, 197, 198–200, 291n, 293n–94n
crazy-idea letters, 180–84, 292n
creation myths, 14
‘Critique of the Foundations of Physics’ (Darwin), 218
Crommelin, A.C.D., 203–4, 206
Crystal Palace exhibition (1851), 42
cubic equations, 274n
Dalai Lama, 156
Darrow, Karl, 247
Darwin, Charles, 83
Darwin, Charles G., 218
Davidson, C. R., 203–4
de Broglie, Louis, 216, 222, 223
Debye, Pieter, 222, 223
decimal numbers, 95, 99
De Magnete (Gilbert), 72
De Motu (Newton), 80–81
De revolutionibus orbium coelestium (Copernicus), 66, 67, 72
Desaguliers, John Theophilus, 85
Descartes, René, 33–34, 45, 59, 84, 99
imaginary numbers named by, 96, 97, 104
vortices concept of, 75, 78, 81
de Sitter, Willem, 201
determinate equations, 15
Devlin, Keith, 91, 106
diagonals, 33, 36–37, 38–39, 39, 40, 90
differential equations, 138, 274n
Dilworth, David, 280n
Diophantine (indeterminate) equations, 15
Diophantus, 14
Dirac, Paul, 247, 296n–97n
displacement laws, 123
‘Does the Inertia of a Body Depend Upon its Energy Content?’ (Einstein), 168–70, 172
Dorato, Mauro, 84
Dostoyevsky, Feodor, 109
Dr. Euler’s Fabulous Formula (Nahin), 91–92
DuBois, W.E.B., 230
Dunn, Stephen, 266
‘Dynamical Theory of the Electromagnetic Field, A’ (Maxwell), 142
dynamic proofs, 31
dynamis, 50
Dyson, Frank, 203, 205–6
E=mc2, see Einstein’s special theory of relativity
‘E=mc2’ (Einstein), 178
ecoterrorism, 92
Eddington, Arthur, 201–4, 205, 206–8
Egyptians, ancient, 26, 273n–74n
Ehrenhaft, Felix, 184
Eidgenössiche Technische Hochschule (ETH), 191–93, 196–97, 222
Einstein, Albert, 17, 33, 45, 156–79, 179, 181, 182, 185–208, 222, 235, 242, 243, 247
contrarian role played by, 130
on Copenhagen interpretation, 259–60
ether disproved by, 166
family of, 191, 193, 197
particle theory espoused by, 217–18
playful attitude of, 183–84
Pythagorean theorem proved by, 44
quantum theory and, 191, 215, 217, 221, 259–60
Roosevelt’s letter from, 175
unified emotional life and career of, 232–34
Einstein: His Life and Universe (Isaacson), 210
‘Einstein A Go-Go’ (Landscape), 156–57
Einstein’s equation for general relativity, 82, 110, 167, 185–208, 227, 268
bending of starlight predicted by, 185–87, 193–95, 198–99, 200, 201–8
Einstein’s equation for general relativity (continued)
conveying meaning of, 209–13
covariance in, 189, 192, 197, 198–200, 293n–94n
equivalence principle in, 189–95, 196
geometry of space-time in, 196–97, 199, 208
gravitational red shift and, 193, 200, 207
Mercury’s orbital precession explained by, 190–91, 194, 198, 200, 202, 206
Minkowski’s space-time concept in, 191–93, 196
Newton’s gravity law vs., 188, 190–91, 207–8
Pythagorean theorem in, 33, 192, 279n
sets of terms in, 199, 208, 293n–94n
space-time curvature in, 185, 186, 196, 206, 207–8
thought experiment associated with, 187–89
Einstein’s special theory of relativity (E=mc2), 33, 92–93, 149, 156–79, 157, 193, 197, 235–36, 239, 267, 268
in atomic physics, 168–69, 171–77
confirmations of, 172–73
as congener, 177–78
contraction of space and time in, 163– 64, 166–67, 191
faster-than-light travel prohibited by, 128, 164
mass-energy concept in, 46–47, 156, 168–77, 178–79, 185, 194
and Newtonian vs. Maxwellian mechanics, 158–64, 165–68, 187, 188
as popular culture icon, 92, 156–57, 177–79, 235
Pythagorean theorem in, 33, 166–67, 167
speed of light in, 33, 156, 157, 158–64, 165, 168–71, 189, 290n
thought experiment associated with, 165, 187
on Time cover, 156, 178–79, 179
‘Einstein’s Third Paradise’ (Holton), 232–34
electrodynamics, electromagnetism, 113, 122, 124–25, 126, 132–51, 158–64, 165–69, 216
displacement current in, 141, 142
effects of, 139–40
ether and, 135, 136, 139, 141, 143
induction in, 135, 136, 138
mathematics of, 135, 136, 137–39, 141
Newtonian view of, 135
physical models of, 139–42, 140, 149
as structural foundation of modern era, 133, 152
telegraphy and, 145, 149–50
see also Maxwell’s equations
electromagnetic fields, 133
electromagnetic waves, 123, 133, 143–44
discovery of, 145–47
light as, 141–42
as traveling through ether, 141–42, 147
electronic state, 135, 138, 140
electrons, 205, 216–17, 222, 225–26, 238, 239, 251, 253, 255–57
, 298n
electrostatic potential ψ, 143, 147, 149, 150, 151
Elegant Universe, The (Greene), 211
Elementary Sketch of Physiology (Magendie), 84
Elements (Euclid), 22, 32, 35, 59, 95, 98, 129, 278n
in 1851 Crystal Palace exhibition, 42
Pythagorean theorem proof in, 22, 24, 27–28, 28, 29, 31, 34, 42, 273n
Elements of Algebra (Euler), 98
Elizabeth I, Queen of England, 57
energy, 112, 118, 121, 123, 125, 129, 168– 69, 215, 216, 217–18, 239, 241
in Einstein’s mass-energy concept, 46–47, 156, 168–77, 178–79, 185, 194
kinetic, 169
energy flux theorem, 289n
entropy, 111, 112, 118, 121–22, 125, 129
see also thermodynamics, second law of
Epitome to Copernican Astronomy (Kepler), 67, 74
equations:
algebraic, 95
classification of, 274n
in crazy-idea letters, 183
creative process in formulation of, 17–18
as cultural icons, 107–10
derivation of term, 14–16
determinate, 15
differential, 138, 274n
human genesis of, 16–18
indeterminate, 15
motivating trigger in birth of, 38
in 1984, 107–8
poems vs., 274n–75n, 277n
in scientific papers, 183
secular, 297n
as tools of ongoing scientific enquiry, 92–93, 105
unexpected productivity of, 147
valuable function of, 105, 106
wonder inspired by, 13–14, 18–20, 44, 271–72
equipartition theorem, 121, 126–27
ether, 49, 75, 161–64, 165, 202
detection of, 144–45, 147–48
earth’s motion with respect to, 126, 144–45, 161–62, 166
Einstein’s disproof of, 166
electrodynamics and, 135, 136, 139, 141, 143
electromagnetic waves as traveling through, 141–42, 147
ether drift, 144–45, 202
Michelson-Morley experiment on, 147–49, 161–64
Et Tu, Babe (Leyner), 110
Euclid, 22, 26, 29, 33, 34, 44, 192
see also Elements (Euclid)
Euler, Leonhard, 61, 91–106, 94
analysis organized by, 95–96, 98–99, 104, 105, 136
background of, 93–94
blindness of, 94, 97–98
death of, 98
Frederick the Great’s epithet for, 97
symbolic notation developed by, 96–97, 98
Euler’s equation, 91–106
description of, 91, 103–4
as evidence in criminal trial, 92
functions linked by, 99–106
as icon, 91–93, 104–6
Experimental Researches in Electricity (Faraday), 135
exponential functions, 99–106
Fabric of the Cosmos, The (Greene), 211
falling apple legend, 69, 70, 88–90
falling bodies:
Aristotle’s theories of, 70–71
experiments on, 50, 52, 53
Galileo’s law of, 57–58, 110
impetus acquired by, 54
law of, 15, 57–58
Faraday, Michael, 135–36, 137–40
electronic state postulated by, 135, 138, 140
lines of force concept of, 135, 136, 137–39
Faraday effect, 135, 139
Farmelo, Graham, 274n
Fermat’s last theorem, 33
Fermi, Enrico, 174–75
Feynman, Richard, 20, 166
on electrodynamics, 133, 145, 151
Euler’s equation praised by, 91
on Newton’s law of gravity, 78
personality of, 232
‘Field Equations of Gravitation, The’ (Einstein), 199
final theory, 68
FitzGerald, George, 126, 146–47, 148, 151, 162–63, 166, 167, 187
Fizeau, Armand, 141
Flanagan, Hallie, 156
flat earth cosmos, 25–26
Flatland: A Romance of Many Dimensions (Abbott), 211
fluxions, theory of, 96
force, 46–48, 51–58, 59, 60, 61–62, 63, 71, 78, 81, 128, 188, 199, 207
continuous, 58, 59, 60
derivation of term, 58
external vs. internal, 53, 59, 78
Galileo’s conception of, 58
Greek sympathies as, 71
heat as, 114–15
impressed, 51–52, 53–55, 60, 61
instantaneous, 58, 59, 60
magnetic, 57, 72
in primitive religion, 47–48, 280n
resistance to, 46, 50, 53, 54, 59, 62, 63, 281n, 282n
forced (violent) motion, 48, 49, 53, 54, 55, 63
formal indication, 269
‘Foundation of the General Theory of Relativity’ (Einstein), 199–200
Fourier, Charles, 86–87
Franklin, Benjamin, 86
Franzen, Jonathan, 154
Fraser, George MacDonald, 43–44, 45
Frayn, Michael, 211, 235, 262–63
Frederick II ‘the Great,’ King of Prussia, 97
Freemasons, 24, 31
Freundlich, Erwin, 194–95, 198
Frisch, Otto, 174
Fuller, Buckminster, 109
functions, 96, 98, 99–106, 274n
H-, 121–22
ψ-, 223–25, 226, 228, 246–47, 248, 251
sine, 97, 100–102
wave, 223–25, 226–28, 264, 265
‘Further Researches on the Thermal Equilibrium of Gas Molecules’ (Boltzmann), 121
Galilean transformations, 160, 162
Galileo Galilei, 15, 22, 33, 56, 58, 59, 60, 62, 82–83
‘book of nature’ image of, 17, 57, 65–68
distinction between mass and weight noted by, 78
effects of gravity measured by, 75
falling-body experiments of, 53
falling body law of, 57–58, 110
space as viewed by, 57
thought experiment of, 57, 62, 81, 160
Galison, Peter, 269–70
Garfield, James A., 30, 30, 31
Gauss, Carl Friedrich, 105
General Principles of Equilibrium and Motion (L. Carnot), 115
geometric proofs, 31
geometry, 22–23, 29, 34, 36–38, 44, 57, 73, 95, 98, 105, 276n
in ancient India, 25
definition of, 95
doubling area of square in, 36–39, 39
non-Euclidean, 196–97
of space-time, 196–97, 199, 208
see also Pythagorean theorem
Gilbert, William, 57, 72, 73–74
Glass Bottom Boat, The (film), 107
God, 76, 92, 168, 183, 225, 261
in books of nature and scripture, 66–68
celestial sphere lent impetus by, 54–55, 282n
cosmic harmonies established by, 72–73, 75
gravity as volition implanted by, 72
impressed force used by, 53
Newton’s accomplishments and, 70
planetary orbits and, 57
Saint-Simon’s vision of, 86
as supreme lawgiver, 84–85
as unmoved mover, 49, 51, 55
Goldhaber, Alfred S., 227–28
Goldstein, Herbert, 184
gravitational red shift, 193, 200, 207
gravity, 58, 70–77
as Cartesian vortices, 75, 78, 81
as centrifugal force, 76, 78, 79
common centre of, 80
falling bodies and, 70–71
as implanted by God, 72
Kepler’s theory of, 73–75
mass and, 61, 69, 78, 81, 82, 188
planetary motions and, 74–77, 79
see also Einstein’s equation for general relativity; Newton’s law of universal gravitation
Greek language,
23, 29, 35, 84, 96, 118, 154
Greeks, ancient, 15, 22, 29, 47–51, 70–71, 273n
idea of proof as originated by, 27, 277n–78n
normative laws of, 84
see also Aristotle; Socrates
Greene, Brian, 211
Grossman, Marcel, 196–97, 233–34
Guillen, Michael, 274n
Habicht, Conrad, 168, 172, 183, 191
Hahn, Otto, 174
Hale, George, 195
Halley, Edmond, 77, 79–80, 81, 88
Halley’s comet, 77
Hardy, G. H., 182
Harmonies of the World (Kepler), 57
Harrison, Peter, 66, 68
Harrison, Richard, 13–14, 18, 272
Harvey, William, 56
Hawking, Stephen, 157
heat, 114–25, 134, 137–38, 215
caloric theory of, 113, 114, 115–17
conservation vs. conversion of, 112, 113, 114–15, 116–17, 118, 119
as force, 114–15
kinetic theory of, 118, 120–21
mechanical equivalent of, 112, 113, 117, 119
see also thermodynamics
Heaviside, Oliver, 18, 132, 149–51, 267
Heaviside’s equations, 150–51
Hegel, G.W.F., 34, 45
Heisenberg, Werner, 16, 129–31, 211, 220–21, 225, 228, 229, 230, 235–60, 237, 261, 263, 265
Heisenberg uncertainty principle, 128, 129–30, 235–60, 267, 268
experimental conditions and, 253, 254, 255–58
matrix mechanics in, 130, 242–54, 257, 258, 259
as popular cultural icon, 235–36 pq-qp=Ih/2πi in, 244, 245, 251–57, 296n–97n
understanding meaning of, 261–65
visualizability in, 238–39, 240, 245–46, 251, 255–58, 260, 265
wave mechanics in, 246–54, 257–58, 259
Helmholtz, Hermann von, 112, 119, 145–46, 148
hermeneutic circle, 267
hermeneutics, 285n
Hertz, Heinrich, 145–47, 151, 202
H-function, 121–22
Hilbert space, 263, 298n
Hilleman, Maurice, 153
Hisâb al-jabr wa’l muquâbalah (al-Khowârizmî), 95, 98
History of Britain (Schama), 152, 154
Hobbes, Thomas, 21–23, 32, 33, 45, 276n
Holton, Gerald, 232–34
Hooke, Robert, 76–77, 78–79, 81, 82, 89
humanities, restoring vitality of, 152–55
Huxley, Thomas, 83
Huygens, Christiaan, 30, 31
hydrogen atom, 216, 245, 247, 294n
ideal-gas law, 229
Ihde, Don, 211–12
imaginary numbers, 96, 97, 99–106, 149
immanent frame, 55
impedance matching, 212–13
impetus, 54–55, 58, 78, 282n
impossibility, science of, 128–31
impressed force, 51–52, 53–55, 60, 61
Imus, Don, 107
indeterminate equations, 15
India, 25, 26, 28, 29–30
induction, 135, 136, 138
inertia, 54, 79
as first law of motion, 61