A Brief Guide to the Great Equations
Page 32
Principia’s Definition Three as, 60
inertial mass, 168–69, 170, 172–73, 188
inertial reference frames, 160, 161, 166–67, 168–70
infinite series, 95–96, 97, 98–99, 100, 101–2, 104
instantaneous force, 58, 59, 60
instantaneous speed, 50, 55–56, 281n
intelligent design, 68
interferential refractometer, 148
Introduction to Infinite Analysis (Euler), 98–104
intuition, 34, 38, 45, 60, 249
invariance, 61–62, 158–64
inverse square laws, 69, 73, 73, 74, 76–77, 78, 79, 82, 89, 190, 207
ionosphere, 149
Irigaray, Luce, 157
irrational numbers, 32, 95, 96, 99–106
Isaacson, Walter, 210
isosceles right triangles, 35–41
Jackson, J. D., 151
Jahrbuch der Radioaktivität, 189–90
James, William, 216
Jammer, Max, 219, 237, 297n
Jefferson, Thomas, 86
Jordan, Pascual, 130, 236–37, 243, 244– 46, 253, 254, 255, 257, 298n
Joule, James Prescott, 112, 117, 118, 119
Jupiter, 194–95
satellites of, 145, 284n
Kelvin, William Thomson, Lord, 113, 117, 118, 121, 134, 136–39
‘Nineteenth Century Clouds’ talk of, 126–27, 164, 191, 215
Kepler, Johannes, 22, 57, 67, 72–75, 78
elliptical orbits discovered by, 74–75, 76, 79, 284n
laws of motion formulated by, 75, 76, 79, 81
Khowârizmî, Mohammed ibn Musa al-, 95, 98
kinesis, 48
kinetic energy, 169
kinetic theory of gases, 118, 120–21
knowledge, 32, 45, 267
acquisition of, 19, 35–39, 40
matrix of, 35–36, 40
objective, 61–62
Kohlrausch, Rudolph, 141
Konigsberg bridge problem, 98
Kramers, Hendrik, 218–19, 225, 236– 37, 240
Latin, 14–15, 29, 58, 95
Lavoisier, Antoine, 114, 115, 291n
Lederman, Leon, 271–72
Leibniz, Gottfried, 30, 31, 59, 96
Leonardo da Vinci, 30, 31, 91
Leviathan (Hobbes), 23
Levi-Cività, Tullio, 197
Leyner, Mark, 110
Lick observatory, 202–3
Life on the Mississippi (Twain), 19
light, 76, 126–27, 143, 215
black body radiation and, 122–25
as electromagnetic wave, 141–42
graininess of, 215, 217
gravitational effects on, 190, 193–95, 196, 198–99, 200, 201–8
intensity of, 73
magnetism’s effect on, 135, 139
Newtonian value of, 194, 199
Newton’s work on, 79
particle theory of, 217–18
light (continued)
photons of, 217, 256, 257
wave theory of, 218–19
light, speed of, 126, 141
constancy of, 158–64, 165–68
in Einstein’s special relativity theory, 33, 156, 157, 158–64, 165, 168–71, 189, 290n
in ether, 144–45, 147–48, 161, 164
Lindberg, David C., 71, 282n
linear equations, 274n
Linklater, Kristin, 236
Lloyd, G.E.R., 277n, 278n
local motion, 48, 49–50, 282n
Lodge, Oliver, 146, 202
logarithms, 96, 100, 103–4
Loomis, Elisha S., 31, 32, 45, 279n
Lorentz, Hendrik, 126, 148, 163–64, 166, 187, 198, 199, 204–5
Lorentz transformations, 163–64
Loschmidt, Josef, 121–22
Lyceum, 51, 52
McEwan, Ian, 154
Mach, Ernst, 195
Madison, James, 86
Magendie, François, 84
magnetic vector potential A, 138, 143, 147, 149, 150, 151
magnetism, 134, 135, 136, 139
Gilbert’s work on, 57, 72
see also electrodynamics, electromagnetism
mail qasrī, 54
Manhattan Project, 175–77
Maor, Eli, 33
Marburger, John H., III, 256, 258, 298n
Marx, Karl, 87
mass, 47, 50, 59, 60, 63, 82, 128, 217
in Einstein’s mass-energy concept, 46–47, 156, 168–77, 178–79, 185, 194
Galileo and, 58
gravity and, 61, 69, 78, 81, 82, 188
impetus and, 54, 55
inertial, 168–69, 170, 172–73, 188
Mathematical Principles of Natural Philosophy (Newton), 17
mathematics:
analysis, 95–96, 98–99, 104, 105, 136
Arab, 95
astrology and, 72–73
commutative law in, 242–43, 244, 251–52, 297n
of electrodynamics, 135, 136, 137–39, 141
‘=’ sign in, 108
in Galileo’s Assayer, 65, 67
historically contingent development of, 105
as Kepler’s final cause, 57
magic of, 42–45
neighbourhoods of, 93–99
symbolic notation of, 15–16, 34, 61, 96–97, 98, 244, 273n–74n, 281n, 297n
tensors in, 192, 196–97
matrix mechanics, 220–21, 223, 225, 226, 230
in Heisenberg uncertainty principle, 130, 242–54, 257, 258, 259
Maxwell, James Clerk, 16, 18, 83, 113, 120–21, 123, 126, 132–51, 134, 152, 191, 227
‘demon’ thought experiment of, 120–21, 130
Encyclopaedia Britannica edited by, 143, 144
ether detection method proposed by, 144–45
mechanical models made by, 136–37, 139–42, 140, 238
statistical approach of, 120–21, 221
Maxwell’s equations, 18, 132–51, 182–83, 216, 238
analogies in, 113, 136–37, 139–43, 151
confirmation of, 146–47
Einstein’s special relativity theory and, 158–64, 165–68, 187, 188
electromagnetic theory integrated by, 136–37
electrostatic potential ψ in, 143, 147, 149, 150, 151
Heaviside’s reformulation of, 132, 149– 51, 267
magnetic vector potential A in, 138, 143, 147, 149, 150, 151
in Treatise on Electricity and Magnetism, 142–45, 149
see also electrodynamics, electromagnetism
Mayer, Robert, 113, 119
mean speed theorem, 282n
Meitner, Lise, 174
Meno (Plato), 35–41, 90, 168
Meno’s paradox, 35–39
Mercury, orbital precession of, 190–91, 194, 198, 200, 202, 206
Michelangelo, 19–20, 91
Michelson, Albert, 112, 126, 147–49, 161–64
Middle Ages, 15, 24, 26, 71, 95
Minkowski, Hermann, 33, 191–93, 196
models, mechanical, 136–37, 139–42, 140, 238
moon test, 81, 82
Morelli, Giovanni, 86–87
Morley, Edward, 126, 147–49, 161–64
motion, 15, 46–64, 201
absolute vs. relative, 60–61
Aristotle’s theories of, 48–58, 70–71
bodies at rest vs., 72
celestial, see celestial sphere
changes in nature as, 48–51, 56
of earth, 66
of earth with respect to ether, 126, 144–45
forced or violent, 48, 49, 53, 54, 55, 63
Kepler’s laws of, 75, 76, 79, 81
of light, 33
local, 48, 49–50, 282n
natural, 48–49, 52, 53, 54, 55, 58, 63, 70
projectile, 51–52, 53–54, 282n
tidal, 70, 71
see also falling bodies; force; Newton’s second law of motion
Nahin, Paul J., 91–92
natural logarithms, 96, 100, 103–4
natura
l motion, 48–49, 52, 53, 54, 55, 58, 63, 70
Nautical Almanac Office, 145, 147
navigation, 24
negative numbers, 96
Nernst, Walther, 215
Neugebauer, Otto, 278n–79n
neutrons, 172, 174
New Astronomy (Kepler), 57
‘New Relationship Between the Radiation From a Black Body and the Second Law of Thermodynamics, A’ (Wien), 123
Newton, Isaac, 15, 17, 19–20, 59–64, 59, 69–87, 88–90, 101, 116, 186, 206–7, 221, 265, 268
abstract world-stage created by, 62–64, 81
calculus as fluxion theory of, 96
at Cambridge, 77, 78, 79–81, 88
distinction between mass and weight noted by, 78
God viewed as supreme lawgiver by, 84–85
Halley’s visit to, 77, 79–80, 81
Hooke’s relationship with, 76–77, 78–79, 81, 82, 89
light experiments of, 79
mechanical universe of, 85
personality of, 78, 80, 89–90
Newtonian mechanics, 120, 124, 133, 135, 183, 201, 291n
Einstein’s special relativity theory and, 158–64, 165–68, 187, 188
particles in, 217, 227
quantum physics and, 216–17, 219, 238, 239, 240, 247, 250, 258–59, 263, 264–65
‘Newtonian System of the World, the Best Model of Government, The’ (Desaguliers), 85
Newtonian value, 194, 199
Newton’s law of universal gravitation, 69–87, 186, 194, 199, 267
Einstein’s general relativity theory vs., 188, 190–91, 207–8
falling apple legend of, 69, 70, 88–90
inverse square law of, 69, 73, 73, 74, 76–77, 78, 79, 82, 89, 190, 207
Mercury’s orbital precession and, 190–91
as paradigm of successful science, 83–85, 90
political theorists influenced by, 85–87, 268
Newton’s second law of motion, 19–20, 46–64, 86, 114, 122, 264, 267
acceleration in, 50, 52, 56, 58, 59, 61–62, 128, 281n, 282n
formulation of, 47, 59–64
invariance of, 61–62, 158–64
mass in, 47, 50, 59, 60, 63, 82, 128
see also force; motion Newton’s third law of motion, 15, 61, 62, 80
New York Times, 148, 176, 210
Nicolson, Marjorie Hope, 285n
Nietzsche, Friedrich, 184
1984 (Orwell), 87, 107–8, 109 ‘Nineteenth Century Clouds over the Dynamic Theory of Heat and Light’ (Kelvin), 126–27, 164, 191, 215
Nobel Prize, 20, 91, 112, 113, 149, 153, 215, 261
noetic-noematic correlation, 159
normative laws, 84, 85
‘Note on the Electromagnetic Theory of Light, A’ (Maxwell), 289n Notes from Underground (Dostoyevsky), 109
nuclear fission, 174–77
objective knowledge, 61–62
objectivity, 159, 160, 170, 189, 291n
Ode to Newton (Halley), 88
‘On Electromagnetic Waves in Air and Their Reflection’ (Hertz), 146
1+1=2, 13–14, 15, 18, 45, 46, 108, 272, 274n
1+1=4, 109
‘On Faraday’s Lines of Force’ (Maxwell), 137–39
‘On Irreversible Radiation Processes’ (Planck), 124–25
On Motion (Strato), 52
‘On Physical Lines of Force’ (Maxwell), 139–42
‘On Quantum Mechanics’ (Born and Jordan), 244–45
‘On Quantum Mechanics II’ (Born, Heisenberg and Jordan), 245–46
‘On the Electrodynamics of Moving Bodies’ (Einstein), 165–68
‘On the Influence of Gravitation on the Propagation of Light’ (Einstein), 193–95
‘On the Quantum-Mechanical Reinterpretation of Kinematic and Mechanical Relations’ (Heisenberg), 220–21, 241–44, 257
On the World Systems (Galileo), 33
Oppenheimer, J. Robert, 175–76
optics, 136, 217
Oresme, Nicholas, 56
orreries, 140
Ørsted, Hans Christian, 134
Orwell, George, 87, 107–8, 109 ‘Outline of a General Theory of Relativity and a Theory of Gravitation’ (Einstein and Grossman), 197, 201–2
overall speed, 50, 281n–82n
Oxford ‘calculators,’ 56
packing fraction, 173
Pais, Abraham, 176, 184, 210, 291n
Pappus of Alexandria, 29, 283n
particle accelerators, 172
particle theory, 217–19, 226–28, 263, 264, 265
Pascal, Blaise, 29, 40
Pauli, Wolfgang, 182, 226–27, 297n
Heisenberg uncertainty principle and, 236–37, 238, 244, 245, 247, 248, 251–53, 254–55, 257
Pauling, Linus, 182
People’s History of the United States, A (Zinn), 152–54
percussive force, 55
perfected phenomena, 51
Persia, 54, 115
Peter I ‘the Great,’ Czar of Russia, 94
Phaedrus (Plato), 41
Philoponus, John, 53–54, 56
photons, 217, 256, 257
Planck, Max, 112, 113, 122, 172, 233, 247, 250
black body radiation studied by, 123– 25, 214–15
E=hv formula of, 110, 222
quantum theory and, 214–15
second law of thermodynamics symbolically formulated by, 111
Planck’s constant, 244
Plato, 33, 35–41, 45, 110, 277n
Plimpton 322 cuneiform tablet, 24, 25, 26, 28, 278n–79n
Podolsky, Boris, 259
poems, 274n–75n, 277n
Poincaré, Henri, 148–49, 164, 187, 215–16
political philosophy, 23, 85–87, 268
polygonal spirals, 103, 104
Posidonius, 71
‘Postulates of Impotence’ (Whittaker), 129, 253
prime numbers, infinity of, 32
Principia (Newton), 19–20, 86
contents of, 59–62, 283n
gravity law in, 70, 77, 81–82
Principia Mathematica (Whitehead and Russell), 15
probabilities, 226–29, 251, 252, 253
probability coefficients, 218, 221
projectile motion, 51–52, 53–54, 282n
proofs, 27, 29, 31, 32, 42–45, 98
certainty vs., 33
visual presentations of, 42–43, 43
see also Pythagorean theorem, proofs of Protestant Reformation, 66
protons, 172, 216
Pythagoras, 17, 21, 24, 27, 33, 35, 44, 277n, 278n Pythagorean Proposition, The (Loomis), 31, 279n
Pythagorean theorem, 17, 21–41, 42–45, 161, 267, 271
ancient discovery of, 21, 24–26, 28, 277n–78n
in Einstein’s general relativity theory, 33, 192, 279n
in Einstein’s special relativity theory, 33, 166–67, 167
in Euler’s work, 101
as Freemason symbol, 24
Hobbes’s initial encounter with, 21–23, 32, 33, 276n
independent discoveries of, 25
in Plato’s Meno, 35–41
practical applications of, 24, 25–26, 31, 32–33
rediscovery of, 21
rule of, 23–26, 27, 28, 31, 32–33, 34
Pythagorean theorem, proofs of, 23–24, 27–41, 42–45, 87, 268
accessibility of, 32, 33–34
as emblematic demonstration of reasoning, 33–34
in Euclid’s Elements, 22, 24, 27–28, 28, 29, 31, 34, 42, 273n
fascination of, 21, 31–35
new, 29–31, 30, 44–45
Paris science museum display of, 42
Schopenhauer on, 34
Pythagorean Theorem, The: A 4,000–Year History (Maor), 33
Pythagorean triplets, 24–25, 24, 161, 278n–79n
quadratic equations, 274n
quanta, 217–18
‘Quantization as a Problem of Proper Values’ (Schrödinger), 223–25, 251
quantum leap, 216
quantum physics, 47, 104, 113, 125, 127, 130, 191, 211, 214–29, 230, 235–60, 261–65
classical models of, 238–39
classical physics and, 216–17, 219, 238, 239, 240, 247, 250, 258–59, 263, 264–65
Copenhagen interpretation of, 249, 259–60
discontinuities in, 239, 248–50, 252– 53, 256
growing extension of, 215–21
1911 Solvay conference on, 215–16, 222
Planck’s introduction of, 214–15
see also Heisenberg uncertainty principle; Schrödinger’s equation
quantum states, 224–25
Quartered Safe Out Here: A Recollection of the War in Burma (Fraser), 43–44
quaternion proofs, 31
radiation, 122, 172, 216, 250
black body, 123–25, 214–15
radium, 168, 172
Ramanujan, Srinivasa, 102–3, 182
rational numbers, 95, 99–106
Rayleigh, Lord, 127, 163
red shift, gravitational, 193, 200, 207
reference frames, 159–64, 166–70, 189
Reflections on the Motive Power of Heat (S. Carnot), 116–17
religion, 65–66
primitive, 47–48, 280n
Renaissance, 66, 97
rest frames, 166, 169, 170, 290n
Rhind papyrus, 273n–74n
Ricci-Curbastro, Gregorio, 197
Riemann, Bernhard, 196–97
Rigden, John, 168
right triangles, 21–41, 97
isosceles, 35–41
sine function of, 97, 100–102
see also Pythagorean theorem
Roosevelt, Franklin Delano, 175
Rosen, Nathan, 259
Rosencrantz and Guildenstern Are Dead (Stoppard), 71
Rosenthal-Schneider, Ilse, 205
Royal Astronomical Society, 186–87, 201–2, 203–7
Royal Society of London, 76, 79, 85, 116, 147, 185–87, 203–7
rules, 42–45
definition of, 23
of Pythagorean theorem, 23–26, 27, 28, 31, 32–33, 34
Rules for the Direction of the Human Mind, The (Descartes), 33–34
Rumford, Count, 113, 115–16
Russell, Bertrand, 15
Russian Academy of Sciences, 94, 97–98
Rutherford, Ernest, 173, 215, 216
Saint-Simon, Henri de, 86
Santorio, Santorio, 56
Saturday (McEwan), 154
Schama, Simon, 152, 154
Schopenhauer, Arthur, 34, 45
Schrödinger, Erwin, 220, 221–25, 221, 230, 246–54, 257–58, 268
Schrödinger’s cat, 228
Schrödinger’s equation, 214–29, 268
configuration space in, 224, 225, 227, 246, 247
interpretations of, 225–29, 251–52
probabilities in, 226–29, 251
ψ-function in, 223–25, 226, 228, 246–47, 248, 251
as visualizable theory, 218–19, 220, 221, 223–24, 246, 249, 251, 252
as wave equation, 221, 222–25, 226–28, 246–54, 257–58, 268