Index A cosmic rays, 108–109 F absolute stationary space, 26, curvatures, in space-time, F = ma equation, 22, 47, 95, 28–31, 33, 35 140, 162 109, 111–112 acceleration, 14–16, 69–72, Cygnus, 164 Friedman, Alexander Alexandrov- 95–96, 120, 124–132. See ich, 150 also equivalence principle D action and reaction, law of, 22, 95 destructive interference, 41–42 G adding velocity, 43, 44–46, 48–49 diffraction, light, 41–42 Galilean principle of relativ- Alpha Centauri, 80–81 dispersion, light, 40–41 ity, 17–22, 33, 47–48, Andromeda galaxy, 81–82 109–111 anomalous perihelion, 162, 164 E Galilean transformation, 47–48, antiparticles, 102–103 Earth’s movement, 20–21, 35, 94 109–111 Einstein, Albert Galilei, Galileo, 17 B on gravity and acceleration, gamma (g) rays, 40, 102–103 bending light, 16, 133–142, 120, 131 general relativity theory. See rela- 162–163 on Newtonian Mechanics, tivity, general theory of Big Bang theory, 150–152 34–36 Global Positioning System black holes, 162, 164 on speed of light, 34–37 (GPS), 165 Einstein field equations, 162 gravitational lensing, 162–163 C electrical energy, 98 gravitational potential, 158, centrifugal force, 127–129 electromagnetic radiation, 24–26, 160–162 centripetal force, 129 40, 103 gravity, 16 conservation of energy, law of, electrons, 43, 102–103 acceleration and, 14–16, 97–99 elementary particles, 108–109 69–72, 95–96, 124–132 2 conservation of mass, law of, E = mc (mass-energy equiva- elimination of, 131–133 97–98 lence), 99–102, 112–113 equivalence principle and, 72, constructive interference, 41–42 energy 120–121, 131 contraction of length, 86–91, conservation of, law of, 97–99 light bending, 16, 133–142, 106–109 electrical, 98 162–163 calculating, 106–107 kinetic, 98, 113, 160 moon’s vs. Earth’s, 94 and muons, 108–109 mass-energy equivalence time dilation and, 70–72, 2 coordinate systems, 28–29 (E = mc ), 99–102, 143–148 and Galilean transformation, 112–113 warped space-time, 136, 47–48, 109 pair annihilation, 102–103 141–144, 158, space-time, 37 equivalence principle, 72, 162, 164 and special relativity theory, 120–121, 131 zero-gravity space, 94–95 70–71, 120 ether, 26–30 great circles, 140 ether wind, 31–33 The Manga Guide to Relativity © 2011 by Hideo Nitta, Masafumi Yamamoto, and TREND-PRO Co., Ltd. RELATIVITY_03.indb 175 3/15/2011 3:28:23 PM H measuring time by, 58, 60–65, perceived motion, 20–21 Hubble, Edwin, 150–152 78–79 uniform linear motion, 18, 69, properties of 95, 134 I dispersion, 40–41 muons, 108–109 interference and diffraction, inertia, law of, 18, 22, 95, 123 41–42 N inertial forces polarization, 42 centrifugal force, 127–129 near–light speeds. See also speed reflection, 40–41, 58–59 centripetal force, 129 of light refraction, 40–41 examples of, 120–129 and length contraction, 86–91 scattering, 42 inertial reference frames, 15 and mass, 92 speed of. See speed of light and Newton’s three laws of muons traveling at, 108–109 types of, 40–42 motion, 18 and time dilation, 54–55, light clocks, 58, 60–65, 78–80 and the Galilean principle of 57–63, 73–75 Lorentz transformation, 48, relativity, 19, 22, 47 and the twin paradox, 65–68 106–107, 111–112 and space-time, 139 Newtonian Mechanics and special relativity theory, basis for, 22 M 34, 69–70, 120–122 Einstein on, 34–36 infrared light, 40 mass, 94 Galilean principle of relativity interference, light, 41–42 conservation of mass, law of, and, 47–48 97–98 expansion of space, 151 K F = ma equation, 22, 47, 95, speed of light and, 25, 32, 43, 109, 111–112 112–113 kinetic energy, 98, 113, 160 positron/electron collisions, time and space as separate, 37 L 102–103 Newtonian velocity addition, 43, speed of light and, 92–97, 44–45, 48–49 law of action and reaction, New- 109–113 Newton’s three laws of motion, ton’s, 22, 95 vs. weight, 93–94 22, 95 law of conservation of energy, mass-energy equivalence equation of motion (F = ma), 97–99 2 (E = mc ), 99–102, 22, 47, 95, 109, law of conservation of mass, 112–113 111–112 97–98 maximum velocity, 92–93 law of action and reaction, law of inertia, Newton’s, 18, 22, Maxwell, James Clerk, 24 22, 95 95, 123 Maxwell’s equations, 24–26, 40 law of inertia, 18, 22, 95, 123 laws of motions. See Newton’s medium(s), 26–27, 40. See non-inertial reference frames, 15 three laws of motion also ether nonrelatavistic addition of velocity, length, contraction of, 86–91, Mercury, anomalous perihelion 43, 44–45, 48–49 106–109 procession of, 162, 164 calculating, 106–107 Michelson, Albert Abraham, 32 P muons and, 108–109 Milky Way galaxy, 35, 81–82 pair annihilation, 102–103 lensing, gravitational, 162–163 Morley, Edward Williams, 32 parabolas, 134, 137–139 life spans, muon, 108–109 motion. See also Newtonian particles, 102–103 light Mechanics perceived motion, 20–21 bending of, 16, 133–142, of Earth, 20–21, 35 perihelion, 162, 164 162–163 laws of, polarization, light, 42 as electromagnetic wave, action and reaction, 22, 95 polarizing filters, 42 24–26, 40 F = ma equation, 22, 47, positrons, 102–103 electrons and, 102 95, 109, 111–112 Pythagorean theorem, 61–63, Maxwell’s equations, 40–41 inertia, 18, 22, 95, 123 73–75, 78–80 176 Index The Manga Guide to Relativity © 2011 by Hideo Nitta, Masafumi Yamamoto, and TREND-PRO Co., Ltd. RELATIVITY_03.indb 176 3/15/2011 3:28:23 PM R speed of light, 22–24. See also U radio waves, 40, 165 near–light speeds ultraviolet rays, 40 reference frames as a constant, 24–26, 30, 33, uniform linear motion, 18, 69, inertial references frames. See 36–37, 43, 57 95, 134 inertial reference frames and Einstein, 34–37 universe, relativity and, 149–152 non-inertial references electromagnetic waves and, Urashima effect. See time dilation frames, 15 24–26, 40 reflection, light, 40–41, 58–59 ether and, 26–30 V ether wind and, 31–33 refraction, light, 40–41 velocity, mass-energy equivalence relativistic addition of velocity, 44, adding of, 43, 44–46, 48–49 (E = mc2), 99–102, 46, 47 and length, contraction of, 112–113 relativity 86–91 maximum velocity, 92–93 Galilean principle of, 17–22 mass and, 96–97, 113 Maxwell’s equations and, general theory of, 14–16 maximum, 92–93 24–26, 40 bending light, 16, visible light, 40 133–142, 162–163 Newtonian Mechanics and, 25, Big Bang theory and, 32, 43, 112–113 W relativistic addition of velocity, 150–152 wavelengths, 40, 42 44, 46, 47 equivalence principle and, weight, 92–94. See also mass weight/mass and, 92–97 72, 120–121, 131 weightlessness, 94–95, 121, SPring-8 Lab, 43 time dilation, 70–71, 131–132, 145 stars 158–162 white light, 40–41 universe, expanding and Alpha Centauri, 80–81 black holes and, 162, 164 contracting, 150–151 X special theory of, 14–15, 34–37 x-rays, 40, 164 time and space as T coordinate system, time dilation, 53–66 Z 37, 91 calculating, 80–82 twin paradox and time equation for, 88, 90 zero-gravity space, 94–95 dilation, 67–73 general relativity theory and, and the universe, 149–152 70–71, 143–148, 158–162 S measuring with light clocks, scattering, light, 42 58, 60–65, 78–80 simultaneity mismatch, 44–46 twin paradox and, 67–73 slowing of time. See time dilation transformation, Galilean, 47–48, solar system, 35, 80 109–111 space-time, 37, 139–144, 158, transformation, Lorentz, 48, 162, 164 106–107, 111–112 special relativity theory. See rela- twin paradox, 67–73 tivity, special theory of Index 177 The Manga Guide to Relativity © 2011 by Hideo Nitta, Masafumi Yamamoto, and TREND-PRO Co., Ltd. RELATIVITY_03.indb 177 3/15/2011 3:28:23 PM.