Questioning the universe

Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business A TA Y L O R & F R A N C I S B O O K CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2009 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S Government works Version Date: 20140113 International Standard Book Number-13: 978-1-4200-8259-3 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint Except as permitted under U.S Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers For permission to photocopy or use material electronically from this work, please access www.copyright com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400 CCC is a not-for-profit organization that provides licenses and registration for a variety of users For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com Contents Preface xi Acknowledgments xiii The Author xv Chapter Units and Powers of 10 .1 1.1 Units 1.2 Powers of 10 Questions/Problems Chapter Physics and Its Methodology 2.1 What Is Physics? .5 2.2 Methodology .5 2.2.1 The First Scientist 2.2.2 Why Do You Believe? 2.2.3 Back to the Questions 2.2.4 How Do We Answer the Questions? .7 2.2.5 The Need to Be Quantitative .8 2.2.6 Theories 2.2.7 Models 2.2.8 Aesthetic Judgments 10 2.3 End-of-Chapter Guide to Key Ideas 11 Questions/Problems 11 Chapter Motion 13 3.1 3.2 Relating the Variables of Motion 14 Graphs of One-Dimensional Motion 15 3.2.1 Constant Speed 15 3.2.2 Constant Acceleration 17 3.3 Two-Dimensional Motion 19 3.4 End-of-Chapter Guide to Key Ideas 21 Questions/Problems 21 Chapter Forces 23 4.1 The Fundamental Forces 23 4.2 A Specific Force Law: Newtonian Gravity .26 4.2.1 Weight 27 v vi Contents 4.3 4.4 4.5 4.6 4.7 How Does Force Affect Motion? Newton’s Second Law 27 Newton, the Apple, and the Moon 29 Combining Two Laws 29 The Mass of the Earth 30 Newton’s First Law 32 4.7.1 What and Where Is the Force? 33 4.8 Newton’s Third Law 33 4.8.1 How Does a Horse Pull a Wagon? 34 4.8.2 How Can We Walk? 34 4.9 End-of-Chapter Guide to Key Ideas 35 Questions/Problems 35 Chapter Electromagnetism 39 5.1 The Electric Force Law 39 5.2 Unifying Electricity and Magnetism .40 5.2.1 Ampere’s Law .40 5.2.2 Faraday’s Law 41 5.2.3 The Lorentz Force 41 5.2.4 Back to Ampere’s Law 41 5.2.5 Where Are the Moving Charges? 42 5.3 End-of-Chapter Guide to Key Ideas 43 Questions/Problems 43 Chapter The Field Concept 45 6.1 What Is the Connection? 45 6.2 Action at a Distance 45 6.2.1 Is This a Legitimate Explanation? 46 6.3 The Field Concept 46 6.3.1 How Does This Help Explain Noncontact Forces? 46 6.3.1.1 Thinking Like a Physicist 48 6.3.1.2 Is There a Way to Tell the Difference? 48 6.3.2 Understanding the Time Delay 49 6.3.2.1 The Speed and Identity of the Kink 50 6.4 Back to Contact Forces 50 6.5 End-of-Chapter Guide to Key Ideas 51 Questions/Problems 51 Chapter The Character of Natural Laws 53 7.1 Causality 53 7.2 The Prime Directive 53 Contents vii 7.3 Symmetry 54 7.4 Symmetry and the Laws of Nature 55 7.4.1 Space Translation Symmetry 56 7.4.2 Time Translation Symmetry 57 7.4.3 Time Reversal (Reflection) Symmetry 57 7.4.4 Matter-Antimatter Symmetry (Matter Reflection) 58 7.4.5 Space Reflection Symmetry (Parity) 59 7.5 End-of-Chapter Guide to Key Ideas 59 Questions/Problems 60 Chapter Conservation Laws 61 8.1 Conservation of Momentum 61 8.2 Conservation of Energy 67 8.2.1 The Different Forms of Energy 67 8.2.2 Conversion of Energy 69 8.2.3 A Specific Example: The Roller Coaster 69 8.3 A Nonconservation Law: The Second Law of Thermodynamics 71 8.4 End-of-Chapter Guide to Key Ideas 75 Questions/Problems 75 Chapter The History of the Atom 79 9.1 The Greek Model 79 9.2 Thomson’s “Plum Pudding” Model 79 9.3 The Rutherford Experiment 80 9.4 The Planetary Model 81 9.5 What Do We Do Now? 82 9.6 The Atom Today 82 9.7 The Electron Volt: A Useful Energy Unit .84 9.8 End-of-Chapter Guide to Key Ideas 85 Questions/Problems 85 Chapter 10 The Nucleus 87 10.1 Nuclear Properties 87 10.2 Why Neutrons? 88 10.3 Nuclear Decays 89 10.3.1 Alpha Decay 90 10.3.2 Beta Decay .90 10.3.3 Gamma Decay 92 10.4 Half-Life and Carbon Dating 92 viii Contents 10.5 The Full Beta Decay Story 95 10.5.1 The Prediction 95 10.5.2 The Experimental Results .96 10.5.3 What Do We Do Now? 97 10.5.3.1 Look Closely at the Theory 98 10.5.3.2 Look Closely at the Experimental Results 98 10.5.3.3 A Possible Explanation 99 10.6 End-of-Chapter Guide to Key Ideas 101 Questions/Problems 101 Chapter 11 The Nature of Light 103 11.1 Introduction 103 11.2 Properties of Particles 103 11.3 Properties of Waves 103 11.3.1 Wave Vocabulary 104 11.4 Is Light Made Up of Waves or Particles? 109 11.5 Back to Diffraction 111 11.6 Why the Sky Is Blue 111 11.7 End-of-Chapter Guide to Key Ideas 112 Questions/Problems 112 Chapter 12 The Theory of Relativity 115 12.1 Introduction 115 12.2 Frames of Reference and Relative Speeds 115 12.3 Galilean Relativity 117 12.4 Maxwell and the Ether 119 12.4.1 The Speed of Waves 119 12.4.2 The Ether 121 12.5 The Michelson Morley Experiment 122 12.5.1 An Analogy: Boats in a River 123 12.5.2 The Real Experiment 126 12.5.3 The Lorentz Contraction 130 12.5.4 Another Crazy Idea 131 12.6 Assumptions We Take for Granted 132 12.7 The Postulates of Special Relativity 134 12.7.1 Some Interesting Facts about Einstein and the Birth of Relativity 134 12.8 Consequences of the Postulates of Relativity 135 12.8.1 The Relativity of Simultaneity 135 12.8.2 Time Dilation 137 12.8.2.1 The Light Clock 138 Contents ix 12.8.2.2 Useful Definitions 140 Length Contraction 142 12.8.3.1 Length and Lorentz Contraction 144 12.9 E = mc2 and All That 144 12.10 Back to Addition of Speeds 146 12.11 The Car in the Garage Paradox 147 12.12 The Twin Paradox and Space Travel 148 12.13 Relativity and You 149 12.14 End-of-Chapter Guide to Key Ideas 150 Questions/Problems 150 12.8.3 Chapter 13 Quantum Mechanics 155 13.1 Introduction 155 13.2 Max Planck and the Beginnings of Quantum Theory 155 13.3 The Photoelectric Effect 156 13.4 The Bohr Atom 158 13.5 de Broglie Waves 160 13.6 Time to Stop and Catch Our Breath 162 13.7 The Heisenberg Uncertainty Principle 163 13.8 The Schrodinger Equation: An Equation for the Waves 165 13.9 Does God Play Dice? 167 13.10 End-of-Chapter Guide to Key Ideas 170 Questions/Problems 170 Chapter 14 The Standard Model of Elementary Particle Physics 173 14.1 14.2 14.3 14.4 14.5 14.6 Introduction 173 The Basic Ideas of the Standard Model 174 The Unification of Forces 174 Bosons: The Particles Associated with Forces 175 Electroweak Unification 176 The Unification of Matter 177 14.6.1 Two Classes of Matter Particles 178 14.6.2 Similarities 178 14.6.3 Differences 179 14.6.4 More about Quarks 179 14.6.5 More about Leptons 180 14.7 A Mystery 180 14.8 Particle Flowchart 181 14.9 End-of-Chapter Guide to Key Ideas 181 Questions/Problems 182 Index A Ability, as defined in physics, 67 Absolute frame of reference, 115, 121 Acceleration, 1, 13, 29, 190 centrifugal, 20 centripetal, 20, 21 constant, 17–19 defined, 14 kink and, 49 mass and, 30 measurement, Action at a distance, 45–46 Addition of speeds, 146–147 equation, 146 Aesthetic judgment, 10 Ampere’s law, 40–41, 41–42 Antiproton, 58 Atom(s) ad hoc assumptions, 82 Bohr, 158–160 current concepts, 82–84 Greek model, 79 history of, 79–86 light emitted from, 187 nuclear decay, 89–92 alpha, 90 beta, 90–92, 95–100 equations, 90, 91, 92 gamma, 92 half lives, 92 nucleus, 87–103 neutron number vs atomic number, 89 neutrons, 88 properties of, 87–88 protons, 88 planetary model, 81 “plump pudding” model, 79–80 questions and problems, 85–86 Rutherford’s experiment, 80–81 Thomson’s model, 79–80 Atomic energy, 68–69 Atomic weight, 88 B Baryons, 179 Big Bang, light from, 190 Bohr, Neil atom, 158 Bohr atom, 158–160 Bomb(s) mass, 64 de Broglie, Louis, 160 de Broglie waves, 160–162 C Car in garage paradox, 147–148 Carbon dating, 92–95 Causality, 53 Cavendish experiment, 31 Centrifugal force, 23 Charged objects, nature of, 45 Clock defined, 138 light, 138–140 Conjecture, Connection, 45 Conservation laws, 61–77 defined, 67 energy, 67–71 momentum, 61–66 questions and problems, 76–77 roller coasters as examples, 69–71 Conservation of energy, 145 Conservation of mass, 64, 145 Conservation of momentum, 61–66 ball in air system, 62–64 explosive example, 64–66 Contact force, 45, 50–51 Cosmic microwave background radiation, 190, 195 Cosmic ray neutrons, 94 Cosmic rays, 142 Cosmology, 185–200 Coulomb, Charles, 39 Coulombs, Coulomb’s law, 39, 45, 56 D Dark energy, mass-energy and, 197 Distance, 132 measuring cosmic, 187–190 standard candle technique for, 189 Down quarks, 179 203 204 E Earth distance from sun, gravitational pull, 26, 29 mass, 27, 30–32, 37, 63 rotation, 13 speed, 122 (See also Michelson Morley experiment) ultimate energy source, 13 Einstein, Albert, 10, 13, 24, 26, 39, 134–135 See also Theory of relativity Electric charge, measurement of, Electric force law, 39–40 Electricity, unifying magnetism and, 40–43 Electromagnetic energy, 69 Electromagnetic force, 23, 24, 39–44 Feynman diagrams, 177 Electromagnetism, 39–44 Electron(s) kinetic energy, 97 mass, 40, 85 velocity, 95 Electron volt, 84–85 Energy atomic, 68–69 electromagnetic, 69 electron volt, 84–85 forms of, 67–69 heat, 68 inversion of, 69 kinetic, 67 mass, 69, 85, 96, 145 measurement, nuclear, 69 potential, 67–68, 83 quantization, 156 Entropy, 72 F Falsifiable theory, Faraday’s law, 41 Feynman diagrams, 177 Field concept, 46–50 kink in, 49–50 noncontact forces and, 46–48 questions and problems, 51–52 stationary charge, 49 time delay and, 49–50 Force(s), 23–37 See also specific types, e.g., Electromagnetism, etc fundamental, 23–26 measurement, motion and, 27–28 particles, 176 Index questions and problems, 35–37 unification, 25 Force particles, fundamental interactions and properties of, 176 Frame of reference, absolute, 115, 121 G Galilean relativity, 117–119, 131 Geometric parallax, 187, 188 Grand unified theory (GUTS), 26 evolution of universe and, 192 Gravity, 23, 24 Cavendish’s experiment, 31–32 celestial vs terrestrial, 29 Einstein’s theory, 117 as function of distance, 27 mass and, 26, 27, 29 Newtonian, 26–27 terrestrial vs celestial, 29 GUTS See Grand unified theory (GUTS) H Half life, 92 Heat energy, 68 Heisenberg, Werner, 10, 163 Heisenberg uncertainty principle, 163–165 Hertz, Heinrich, 156 Hubble, Edwin, 185–186 Hypothesis, I Idea, Interferometer, 126, 127, 128 Invariants, 55 Isotopes, 93 K Kinetic energy, 67, 91 electron, 97 mass-energy vs., 177 Kink, 49–50 L Length contraction, 142–144 Light nature of, 103–113 particles, 103 as particles or waves, 109–111 questions and problems, 112–113 relativity and speed of, 103 Index waves, 103–109 constructive interference, 106 destructive interference, 106 diffraction, 107–109, 111 frequency, 104 interference, 106–107 length, 104 longitudinal, 105 period, 104 polarization, 105 speed, 104–105 superposition, 105 transverse, 105 types of, 105 as waves or particles, 109–111 Linear density, 104 Lorentz contraction, 130–131, 144 Lorentz law, 41 M Magnetism, unifying electricity and, 40–43 Mass acceleration, 30 of bomb, 64 conservation of, 64 of earth, 27, 30–32, 37, 63 of electron, 40, 85 energy and, 69, 85, 96, 145 gravity and, 26, 27, 29 measurement, 1, 30, 35, 36 motion, 10 of neutrino, 100, 102 of neutron, 85, 87 per unit length, 104 proper, 145 of protons, 85, 87 rest, 145 of sun, 37 weight and, 27, 28 Mass-energy, 69, 177, 192, 197 conversions, 146 dark energy and, 197 kinetic energy vs., 177 Matter-antimatter symmetry, 58–59 Matter particles classes of, 177–178 differences, 179 flow chart, 181 similarities, 179 Matter reflection symmetry, 58–59 Maxwell, James Clerk, 119–122 Measured speed, 119 Michelson, Albert, 122 Michelson Morley experiment, 122–132 Lorentz contraction, 130–131, 144 205 Models, 9–10 Momentum, 61 ball in air example, 62–64 conservation of, 61–66 explosive example, 64–66 external force and, 62, 63 internal force and, 63 measurement, Morley, Edward, 129 Motion, 13–22 centrifugal acceleration, 20 centripetal acceleration, 20 change in speed, 19 circular, 19 constant acceleration, 17–19 constant speed, 15–17 distance vs position, 13 force and, 27–28 forces and, 27–28 graphs of one-dimensional, 15 Newton’s second law, 27–28 position vs distance, 13 questions and problems, 21–22 speed vs velocity, 13–14 two-dimensional motion, 19–20 variables, 13, 14–15 velocity vector for circular, 19 velocity vs speed, 13–14 Moving charges, 42–43 Muon, 141 N Natural laws, 53–60 causality, 53 prime directive, 53–54 symmetry and, 55–59 Neutrino, 100, 102 Neutron(s), 88–89 mass, 85, 87 Newton, Isaac, 61, 103 Newtonian gravity, 26–27 Newtonian laws, 27–35 combining, 29–30 conservation of momentum and, 76 first, 32–33 momentum and, 64 second, 27–28, 30, 165, 166 third, 33–35 Newtons, Noncontact forces, 46–48 Nuclear decay equation, 91 Nuclear energy, 69 Nuclear force, 24, 87 saturation, 88 Nucleon, 88 206 P Parity, 59 Particle physics standard model of elementary, 173–183 basic ideas, 174 bosons, 175–176 electroweak unification, 176–177 questions and answers, 182–183 unification of forces, 174–175 unification of matter, 177–180 Particles, properties of, 103 Photoelectric effect, 156–158 Physics defined, methodology, 5–11 questions and problems, 11 theory, 8–9 falsifiable, Planck, Max, 155–156 Planck time, 192 Planck’s constant, 163, 164, 176 Planck’s length, 198 Planck’s mass, 192, 198 Planck’s time, 191, 192, 198, 199 Postulates of special relativity, 133–135 consequences of, 135–144 Potential energy, 67–68, 83 Powers of 10, 2–3 Prime directive, 53–54 Proper mass, 145 Proton(s) mass, 85, 87 upper atmosphere and, 142 velocity, 95 Q Quantum mechanics, 155–172 historical perspectives, 155–156 questions and problems, 170–172 Quantum theory, 156 R Reference frames, 115–117 Relativity causality and, 53 dilated time, 140 Galilean, 117–119, 131 genetic effects, 149 improper time, 140 postulates, 133–144 prediction, 53 proper observer, 140 proper time, 140 Index questions and problems, 150–154 of simultaneity, 135–137 special, 133–135 speed of light and, 103 Rest mass, 145 S Schrodinger, Erwin, 10, 165 Schrodinger equation, 165–167 Simultaneity, relativity of, 135–137 Space reflection symmetry, 59 Space translation symmetry, 56–57 Space travel, 148–149 Speed, 1, 132 Standard candle technique, 189 Stars cepheids, 189 distant, 189–190 nearby, 187–189 standard candle, 189 supernovae, 189–190 Sun, 129 distance from earth, as energy source, 24, 74 mass, 31, 32, 37 ultimate fate, 74 Sunsets, 112 Symmetry, 54–60, 118 defined, 54–55 laws of nature and, 55–59 matter-antimatter, 58–59 matter reflection, 58–59 questions and answers, 59–60 reflection, 57 space reflection, 59 space translation, 56–57 time reversal, 75 time translation, 57 Weyl’s definition, 54–55 T Theory, 8–9 Theory of everything (TOE), 26 Theory of relativity, 26, 53, 103, 115–154 causality and, 53 equation, 144–146 ether and, 119–122 frame of reference and relative speeds, 115–117 Maxwell and, 119–122 tests, universe and, 186 Thermodynamics defined, 72 second law, 71–75 Index Time dilation, 137–142 light clock, 138 useful definitions, 140–142 TOE See Theory of everything (TOE) Twin paradox, 148–149 207 standard candle, 189 supernovae, 189–190 theory of relativity and, 186 Up quarks, 179 W U Units English system, metric system, MKS system, 1, 67 questions and problems, Universe acceleration, 190 dark energy, 197–198 dark matter, 196–197 evolution of, 190–196 formation of atoms, 195–196 formation of nuclei, 195 formation of particles, 195 formation of stars and galaxies, 196 grand unified theory and, 192 expansion of, 185–190 heat of death, 74 laws, questions and problems, 198–200 stars cepheids, 189 distant, 189–190 nearby, 187–189 Wave(s) de Broglie, 160–162 equation for, 165–167 light, 103–109 constructive interference, 106 destructive interference, 106 diffraction, 107–109, 111 frequency, 104 interference, 106–107 length, 104 longitudinal, 105 period, 104 polarization, 105 speed, 104–105 superposition, 105 transverse, 105 types of, 105 speed, 119–120 Weight, 27 mass and, 27, 28 Work, as defined in physics, 67 Y Young, Thomas, 103 EINSTEIN General Relativity Weakest Gravity Maxwell Electromagnetism Figure 4.1  The unification of forces Time Space Earthly Motion NEWTON Planetary Motion Light Magnetism Electricity Strongest Strong Force Weak Force Electromagnetic Theory Electroweak Theory ? Fundamental Forces Today Grand Unification ? ? ? Super Unification ? TOE ? Figure 6.3  Two atoms (hand and table) close to each other The dashed ellipses represent the electron (blue) orbits that circle the nucleus (red circles) This is not to scale since the size of the electron orbits is about 100,000 times the size of the nucleus Before v2 = ? 10 m/sec m1 = kg After m2 = kg Figure 8.1  Explosion of a 10 kg bomb initially at rest 15 m/sec Before v1 = 20m/sec v2 = ? m1 = kg m2 = kg After Figure 8.2  A 10 kg bomb moving with a speed of 15 m/s before exploding Electrons scattered throughout Diffuse positive charge n+ (a) (b) Figure 9.1  (a) If the plum pudding model were correct, alpha particles would pass through the atom with little or no deflection (b) What Rutherford observed was that some alpha particles were deflected through large angles, indicating the presence of a massive nucleus (From Ted Ankara; library.tedankara.k12.tr/chemistry/vol3/vo13.html) Neutron (Mn = 939 MeV) vp ve Mp = 938 MeV Me = 0.51 MeV Figure 10.3  A picture of beta decay where a neutron decays (explodes) into a proton and an electron (a) (b) Figure 11.5  Diffraction of waves through an opening In the upper part of the figure (a), the opening is small or comparable to the wavelength, and a good deal of the wave is bent behind the barrier On the lower part (b), the opening is a good deal larger than the wavelength, and most of the wave goes forward, more like particles would behave (From ChiuKing Ng; www.ngsir.netforms.com) Figure 11.7  The result of shining light on two slits showing a typical intereference pattern for waves (From M Goldmen; www.colorado.edu/physics/2000/images/two_slit_logo.jpg) edge of atmosphere sun white light red light blue light EARTH Figure 11.8  Why the sky is blue and sunsets are red Nucleus Figure 13.1  de Broglie wavelengths in the circular electron orbit in the atom This particular configuration corresponds to three integral number of wavelengths (n = 3) e− e− γ e− e− Figure 14.2  In our most modern view of forces, two electrons exchange a photon (γ), the force carrier associated with the electromagnetic force e− e− e− γ e− e− e− e− Z0 e− Figure 14.3  Feynman diagrams depicting the force between two electrons due to the exchange of a photon (electromagnetic force) and the exchange of a Z0 When the kinetic energies of the electrons are much greater than the mass-energy of the Z0 (100 GeV), the force due to either exchange becomes the same For energies below 100 GeV, the two forces not behave the same Figure 14.4  The ultimate makeup of matter (From Desy; www.zms.desy.de/e548/e550/ e6943/e83/imageobject148/kristall_quark_hr_ger.jpg) u u g u g u g g = gluon d d Figure 14.6  A proton is made up of three quarks: two up quarks and one down quark The quarks are held together by the exchange of the strong force carriers, the gluons AU sun distance star distance parallax angle AU sun star Figure 15.1  Two examples of parallax measurements: one for a relatively nearby star and one for a star farther away The parallax angle is smaller the farther the star Figure 15.2  The evolution of the universe from the big bang to the present (Adapted from Moment of Creation by James Trefil.) ... So, the slope of the graph of v versus t is the acceleration Since the two lines are parallel, they have the same slope and hence the same acceleration Then what is the difference between the. .. the expression (v2/R) comes about One power of v comes from the change in the velocity vector, and the other power of v comes from the fact that the faster the car is moving, the smaller is the. .. the wheel, the only force acting on the wagon is the pull due to the horse This is what causes the wagon to accelerate On the other hand, there are two forces acting on the horse One is the frictional