Revolution in Physics Benjamin Crowell Book 6 in the Light and Matter series of introductory physics textbooks www.lightandmatter.com The Modern The Modern Revolution in Physics The Light and Matter series of introductory physics textbooks: 1 Newtonian Physics 2 Conservation Laws 3 Vibrations and Waves 4 Electricity and Magnetism 5 Optics 6 The Modern Revolution in Physics The Modern Revolution in Physics Benjamin Crowell www.lightandmatter.com Light and Matter Fullerton, California www.lightandmatter.com © 2000 by Benjamin Crowell All rights reserved. Edition 2.0 rev. 2002-06-03 ISBN 0-9704670-6-0 Brief Contents 1 Relativity, Part I 11 2 Relativity, Part II 29 3 Rules of Randomness 45 4 Light as a Particle 63 5 Matter as a Wave 77 6 The Atom 97 Contents 1 Relativity, Part I 11 1.1 The Principle of Relativity 12 1.2 Distortion of Time and Space 13 1.3 Applications 20 Summary 26 Homework Problems 27 2 Relativity, Part II 29 2.1 Invariants 30 2.2 Combination of Velocities 30 2.3 Momentum and Force 32 2.4 Kinetic Energy 33 2.5 Equivalence of Mass and Energy 35 2.6* Proofs 38 Summary 40 Homework Problems 41 3 Rules of Randomness45 3.1 Randomness Isn’t Random 46 3.2 Calculating Randomness 47 3.3 Probability Distributions 50 3.4 Exponential Decay and Half-Life 53 3.5∫ Applications of Calculus 58 Summary 60 Homework Problems 61 4 Light as a Particle 63 4.1 Evidence for Light as a Particle 64 4.2 How Much Light Is One Photon? 65 4.3 Wave-Particle Duality 69 4.4 Photons in Three Dimensions 73 Summary 74 Homework Problems 75 5 Matter as a Wave 77 5.1 Electrons as Waves 78 5.2*∫ Dispersive Waves 82 5.3 Bound States 84 5.4 The Uncertainty Principle and Measurement 86 5.5 Electrons in Electric Fields 90 5.6*∫ The Schrödinger Equation 91 Summary 94 Homework Problems 95 6 The Atom 97 6.1 Classifying States 98 6.2 Angular Momentum in Three Dimensions 99 6.3 The Hydrogen Atom 101 6.4* Energies of States in Hydrogen 104 6.5 Electron Spin 106 6.6 Atoms With More Than One Electron 107 Summary 109 Homework Problems 110 Exercises 113 Solutions to Selected Problems 117 Glossary 119 Index 121 Photo Credits 125 [...]... homebody brother is the one who travels backward on the receding earth, and then returns as the earth approaches the spaceship again, while in the frame of reference fixed to the spaceship, the astronaut twin is not moving at all It would then seem that the twin on earth is the one whose biological clock should tick more slowly, not the one on the spaceship The flaw in the reasoning is that the principle... sources of the magnetic field Einstein could not tolerate this disagreement between the treatment of relative and absolute motion in the theories of matter on the one hand and light on the other He decided to rebuild physics with a single guiding principle: Einstein’s Principle of Relativity Both light and matter obey the same laws of physics in any inertial frame of reference, regardless of the frame’s... difference in the speed of light beams traveling east-west and north-south The motion of the earth around the sun at 110,000 km/hour (about 0.01% of the speed of light) is to our west during the day Michelson and Morley believed in the ether hypothesis, so they expected that the speed of light would be a fixed value relative to the ether As the earth moved through the ether, they thought they would... are specifically about Einstein’s theory of relativity, but Einstein also began a second, parallel revolution in physics known as the quantum theory, which stated, among other things, that certain processes in nature are inescapably random Ironically, Einstein was an outspoken doubter of the new quantum ideas, being convinced that the Old One [God] does not play dice with the universe,” but quantum... to the x axis The transformation is simple: x′ = t′ = x – vt t Again we have an equation with constants multiplying the variables, but now the variables are distance and time The interpretation of the –vt term is that the observer moving with the origin x′ system sees a steady reduction in distance to an object on the right and at rest in the x system In other words, the object appears to be moving... effect in nonrelativistic physics, because the velocities of the moving molecules are all in random directions, so the random motion’s contribution to momentum cancels out In our collision, the final combined blob must therefore be moving a little more slowly than the expected v/2, since otherwise the final momentum would have been a little greater than the initial momentum To an observer who believes in. .. happened if the velocity of the rocket had been reversed This would be equivalent to reversing the direction of time, like playing a movie backwards, and it would also be equivalent to interchanging the roles of the rocket and the asteroid, since the rocket pilot sees the asteroid moving away from her to the left The reversed transformation from the x′,t′ system to the x,t system must therefore be the one... m/s, the dog’s velocity in my frame of reference is 2 m/s According to everything we have learned about motion, the dog must have different speeds in the two frames: 5 m/s in the sidewalk’s frame and 2 m/s in mine How, then, can a beam of light have the same speed as seen by someone who is chasing the beam? In fact the strange constancy of the speed of light had shown up in the now-famous Michelson-Morley... ideas about measurement contain hidden assumptions If, for instance, we want to measure the length of a box, we imagine we can lay a ruler down on it, take in the scene visually, and take the measurement using the ruler’s scale on the right side of the box while the left side of the box is simultaneously lined up with the butt of the ruler The assumption that we can take in the whole scene at once with... an effect on the velocity of light along an east-west line For instance, if they released a beam of light in a westward direction during the day, they expected that it would move away from them at less than the normal speed because the earth was chasing it through the ether They were Section 1.2 Distortion of Time and Space 13 surprised when they found that the expected 0.01% change in the speed of . Revolution in Physics Benjamin Crowell Book 6 in the Light and Matter series of introductory physics textbooks www.lightandmatter.com The Modern The Modern Revolution in Physics The Light. and the next are specifically about Einstein’s theory of relativity, but Einstein also began a second, parallel revolution in physics known as the quantum theory, which stated, among other things,. Morley believed in the ether hypoth- esis, so they expected that the speed of light would be a fixed value relative to the ether. As the earth moved through the ether, they thought they would observe