Light and Matter Fullerton, California www.com Copyright c 2002-2004 Benjamin Crowell All rights reserved. April 1, 2006 ISBN 0-9704670-8-7 Permission is granted to copy, distribute and/or modify this docu- ment under the terms of the Creative Commons Attribution Share- Alike License, which can be found at creativecommons. The license applies to the entire text of this book, plus all the illustra- tions that are by Benjamin Crowell. All the illustrations are by Benjamin Crowell except as noted in the photo credits or in paren- theses in the caption of the figure.
This book can be downloaded free of charge from www.com in a variety of formats, including editable formats.com Brief Contents 1 The Rules of the Rules 7 2 The Ray Model of Light 21 3 Images 45 4 Conservation of Mass and Energy 61 5 Conservation of Momentum 89 6 Relativity 121 7 Electricity and Magnetism 143 3 www.com Contents 1 The Rules of the Rules 3 Images 1.1 Location and Magnification .2 A Preview of Noether’s Theorem .3 What Are The Symmetries?.2 Real and Virtual Images. 52 Lab 3b: A Real Image. 56 Lab 3d: The Telescope. 58 4 Conservation of Mass and Energy 4.1 Conservation of Mass .2 Conservation of Energy .—Gravitational energy, 2 The Ray Model of Light 64.—Emission and absorption of light, 66.—How many forms of energy?, 67.1 Rays Don’t Rust .3 Newton’s Law of Gravity .2 Time-Reversal Symmetry.4 Noether’s Theorem for Energy.5 Equivalence of Mass and Energy.
74 The inverse-square law, 24.4 The Speed of Light. The principle of inertia, 28. 77 the speed of light, 28. Lab 4a: Conservation Laws.
30 Lab 4b: Conservation of Energy. 84 Seeing by reflection, 30. 32 Lab 2a: Time-Reversal and Reflection Symmetry. 36 Lab 2b: Models of Light.
40 Lab 2c: The Speed of Light in Matter. 43 5 Conservation of Momentum 5.2 The Strong Principle of Inertia. 91 Symmetry and inertia, 91.—Inertial and noninertial frames, 93. 96 Conservation of momentum, 96.com Momentum compared to kinetic energy, 7.—Motion in two Current, 149.—Relativity re- Lab 5b: Frames of Reference.
Lab 5c: Conservation of Momentum. 166 Lab 5d: Conservation of Angular Momen- Electromagnetic signals, 166. 180 Lab 7b: Electrical Measurements. 182 Lab 7c: Is Charge Conserved?.
186 Lab 7e: Electric Fields. 192 Lab 7f: Magnetic Fields. 198 Lab 7h: Light Waves. 200 6 Relativity Lab 7i: Electron Waves .1 The Principle of Relativity.2 Distortion of Time and Space.
133 Combination of velocities, 133.—Equivalence of mass and energy, 137. 139 7 Electricity and Magnetism 7.—Charge and electric field, 145. Appendix 1: Photo Credits 207 5 www.com Why do I get dizzy? Am I really spinning, or is the world going around me? Humans are naturally curious about the universe they live in. Chapter 1 The Rules of the Rules Since birth, you’ve wanted to discover things.
You started out by putting every available object in your mouth. Later you began asking the grownups all those “why” questions. None of this makes you unique — humans are naturally curious animals. What’s unusual is that you’ve decided to take a physics course.
There are easier ways to satisfy a science requirement, so evidently you’re one of those uncommon people who has retained the habit of curiosity into adulthood, and you’re willing to tackle a subject that requires sustained intellectual effort. Bravo! A reward of curiosity is that as you learn more, things get simpler. “Mommy, why do you have to go to work?” “Daddy, why do you need keys to make the car go?” “Grandma, why can’t I have that toy?” Even- tually you learned that questions like these, which as a child you thought to be unrelated, were actually closely connected: they all had to do with capitalism and property. As a scientific example, William Jones announced in 1786 the discovery that many languages previously thought to be un- related were actually connected.
Jones realized, for example, that there was a relationship between the words “bhratar,” “phrater,” “frater,” and “brother,” which mean the same thing in Sanskrit, Greek, Latin, and En- glish. Many apparently unrelated languages of Europe and India could thus be brought under the same roof and understood in a simple way. For an even more dramatic example, imagine trying to learn chemistry hun- dreds of years ago, before anyone had discovered the periodic table or even the existence of atoms. Chemistry has gotten a lot simpler since then! 7 www.com Sometimes the subject gets simpler, but it takes a while for the text- books to catch up.
For hundreds of years after Hindu mathematicians incorporated negative numbers into algebra, European texts still avoided them, which meant that students had to endure a lot of confusing mumbo jumbo when it came to solving an equation like x + 7 = 0. Physics has been getting simpler, but most physics books still haven’t caught up. (Can you detect the sales pitch here?) The newer, simpler way of understanding physics involves symmetry. 8 Chapter 1 The Rules of the Rules www.1 Symmetry The concept of symmetry goes back to ancient times, but the deep link between physics and symmetry was discovered by Emmy Noether (rhymes with “loiter”).
What do we mean by symmetry? Figure b shows two examples. The galaxy has a symmetry because it looks the same when you turn your book upside-down. The orchid has a different type of symmetry: it looks the same in a mirror. Reflection and 180-degree rotation are examples of transformations, i., changes in which every point in space is systematically relocated to some other place.
We say that a thing has symmetry when transforming it doesn’t change it. As shown in figure c, some objects have more than one symmetry, although most have none. The daughter of a prominent German mathematician, she did not show any early precocity at mathematics — as a teenager she was more interested in music and dancing. She received her doctorate in 1907 and rapidly symmetry under built a world-wide reputation, 180-degree rotation but the University of Göttingen refused to let her teach, and her colleague Hilbert had to advertise her courses in the university’s catalog under his own name.
A long controversy ensued, with her opponents asking what the country’s soldiers would think when they returned home and were expected to learn at the symmetry under feet of a woman. Allowing her right-left reflection on the faculty would also mean letting her vote in the academic senate. Said Hilbert, “I do not b / Two types of symmetries. see that the sex of the candidate is against her admission as a privatdozent [instructor].
After all, the university senate is not a bathhouse.” She was finally admitted to the faculty in 1919. Self-check A A Jew, Noether fled Germany in What symmetry is possessed by most of the designs in a deck of cards? 1933 and joined the faculty at Why are they designed that way?. 20 Bryn Mawr in the U. Palindromes example 1 A palindrome is a sentence that is the same when you reverse it: I maim nine men in Saginaw; wan, I gas nine men in Miami.com no symmetry both rotation and reflection c / Most object have no symmetries.
Some have more than one. Discussion Questions A What symmetries does a human have? Consider internal features, external features, and behavior. If you woke up one morning after having been reflected, would you be able to tell? Would you die? What if the rest of the world had been reflected as well? 10 Chapter 1 The Rules of the Rules www.2 A Preview of Noether’s Theorem How does symmetry relate to physics? Long before Noether’s work, it had been recognized that some physical systems had symmetry, and their symmetries could be helpful for predicting their behavior. If the skaters in figure d have equal masses, symmetry tells us that they will move away from each other at equal speeds after they push off.
The one on the right looks bigger, however, so the symmetry argument doesn’t quite work. If you look at the world around you, you will see many approximate examples of symmetry, but none that are perfect. Most things have no symmetry at all. Until Noether’s work, that was the whole story.
Symmetry was on the sidelines of physics. d / What will happen when the two ice skaters push off from Noether’s approach was different. The universe is made out of each other? particles, and these particles are like the players on a soccer field or the pieces on a checkerboard. The arrangement of the players on the soccer field normally has no symmetry at all.
The symmetry is in the rules: the rules apply equally to both sides. Likewise, the physical arrangement of the checkers on the board in figure e has 180-degree rotation symmetry, but this is spoiled in figure f after a couple of moves. We don’t care about the asymmetry of the pieces. In Noether’s approach, what’s important is the symmetry of the rules.
If we think of the checkerboard as a little universe, then these rules are like the laws of physics, and their symmetry allows us to predict certain things about how the universe will behave. For instance, suppose we balanced the board carefully on a knife edge running from left to right below its centerline. The position in figure e balances, and so does the one in figure f. The rules required both e / The starting position in red and black to move one piece diagonally forward one step, so we checkers.
were guaranteed that after each side had made one move, the setup would balance again.1 Noether’s greatest achievement was a principle known as Noether’s theorem. We are not yet ready to state Noether’s the- orem exactly, but roughly speaking, here’s what it says: The laws of physics have to be the way they are because of symmetry. 1 This symmetry won’t continue indefinitely, because at some point one player will jump one of the other player’s pieces, or get a king and make a backwards move. That just shows that a game like checkers is an imperfect metaphor for f / The board after two moves.
the laws of physics. The particles in the universe don’t take turns moving, so we don’t have situations where one particle sits still while another one “jumps” it. It is possible for a particle of matter and a particle of antimatter to annihilate one another — the process is probably occurring in the room you’re in right now, due to natural radioactivity — but neither particle exists afterwards, so the symmetry is more perfect than in checkers. The laws of physics are also deterministic; there is no choice involved, as in a game.2 A Preview of Noether’s Theorem 11 www.3 What Are The Symmetries? What are the actual symmetries of the laws of physics? It’s tempting to try to determine them by pure reason, or by aesthetic arguments.
Why, for example, would God have chosen laws of physics that didn’t treat right and left the same way? That would seem ugly. The trouble with this approach is that it doesn’t work. For example, prehistoric peoples observed the rising and setting of the sun, the moon, the stars, and the four naked-eye planets. They all appeared to be going in circles, and a circle is a very sym- metric shape: it remains the same under rotation through any angle at all.
It became accepted dogma among the ancient astronomers that these heavenly bodies were attached to spinning crystal spheres. When careful observations showed that the motion of the planets wasn’t quite circular, they patched things up by imagining smaller crystal spheres riding on the big ones. This bias toward spheres and circles was hard to shake because the symmetry of the shapes was g / Due to the earth’s rota- so appealing.