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First Edition Britannica Educational Publishing Michael I. Levy: Executive Editor J. Luebering: Senior Manager Marilyn L. Barton: Senior Coordinator, Production Control Steven Bosco: Director, Editorial Technologies Lisa S.
Braucher: Senior Producer and Data Editor Yvette Charboneau: Senior Copy Editor Kathy Nakamura: Manager, Media Acquisition Erik Gregersen: Associate Editor, Science and Technology Rosen Educational Services Nicholas Croce: Editor Nelson Sá: Art Director Cindy Reiman: Photography Manager Matthew Cauli: Designer, Cover Design Introduction by Erik Gregersen Library of Congress Cataloging-in-Publication Data The Britannica guide to relativity and quantum mechanics/edited by Erik Gregersen. — (Physics explained) “In association with Britannica Educational Publishing, Rosen Educational Services.” Includes bibliographical references and index. Relativity (Physics)—Popular works. Quantum theory—Popular works.
Title: Guide to relativity and quantum mechanics. Title: Relativity and quantum mechanics.11—dc22 2010027855 On the cover, p. iii: Einstein’s famous formula.com On page x: Composite image of warped space-time. Victor de Schwanberg/Photo Researchers, Inc.
On page xviii: A wormhole is solution of the field equations in Einstein’s theory of general relativity that resembles a tunnel between two black holes. Jean-Francois Podevin/Photo Researchers, Inc. On pages 1, 24, 51, 90, 112, 234, 237, 241: Matter from a star spiraling onto a black hole. ESA, NASA, and Felix Mirabel (French Atomic Energy Commission and Institute for Astronomy and Space Physics/Conicet of Argentina) www.com CONTENTS 22 Introduction x Chapter 1: Relativity 1 The Mechanical Universe 1 Light and the Ether 2 Special Relativity 4 Einstein’s Gedankenexperiments 4 Starting Points and Postulates 5 Relativistic Space and Time 6 Relativistic Mass 10 Cosmic Speed Limit 11 2 E = mc 11 The Twin Paradox 11 Four-Dimensional Space-Time 12 Experimental Evidence for Special Relativity 22 Chapter 2: General Relativity 24 Principle of Equivalence 24 Curved Space-Time and Geometric Gravitation 26 The Mathematics of General Relativity 28 Cosmological Solutions 28 Black Holes 29 27 Experimental Evidence for General 30 Relativity 29 Unconfirmed Predictions of General Relativity 31 Gravitational Waves 31 Black Holes and Wormholes 34 Applications of Relativistic Ideas 35 Elementary Particles 35 Particle Accelerators 36 Fission and Fusion: Bombs and Stellar Processes 36 The Global Positioning System 37 Cosmology 37 www.com Relativity, Quantum Theory, and Unified Theories 46 Intellectual and Cultural Impact of Relativity 47 Chapter 3: Quantum Mechanics: Concepts 51 Historical Basis of Quantum Theory 51 Early Developments 52 Planck’s Radiation Law 52 Einstein and the Photoelectric Effect 53 73 Bohr’s Theory of the Atom 54 Scattering of X-rays Broglie’s Wave Hypothesis 58 59 91 Basic Concepts and Methods 60 Schrödinger’s Wave Mechanics 61 Electron Spin and Antiparticles 64 Identical Particles and Multielectron Atoms 69 Time-Dependent Schrödinger Equation 74 Tunneling 76 Axiomatic Approach 78 Incompatible Observables 80 Heisenberg Uncertainty Principle Quantum Electrodynamics 83 87 97 Chapter 4: Quantum Mechanics: Interpretation 90 The Electron: Wave or Particle? 90 Hidden Variables 92 Paradox of Einstein, Podolsky, and Rosen 94 Measurement in Quantum Mechanics 98 Applications of Quantum Mechanics 101 Decay of a Meson 101 www.com Cesium Clock 104 A Quantum Voltage Standard 107 114 Bose-Einstein Condensate 109 Chapter 5: Biographies 112 Carl David Anderson 112 Hans Bethe 113 David Bohm 118 Niels Bohr 120 Max Born 128 Satyendra Nath Bose 132 Louis-Victor, 7e duke de Broglie 132 Edward Uhler Condon 135 Clinton Joseph Davisson 137 P.
Dirac 137 Sir Arthur Stanley Eddington 143 Albert Einstein 146 Enrico Fermi 163 Richard P. Feynman 169 Aleksandr Aleksandrovich Friedmann 173 George Gamow 174 Hans Geiger 176 Murray Gell-Mann 177 Walther Gerlach 179 121 Lester Halbert Germer 179 Samuel Abraham Goudsmit 180 Werner Heisenberg 182 Pascual Jordan 190 Brian D. Josephson 192 Max von Laue 194 Hendrik Antoon Lorentz 195 Ernst Mach 196 A. Michelson 198 Hermann Minkowski 201 Edward Williams Morley 202 Wolfgang Pauli Max Planck 203 207 159 www.com Henri Poincaré 215 Erwin Schrödinger 220 Karl Schwarzschild 223 Julian Seymour Schwinger 224 Arnold Sommerfeld 226 Otto Stern 227 Tomonaga Shin’Ichirō 229 George Eugene Uhlenbeck 230 Wilhelm Wien 231 Conclusion Glossary 232 234 223 Bibliography 237 Index 241 226 www.com 7 Introduction 7 T his volume deals with relativity and quantum mechan- ics.
Both of these are quite new areas of physics. The beginning of relativity can be dated quite precisely, to the year 1905, when a clerk in the Swiss patent office published a paper “On the Electrodynamics of Moving Bodies.” The beginnings of quantum mechanics can be dated to 1900 when the German physicist Max Planck explained the emission of light from a blackbody as the emission not of a continuous stream of particles or waves, but a stream of discrete packets of energy called quanta. Relativity was driven by the need to explain light. The Scottish physicist James Clerk Maxwell had published four equations that explained electricity and magnetism.
These equations described the speed of an electromag- netic wave. That speed was one with which scientists were already well acquainted. It was 299,000 km (186,000 miles) per second, the speed of light. Since light was an electromagnetic wave, it must be a wave in something, like waves in water or sound in air.
As anyone who has ever looked up at the night sky knew, light crossed the vast emptiness of interstellar space from one star to another, which meant the vast emptiness was not empty at all. There was something there, something that had not been detected. This material, which came to be called the ether, had to be everywhere in the universe. Thomas Young said the ether pervaded “the substance of all material bodies as freely as wind passes through a grove of trees.” An American physicist named Albert Michelson devised an extremely clever experiment to detect the ether’s effects.
Light travelling in the same direction that Earth was mov- ing through the solar system should be travelling at a speed that is the sum of two velocities: the velocity of Earth plus the velocity of light. Light traveling at a right angle to Earth’s motion should just be traveling at the speed of light.com 7 The Britannica Guide to Relativity and Quantum Mechanics 7 Michelson tried in 1881 to detect the difference in speed and failed. He tried again in 1887 with physicist Edward Morley an experiment that would detect differences much smaller than the 1881 experiment. There was no ether, and furthermore, in defiance of what everyone knew about physics, light traveled at exactly the same speed parallel or perpendicular to Earth’s motion.
This result (or lack of a result) shattered physics. However, Einstein was undaunted by the end of classi- cal physics. He took the invariance of the speed of light as one of his starting points for the theory of relativity. As another, he took that the laws of physics would look the same to all observers.
From this foundation, Einstein developed the theory of special relativity. When one first hears about the consequences of spe- cial relativity, they seem strange and hardly believable. Time runs more slowly in a moving object. Nothing can ever travel faster than light.
However, these strange effects have been observed. Time dilation has been experimen- tally verified in many different ways. It has been tested by clocks on planes flying around the world and by particles entering Earth’s atmosphere from outer space. The agree- ment between measurement and Einstein’s theory has always been exact.
Of course, special relativity is “special” because it does not describe all motion. It did not describe any motion that is accelerated or decelerated. For example, any motion in a gravitational field experiences acceleration. It took Einstein 10 more years to solve the problem of accel- eration, but he did with general relativity.
The results were as unusual as those of special relativ- ity. Gravity was not a force but a bending of space-time, the very structure of the universe. Einstein himself was horrified by the fact that the equations of general relativ- ity implied that the universe was expanding.com 7 Introduction 7 However, just as with special relativity, general rela- tivity has been proven on many occasions. The first great test was looking for the deflection of starlight.
In 1919, English expeditions went to West Africa and Brazil to observe a solar eclipse. General relativity passed the test. (This result was also seen as a triumph for science in that after the carnage of World War I, English scientists put aside national grudges to prove the theory of a German scientist.) Because each is very massive and move within the enormous gravitational field of the other, the effects of general relativity on the motion of the pulsars can be easily measured. General relativity has passed that test.
General relativity introduced new areas for astronomy to explore. Before his death in World War I, German astronomer Karl Schwarzschild found that the equations of relativity allowed an object in which mass was com- pressed into such a small space that the gravitational field would be so enormous that the velocity needed to break free of its gravitational influence would be larger than the speed of light, the cosmic speed limit. This object is called a black hole. (Although such a term is an obvious descrip- tion, it was not so dubbed until 50 years later by American physicist John Wheeler.) Black holes are, of course, hard to observe directly, but there are many objects that seem to contain the requisite mass.
One of these, Sagittarius A* (pronounced “A-star”), resides at the centre of the Milky Way Galaxy. Despite Einstein’s discomfort at the expanding uni- verse, in the 1930s American astronomer Edwin Hubble had measured the distances to many galaxies and found that they were receding from the Milky Way at speeds proportional to their distances. This relation between speed and distance could only be explained by an expand- ing universe. Since the universe was expanding, this meant that early in its existence it was much much smaller and xiii www.com 7 The Britannica Guide to Relativity and Quantum Mechanics 7 therefore hotter.
This hot early universe is seen in the cos- mic microwave background. Relativity is a theory that applies to the large scale of the universe. The other subject of this book, quantum mechanics, is a theory of the extremely small. As with rel- ativity, its results upend common sense notions of matter.
Matter, in everyday experience, is solid, liquid, or gas. It is made up of atoms, which are usually drawn as miniature solar systems, with spheres of protons and neutrons in the center, orbited by moonlike electrons. This drawing does contain some truth but is as much metaphorical as actual. The protons and neutrons that make up the nucleus and the electrons around it sometimes have characteristics of both particles and waves.
Just like the surf pounding the beach or the light wave traveling through space, matter itself can be described as having a wave equation. This mathematical expression is called Schrdinger’s equation, which contains a wave func- tion that has values that depend on position. The square of this function is the probability of finding a particle at a position. This meant that on the subatomic scale, one could not say “the electron is here.” The true statement is “the electron has this probability of being here.
However, it may have a higher probability of being somewhere else.” When this was applied to the hydrogen atom, it solved the mystery of why the electron only seemed to be in certain places within the atom. Any old function could not be a solution to Schrdinger’s equation.