Reasoning About Luck: Probability and Its Uses in Physics

by Vinay Ambegaokar

Overview

This book introduces college students and other readers to the uses of probability and statistics in the physical sciences, focusing on thermal and statistical physics and touching upon quantum physics. Widely praised as beautifully written and thoughtful, Reasoning About Luck explains concepts in a way that readers can understand and enjoy, even students who are not specializing in science and those outside the classroom — only some familiarity with basic algebra is necessary. Attentive readers will come away with a solid grasp of many of the basic concepts of physics and some excellent insights into the way physicists think and work.
"If students who are not majoring in science understood no more physics than that presented by Ambegaokar, they would have a solid basis for thinking about physics and the other sciences." — Physics Today.
"There is a real need for rethinking how we teach thermal physics—at all levels, but especially to undergraduates. Professor Ambegaokar has done just that, and given us an outstanding and ambitious textbook for nonscience majors. I find Professor Ambegaokar's style throughout the book to be graceful and witty, with a nice balance of both encouragement and admonishment." — American Journal of Physics.

Product Details

ISBN-13:	9780486807010
Publisher:	Dover Publications
Publication date:	01/18/2017
Series:	Dover Books on Physics
Edition description:	Reprint
Pages:	256
Sales rank:	1,103,426
Product dimensions:	7.30(w) x 9.50(h) x 0.50(d)

About the Author

Vinay Ambegaokar is Goldwin Smith Professor of Physics Emeritus at Cornell University. He is the 2015 recipient of the prestigious John Bardeen Prize for his theoretical research in the area of superconductivity.

Table of Contents

Preface xiii

1 Introduction I

2 The likely, the unlikely, and the incomprehensible 6

Calculating probabilities 11

Some rules 14

How to permute and combine 16

Terminology 18

Solved problems 19

3 Normality and large numbers 23

The binomial distribution 23

The mean and the standard deviation 30

The normal distribution 38

The laws of averages and large numbers; the central limit theorem 39

Summary 41

Appendix: Another expression for the variance 41

Solved problems 43

4 Examples 48

Polling 48

Testing a vaccine 50

Estimation of need 51

Probability and baseball : the World Series 53

Solved problems 56

5 A little mathematics 60

Powers 60

Exponentials 62

Logarithms 66

Radioactive decay 68

Logarithms and factorials : Stirling's formula 70

Near normality 71

Appendix: The Poisson distribution 73

Solved problems 75

6 Forces, motion, and energy 80

Newton's laws of motion 81

Two examples of acceleration 83

Newton's law of gravitation 89

Energy 92

Solved problems 96

7 Atoms, molecules, and molecular motion 102

Molecules in motion: gases 106

Molecular motion and gas temperature 111

Some comments 114

Units 116

Solved problems 117

8 Disorder, entropy, energy, and temperature 120

Entropy 122

Another derivation 126

Some properties of entropy 127

Maximizing entropy : minimizing order 129

Absolute temperature 134

Gas temperature and absolute temperature are identical 137

Effusion from a thermal enclosure 140

Solved problems 141

9 Heat, work, and putting beat to work 147

Work, heat, and the First Law of Thermodynamics 147

Heat, entropy, and the Second Law of Thermodynamics 153

Thermodynamic reasoning: an example 156

Heat engines 158

Refrigerators and heat pumps 161

Solved problems 162

10 Fluctuations and the arrow of time 168

Fluctuations and the approach to equilibrium: Ehrenfest's dogs 172

Entropy 176

Gibbs entropy in a non-equilibrium context 177

Summary and comments 178

Solved problems 181

11 Chaos 184

A rudimentary pinball machine 190

Logistics 193

Chaos by stretching and folding 196

A brief look back and forward 200

Further reading 201

Solved problems 201

12 Quantum jumps: the ultimate gamble 204

Classical particles and waves 205

Light as a wave 208

The bright spot 210

Light as a particle 211

Probability in quantum mechanics 212

Quantum statistics 216

Emission and absorption of light 220

Further reading 223

Solved problems 224

Index 229

Addenda for the Dover Edition 233