Cover image for Ludwig Boltzmann : the man who trusted atoms
Title:
Ludwig Boltzmann : the man who trusted atoms
Author:
Cercignani, Carlo.
Personal Author:
Publication Information:
Oxford ; New York : Oxford University Press, 1998.
Physical Description:
xvi, 329 pages : illustrations ; 24 cm
Language:
English
ISBN:
9780198501541
Format :
Book

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Summary

Summary

Ludwig Boltzmann arguably played the key role in establishing that submicroscopic structures underlie the ordinary world. He had a tremendous impact on late 19th-century and early 20th-century physics, and he anticipated many contemporary ideas, including Kuhn's theory of scientific revolutions and recent theories of knowledge based on Darwinian principles. This book is the first accessible biography of this important figure. Without relying on equations, it provides a deep look at the full range of his scientific and philosophical ideas, discussing both their original context and their relevance today. The book also gives a concise portrait of Boltzmann's life, which, despite his successes, ended tragically in suicide. Drawing on recent research related to some of Boltzmann's more controversial ideas, this book offers fascinating insights into the birth of modern physics.


Author Notes

Carlo Cercignani is a Professor of Theoretical Mechanics at Politecnico di Milano.


Table of Contents

Figure acknowledgementsp. xvii
Introductionp. 1
1 A short biography of Ludwig Boltzmannp. 5
1.1 Youth and happy yearsp. 5
1.2 The crisisp. 20
1.3 Restlessnessp. 22
1.4 Scientific debates and travelsp. 26
1.5 The tragic fate of a great scientistp. 34
1.6 Boltzmann as a teacherp. 37
1.7 Boltzmann and inventionsp. 38
1.8 Ludwig Boltzmann and his timesp. 39
1.9 A poem by Ludwig Boltzmannp. 46
1.10 Boltzmann's personalityp. 48
2 Physics before Boltzmannp. 50
2.1 From Galileo and Newton to the early atomic theoriesp. 50
2.2 The first connections between heat and mechanical energyp. 56
2.3 The springtime of thermodynamicsp. 59
2.4 Electricity and magnetismp. 65
3 Kinetic theory before Boltzmannp. 71
3.1 Early kinetic theoriesp. 71
3.2 The beginnings of modern kinetic theory and the problem of justifying the Second Lawp. 80
4 The Boltzmann equationp. 86
4.1 Irreversibility and kinetic theoryp. 86
4.2 The great paper of 1872p. 88
4.3 A critique of Boltzmann's approachp. 93
5 Time irreversibility and the H-theoremp. 96
5.1 Introductionp. 96
5.2 Loschmidt's paradoxp. 97
5.3 Poincare's recurrence and Zermelo's paradoxp. 100
5.4 The physical and mathematical resolution of the paradoxesp. 102
5.5 Timers arrow and the expanding universep. 109
5.6 Is irreversibility objective or subjective?p. 112
5.7 Concluding remarksp. 118
6 Boltzmann's relation and the statistical interpretation of entropyp. 120
6.1 The probabilistic interpretation of thermodynamicsp. 120
6.2 Explicit use of probability for a gas with discrete energiesp. 121
6.3 Energy is continuousp. 125
6.4 The so-called H-curvep. 129
7 Boltzmann, Gibbs, and equilibrium statistical mechanicsp. 134
7.1 Introductionp. 134
7.2 A great American scientist of the nineteenth century: J.W. Gibbsp. 135
7.3 Why is statistical mechanics usually attributed to Gibbs and not to Boltzmann?p. 140
7.4 Gibbs's treatisep. 142
7.5 French scientists on statistical mechanicsp. 145
7.6 The problem of trend to equilibrium and ergodic theoryp. 146
7.7 Planck and statistical mechanicsp. 150
8 The problem of polyatomic moleculesp. 153
8.1 The problem of specific heatsp. 153
8.2 The H-theorem for polyatomic moleculesp. 154
8.3 Specific heats againp. 155
8.4 Boltzmann's ideas on specific heats, and twentieth century contributionsp. 157
9 Boltzmann's contributions to other branches of physicsp. 160
9.1 Boltzmann's testing of Maxwell's theory of electromagnetismp. 160
9.2 Boltzmann lays the foundations of hereditary mechanicsp. 161
9.3 Back to electromagnetismp. 162
9.4 A true pearl of theoretical physicsp. 163
9.5 Mathematics and foundations of mechanicsp. 164
10 Boltzmann as a philosopherp. 170
10.1 A realist, but not a naive onep. 170
10.2 Laws of thought and scientific conceptsp. 177
10.3 Ethics, aesthetics, religionp. 181
10.4 Philosophy of sciencep. 184
10.5 Boltzmann's views on scientific revolutionsp. 189
10.6 Boltzmann's education in philosophyp. 191
10.7 Did Boltzmann abandon realism?p. 192
11 Boltzmann and his contemporariesp. 198
11.1 The contacts between Boltzmann and his colleaguesp. 198
11.2 Maxwellp. 198
11.3 Lorentzp. 200
11.4 Boltzmann and the energetistsp. 202
11.5 Planckp. 210
11.6 Students and younger colleaguesp. 211
12 The influence of Boltzmann's ideas on the science and technology of the twentieth centuryp. 214
12.1 Brownian motionp. 214
12.2 Enter Einsteinp. 215
12.3 Black-body radiationp. 217
12.4 Einstein againp. 220
12.5 The role of Boltzmann's ideas during the twentieth centuryp. 223
Epiloguep. 226
Chronologyp. 227
"A German professor's journey into Eldorado"p. 231
Appendicesp. 251
A 3.1 Calculation of pressure in a rarefied gasp. 251
A 4.1 The Liouville equationp. 255
A 4.2 Calculation of the effect of collisions of one particle with anotherp. 259
A 4.3 The BBGKY hierarchyp. 261
A 4.4 The Boltzmann hierarchy and its relation to the Boltzmann equationp. 264
A 4.5 The Boltzmann equation in the homogeneous isotropic casep. 266
A 5.1 Collision-invariantsp. 267
A 5.2 Boltzmann's inequality and the Maxwell distributionp. 271
A 5.3 The H-theoremp. 273
A 5.4 The hourglass modelp. 277
A 6.1 Likelihood of a distributionp. 280
A 7.1 The canonical distribution for equilibrium statesp. 283
A 8.1 The H-theorem for classical polyatomic moleculesp. 287
A 8.2 The equipartition problemp. 291
A 9.1 The Stefan-Boltzmann lawp. 294
A 9.2 Wien's lawp. 295
Referencesp. 297
Indexp. 319