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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Status
Central Library QC16.B64 C47 1998 Adult Non-Fiction Central Closed Stacks
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Summary

Summary

The book presents the life and personality, the scientific and philosophical work of Ludwig Boltzmann, one of the great scientists who marked the passage from 19th to 20th century physics. His rich and tragic life, ending by suicide at the age of 62, is described in detail. A substantialpart of the book is devoted to discussing his scientific and philosophical ideas and placing them in the context of the second half of the 19th century. The fact that Boltzmann was the man who did most to establish that there is a microscopic, atomic structure underlying macroscopic bodies isdocumented, as is Boltzmann's influence on modern physics, especially through the work of Planck on light quanta and of Einstein on Brownian motion. Boltzmann was the centre of a scientific revolution, and he has been proved right on many crucial issues. He anticipated Kuhn's theory of scientificrevolutions and proposed a theory of knowledge based on Darwin. His basic results, when properly understood, can also be stated as mathematical theorems. Some of these have been proved; others are still at the level of likely but unproven conjectures. The main text of this biography is writtenalmost entirely without equations. Mathematical appendices deepen knowledge of some technical aspects of the subject.


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

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