Ludwig Boltzmann The Man Who Trusted Atoms

by Cercignani, Carlo; Penrose, Roger

• ISBN13: 9780198501541
• ISBN10: 0198501544
• Format: Hardcover
• Copyright: 1998-12-10
• Publisher: Oxford University Press

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.

Table of Contents

Figure acknowledgements	xvii
Introduction	1	(4)
1 A short biography of Ludwig Boltzmann	5	(45)
1.1 Youth and happy years	5	(15)
1.2 The crisis	20	(2)
1.3 Restlessness	22	(4)
1.4 Scientific debates and travels	26	(8)
1.5 The tragic fate of a great scientist	34	(3)
1.6 Boltzmann as a teacher	37	(1)
1.7 Boltzmann and inventions	38	(1)
1.8 Ludwig Boltzmann and his times	39	(7)
1.9 A poem by Ludwig Boltzmann	46	(2)
1.10 Boltzmann's personality	48	(2)
2 Physics before Boltzmann	50	(21)
2.1 From Galileo and Newton to the early atomic theories	50	(6)
2.2 The first connections between heat and mechanical energy	56	(3)
2.3 The springtime of thermodynamics	59	(6)
2.4 Electricity and magnetism	65	(6)
3 Kinetic theory before Boltzmann	71	(15)
3.1 Early kinetic theories	71	(9)
3.2 The beginnings of modern kinetic theory and the problem of justifying the Second Law	80	(6)
4 The Boltzmann equation	86	(10)
4.1 Irreversibility and kinetic theory	86	(2)
4.2 The great paper of 1872	88	(5)
4.3 A critique of Boltzmann's approach	93	(3)
5 Time irreversibility and the H-theorem	96	(24)
5.1 Introduction	96	(1)
5.2 Loschmidt's paradox	97	(3)
5.3 Poincare's recurrence and Zermelo's paradox	100	(2)
5.4 The physical and mathematical resolution of the paradoxes	102	(7)
5.5 Time's arrow and the expanding universe	109	(3)
5.6 Is irreversibility objective or subjective?	112	(6)
5.7 Concluding remarks	118	(2)
6 Boltzmann's relation and the statistical interpretation of entropy	120	(14)
6.1 The probabilistic interpretation of thermodynamics	120	(1)
6.2 Explicit use of probability for a gas with discrete energies	121	(4)
6.3 Energy is continuous	125	(4)
6.4 The so-called H-curve	129	(5)
7 Boltzmann, Gibbs, and equilibrium statistical mechanics	134	(19)
7.1 Introduction	134	(1)
7.2 A great American scientist of the nineteenth century: J.W. Gibbs	135	(5)
7.3 Why is statistical mechanics usually attributed to Gibbs and not to Boltzmann?	140	(2)
7.4 Gibbs's treatise	142	(3)
7.5 French scientists on statistical mechanics	145	(1)
7.6 The problem of trend to equilibrium and ergodic theory	146	(4)
7.7 Planck and statistical mechanics	150	(3)
8 The problem of polyatomic molecules	153	(7)
8.1 The problem of specific heats	153	(1)
8.2 The H-theorem for polyatomic molecules	154	(1)
8.3 Specific heats again	155	(2)
8.4 Boltzmann's ideas on specific heats, and twentieth century contributions	157	(3)
9 Boltzmann's contributions to other branches of physics	160	(10)
9.1 Boltzmann's testing of Maxwell's theory of electromagnetism	160	(1)
9.2 Boltzmann lays the foundations of hereditary mechanics	161	(1)
9.3 Back to electromagnetism	162	(1)
9.4 A true pearl of theoretical physics	163	(1)
9.5 Mathematics and foundations of mechanics	164	(6)
10 Boltzmann as a philosopher	170	(28)
10.1 A realist, but not a naive one	170	(1)
10.2 Laws of thought and scientific concepts	177	(4)
10.3 Ethics, aesthetics, religion	181	(3)
10.4 Philosophy of science	184	(5)
10.5 Boltzmann's views on scientific revolutions	189	(2)
10.6 Boltzmann's education in philosophy	191	(1)
10.7 Did Boltzmann abandon realism?	192	(6)
11 Boltzmann and his contemporaries	198	(16)
11.1 The contacts between Boltzmann and his colleagues	198	(1)
11.2 Maxwell	198	(2)
11.3 Lorentz	200	(2)
11.4 Boltzmann and the energetists	202	(8)
11.5 Planck	210	(1)
11.6 Students and younger colleagues	211	(3)
12 The influence of Boltzmann's ideas on the science and technology of the twentieth century	214	(12)
12.1 Brownian motion	214	(1)
12.2 Enter Einstein	215	(2)
12.3 Black-body radiation	217	(3)
12.4 Einstein again	220	(3)
12.5 The role of Boltzmann's ideas during the twentieth century	223	(3)
Epilogue	226	(1)
Chronology	227	(4)
"A German professor's journey into Eldorado"	231	(20)
Appendices	251	(46)
A 3.1 Calculation of pressure in a rarefied gas	251	(4)
A 4.1 The Liouville equation	255	(4)
A 4.2 Calculation of the effect of collisions of one particle with another	259	(2)
A 4.3 The BBGKY hierarchy	261	(3)
A 4.4 The Boltzmann hierarchy and its relation to the Boltzmann equation	264	(2)
A 4.5 The Boltzmann equation in the homogeneous isotropic case	266	(1)
A 5.1 Collision-invariants	267	(4)
A 5.2 Boltzmann's inequality and the Maxwell distribution	271	(2)
A 5.3 The H-theorem	273	(4)
A 5.4 The hourglass model	277	(3)
A 6.1 Likelihood of a distribution	280	(3)
A 7.1 The canonical distribution for equilibrium states	283	(4)
A 8.1 The H-theorem for classical polyatomic molecules	287	(4)
A 8.2 The equipartition problem	291	(3)
A 9.1 The Stefan-Boltzmann law	294	(1)
A 9.2 Wien's law	295	(2)
References	297	(22)
Index	319