Einstein, 1905-2005 (eBook)

Contents 6
Foreword 10
The Genesis of the Theory of Relativity- Olivier Darrigol 12
1 Maxwell’s theory as it was 13
2 Flashback: The optics of moving bodies 15
3 Lorentz’s theory 20
4 Poincar´e’s criticism 23
5 The Lorentz invariance 26
6 Einstein’s theory 31
7 The inertia of energy 37
Conclusions 40
Short bibliography 41
Special Relativity: A Centenary Perspective- Clifford M. Will 43
1 Introduction 43
2 Fundamentals of special relativity 44
2.1 Einstein’s postulates and insights 44
2.2 Time out of joint 45
2.3 Spacetime and Lorentz invariance 47
2.4 Special relativistic dynamics 49
3 Classic tests of special relativity 50
3.1 The Michelson-Morley experiment 50
3.2 Invariance of c 52
3.3 Time dilation 53
3.4 Lorentz invariance and quantum mechanics 53
3.5 Consistency tests of special relativity 54
4 Special relativity and curved spacetime 56
4.1 Einstein’s equivalence principle 57
4.2 Metric theories of gravity 58
4.3 Effective violations of local Lorentz invariance 58
5 Is gravity Lorentz invariant? 61
6 Tests of local Lorentz invariance at the centenary 63
6.1 Frameworks for Lorentz symmetry violations 63
6.2 Modern searches for Lorentz symmetry violation 65
7 Concluding remarks 65
References 66
The Geometry of Relativistic Spacetime- Jacques Bros and Ugo Moschella 69
From Euclid’s Geometry to Minkowski’s Spacetime- Jacques Bros 70
Introduction and general survey 70
1 On the use of geometry in mathematical physics and the concept of spacetime 76
1.1 Geometry of description and geometry of representation 76
1.2 The use of geometry in more than three dimensions 77
1.3 Galilean spacetime as a geometry of representation of motion phenomena 78
2 Postulates and construction of Minkowski’s spacetime 80
2.1 The postulates and the light-cone structure of spacetime 81
2.2 Simultaneousness revisited 85
2.3 Space-ships’ flight: the anniversary curve 90
2.4 Minkowskian (pseudo-)distance and the inverse triangular inequality: the twin “paradox” 91
2.5 Spatial equidistance and the “Lorentz contraction” of lengths 94
2.6 Lorentz transformations in the Minkowskian plane and two-dimensional Lorentz frames 96
2.7 The four-dimensional Minkowski’s spacetime tetrads, Lorentz group and Poincar´e group
3 Accelerated motions and curved world-lines 108
3.1 Curvilinear distances and the slowing down of clocks 108
3.2 Minkowski’s description of accelerations 111
3.3 A comfortable trip for the “Langevin traveler” 113
4 On the visual appearance of rapidly moving objects: Lorentz contraction revisited 117
5 The Minkowskian energy-momentum space: E = mc2 and particle physics 122
6 Toward simple geometries of curved spacetimes 127
References 129
The de Sitter and anti-de Sitter Sightseeing Tour-Ugo Moschella 130
Introduction 130
1 An analogy: non-Euclidean spaces of constant curvature 130
2 The de Sitter universe 132
3 Anti-de Sitter 136
4 Epilogue 142
References 143
Experiments with Single Photons- Philippe Grangier 145
1 Back to the beginning: Einstein’s 1905 and 1909 articles 145
2 Quantum optics and the photon 147
3 Using single photons: Quantum Key Distribution 149
4 Single photon sources 152
5 Coalescing photons 154
6 “En guise de conclusion”: towards entangled photons on demand 157
References 158
Einstein 1905­1955: His Approach to Physics- Thibault Damour 160
1 On Einstein’s Epistemology 160
2 Einstein and Philosophy 161
3 Hume, Kant, Mach and Poincar´ 162
4 Scientific Philosophy and Einstein’s Conceptual Innovation 164
5 Einstein and the Theories of Relativity 167
6 Einstein and the Kantian Quantum 168
7 A Crucial Conversation 169
8 “Waves Over Here, Quanta Over There!” 172
9 Einstein’s “Ghost Field”, Born’s “Probability Amplitude”, and Heisenberg’s “Uncertainty Relations” 173
10 A Watershed Moment 176
11 Adventurers in Entangled Reality 178
12 The Mouse and the Universe 181
13 The Multiple World 185
14 The Kantian Quantum 189
References 191
On Boltzmann’s Principle and Some Immediate Consequences Thereof- Albert Einstein 192
Brownian Motion, “Diverse and Undulating”- Bertrand Duplantier 209
1 A brief history of Brownian motion 210
1.1 Robert Brown and his precursors 211
1.2 The period before Einstein 213
1.3 William Sutherland, 1904–05 219
1.4 Albert Einstein, 1905 223
1.5 Marian von Smoluchowski 239
1.6 Louis Bachelier 248
1.7 Paul Langevin 252
1.8 Jean Perrin’s experiments 257
2 Measurements by Brownian .uctuations 263
2.1 Micromanipulation of DNA molecules 263
2.2 Measurement of force by Brownian .uctuations 265
2.3 Theory 267
3 Potential theory and Brownian motion 271
3.1 Introduction 271
3.2 Newtonian potential 272
3.3 Harmonic functions and the Theorem of the Mean 274
3.4 The Dirichlet problem 277
3.5 Relation between potential theory and Brownian motion 277
3.6 Recurrence properties of Brownian motion 283
4 The fine geometry of the planar Brownian curve 287
4.1 The Brownian boundary 287
4.2 Potential theory in the neighborhood of a Brownian curve 291
4.3 Multifractality 292
4.4 Generalized multifractality 297