The foundations of quantum mechanics: historical analysis and open questions – Cesena 2004; Cesena, Italy, 4 – 9 October 2004

Claudio Garola, Arcangelo Rossi, Sandro Sozzo9789812568526, 9812568522

This volume provides a unique overview of recent Italian studies on the foundations of quantum mechanics and related historical, philosophical and epistemological topics. A gathering of scholars from diverse cultural backgrounds, the conference provided a forum for a fascinating exchange of ideas and perspectives on a range of open questions in quantum mechanics. The varied nature of the papers in this volume attests to the achievement of that aim with many contributions providing original solutions to established problems by taking into account recommendations from different disciplines.

---

Table of contents :
CONTENTS……Page 8
Introduction……Page 11
If Bertlmann had Three Feet……Page 28
References……Page 31
Macroscopic Interpretability of Quantum Component Systems……Page 33
1. Three Main Physical Paradigms……Page 34
2. Semimacroscopic and Macroscopic Interpretability of Quantum Component Systems……Page 41
3. Two Environmental (model independent) theorems (Camerino 1988)……Page 46
References……Page 49
1. Introduction……Page 50
2. The Use of Projection Operators……Page 52
3. The Use of Unitary Operators……Page 54
4. Premeasurement Measurement and Information……Page 55
5. Conclusions……Page 56
References……Page 57
1. Introduction……Page 58
2. Convexity models……Page 59
3. The classical frame……Page 61
4. Conditioning in operational probability theory……Page 64
5. Quantum conditioning……Page 67
References……Page 70
Entangled State Preparation in Experiments on Quantum Non-Locality……Page 71
References……Page 76
1. Introduction……Page 78
2. Particles as described by wave equations and the e.m. field described in terms of light quanta: one and the same problem?……Page 80
3. What comes first: The wave or the particle?……Page 82
4. What does it really mean quantizing a field?……Page 84
5. Potentiality and up-to-dateness of Dirac’s work……Page 86
References……Page 88
1. Introduction……Page 90
2. On the meaning of ‘element’. The principle of physical reality and the criterion of physical objectivity……Page 91
3. On the meaning of ‘element’ in the science of Italic tradition……Page 96
4. Quantum mechanics: science or philosophy? The new meaning of ‘element’. Conclusions……Page 99
References……Page 100
1. Mathematics and the third dimension of science……Page 102
2. Mathematics and epistemology……Page 103
3. Mathematics and the principle of disorder……Page 106
References……Page 111
1. Description of a free motion with noise……Page 113
2. The probability distribution of position and velocity……Page 117
3. Speculations on the spatial probability distribution in presence of a potential……Page 118
References……Page 119
1. Introduction……Page 120
2. The Representation of the Irreducible Randomness of Quantum Reality in Phase Space……Page 121
3. Field Quantization in Phase Space and Wave/Particle Duality……Page 124
4. Conclusions……Page 126
References……Page 127
1. Introduction……Page 128
2. Equilibrium Probability Distribution……Page 129
3. Parastatistics in Economics: The Ants of Kirman……Page 135
4. An Application to Stock Price Dynamics: Gibbs’ Limit……Page 137
References……Page 139
1. Theory-neutral Experiments as a Paradigma of Classical Physics……Page 140
2. The Correspondence Principle; Role and Coverage of Instrumental Theories……Page 142
3. The Problem of the Empirical Test of one Theory with the Help of Another……Page 143
4. Pluri-correspondence in Relativity and Quantum Mechanics. Niels Bohr’s Complementarity……Page 144
5. Conclusive Observations……Page 147
References……Page 149
1. The Problem……Page 152
2. Possible solutions……Page 153
3. Bell’s inequality……Page 155
4. Factorizability analysed……Page 156
5. Quantum non-locality and the proposed solutions of the problem……Page 159
6. Critical evaluation……Page 161
7. Concluding remarks……Page 163
References……Page 164
On the Notion of Proposition in Classical and Quantum Mechanics……Page 166
1. Introduction……Page 167
2. The language L(x)……Page 170
3. The poset of physical propositions……Page 172
4. The general notion of testability……Page 174
5. Classical mechanics (CM)……Page 175
6. Quantum mechanics (QM)……Page 177
7. Quantum truth……Page 182
8. The pragmatic interpretation of QL……Page 184
9. Physical propositions and possible worlds……Page 185
References……Page 186
1. Introduction……Page 188
2. Electromagnetic Conception of Nature and Quantum Physics……Page 190
References……Page 194
1. Section 1……Page 196
2. Section 2……Page 198
3. Section 3……Page 199
4. Section 4……Page 202
References……Page 205
1. The de Broglie-Bohm interpretation of quantum mechanics……Page 207
2. Bohmian mechanics……Page 210
3. Double slit interference……Page 211
4. Features of the d.B.B. model……Page 215
References……Page 218
1. The role of a phenomenological pretheory……Page 220
2. Deterministic dynamics of objective states……Page 222
3. A way to microsystems……Page 227
4. Conclusions and outlook……Page 233
References……Page 234
Introduction……Page 235
1. Garbasso the Stark effect and the problematic birth of quantum mechanics in Italy……Page 236
2. Brunetti and the study of process of X-ray emission……Page 241
3. Fermi the “quantum mechanics propagandist”……Page 243
4. Conclusion……Page 245
References……Page 246
1 Introduction……Page 248
2 The definition of momentum in classical and quantum physics……Page 251
3 The diffraction by a single slit and the Fourier transform……Page 254
References……Page 256
1. Introduction……Page 258
2. The Two-Slit Interference Experiment……Page 259
3. A Dynamic Model with Memory Effects at the Barrier……Page 261
4. Interference Pattern and Non-Additivity Paradox……Page 263
5. Conclusions……Page 268
References……Page 269
1. Introduction……Page 270
2. Margenau on the nature of physical reality……Page 271
3. Things and their properties……Page 273
4. Chemical reactivity: intrinsic or relational property?……Page 275
5. Relational properties and scientific realism……Page 280
References……Page 281
1. Introduction……Page 284
2. Formalization of the problem……Page 285
3. A ‘gedanken experiment’ solution……Page 288
References……Page 290
1. Introduction……Page 291
2. In search of a demarcation between given experience and mental creation……Page 292
3. In search of a demarcation between given experience and technological manipulation……Page 296
References……Page 301
1. Introduction……Page 303
2. States and properties……Page 305
3. Von Neumann’s formalization of Quantum Mechanics……Page 306
4. Dirac’s formalization beyond pragmatism and falsificationism……Page 307
References……Page 309
1. Introduction……Page 311
2. Density matrix formalism in quaternionic Hilbert spaces……Page 313
3. Complex and quaternionic maps……Page 314
4. Two spin 1/2 systems in HQ……Page 315
5. Quaternionic description of the compound system……Page 317
References……Page 320
1 Introduction……Page 321
2 Predictability and visibility in a Mach-Zehnder interferometer……Page 323
3 Distinguishability and visibility in a Mach-Zehnder interferometer……Page 327
4 Conclusions……Page 328
References……Page 329
1. Introduction……Page 330
2. Gramsci’s criticism of positivism and his conception of science……Page 331
3. Gramsci and microphysics……Page 333
References……Page 343
1. Two Quantum Mechanics Formulations……Page 345
2. Premises to a New Approach to Quantum Logic……Page 347
3. The Logic of the Heisenberg Formulation……Page 348
4. The “Synthetic” Aspect of Heisenberg’s Argument……Page 351
Conclusions……Page 352
References……Page 353
1. Introduction……Page 355
2. Qubitisation of quantum space-time……Page 357
4. Is quantum space-time in a superposed/entangled state?……Page 359
5. The quantum network of Nature……Page 361
6. Quantum function evaluation at the Planck scale……Page 363
7. Unitary evolution and its consequences……Page 365
8. Conclusions……Page 366
References……Page 367
2 Experimental setup and results……Page 369
References……Page 372