Probing the Structure of Quantum Mechanics

Diederik Aerts9810248474, 9789810248475, 9789812778024

Focuses on the theoretical aspects of applications that arise from new technology and novel research perspectives such as quantum optics and quantum cryptography. For graduate students, researchers and academics in quantum physics.

---

Table of contents :
CONTENTS……Page 6
Probing the Structure of Quantum Mechanics……Page 8
References……Page 21
1 Introduction……Page 27
2 Quantum Axiomatics……Page 29
3 The Representation Theorem……Page 36
4 The Two Failing Axioms of Standard Quantum Mechanics……Page 40
5 Attempts and Perspectives for Solutions……Page 46
References……Page 51
1 Introduction……Page 54
2 A Single Spin 1/2 System……Page 56
3 The Separated Product of Two Spin 1/2 Systems……Page 62
4 The Orthogonality Relation……Page 68
5 Sasaki Regularity……Page 70
6 Discussion……Page 73
References……Page 75
1 Introduction……Page 78
2 Foundations of the Formalism……Page 84
3 Classical and Quantum Entities……Page 90
4 Pre-Order Structures……Page 94
5 Experiments And Preparations……Page 96
6 Meet Properties and Join States……Page 102
7 Operationality……Page 106
8 Conclusion……Page 111
References……Page 112
1 Introduction……Page 118
2 The e-Model……Page 119
3 Structures on the Set of Properties……Page 122
4 Physically Denned Orthogonality Relations……Page 126
5 The N-Model: A Model with Vanishing State Transitions in the Classical Limit……Page 130
6 The G-Z Orthogonality Relation for a General Physical System……Page 132
References……Page 135
1 State Property Systems and Closure Spaces……Page 137
2 Super Selection Rules……Page 143
3 D-classical Properties……Page 144
4 Decomposition Theorem……Page 147
5 Closed Subspaces and ap-Subsystems……Page 149
6 The D-classical Part of a State Property System……Page 151
References……Page 154
1 Introduction……Page 156
2 Prerequisites from Convex Geometry……Page 158
3 Basic Assumptions……Page 161
4 Axioms for Contextual Interactions……Page 162
5 Conclusion……Page 169
References……Page 170
1 Introduction……Page 172
2 Previous Attempts……Page 174
3 A New Hidden Variable Model……Page 176
4 Experimental Measurement of Temporal Correlations……Page 179
5 Conclusion…….Page 193
6 Appendix……Page 194
References……Page 208
1 Introducing the Problem……Page 212
2 Subset Probability……Page 218
3 Reality as a Special Case of Probability……Page 224
4 SEP: The Category of State Experiment Probability Systems……Page 227
5 The Categories SEP and SP……Page 230
References……Page 234
1 Introduction……Page 237
2 Quantum Computation: Main Concepts……Page 239
3 Intermediate Models Between Quantum and Classical……Page 245
4 Computers ‘Between Quantum and Classical’……Page 249
5 Conclusions……Page 251
References……Page 252
1 Introduction……Page 255
2 Buckley-Siler connectives for classical observables……Page 257
3 Generalization of Buckley-Siler approach to the case of fuzzy sets with no underlying sample space……Page 261
4 Buckley-Siler connectives for spin-1/2 observables……Page 263
References……Page 265
1 Introduction……Page 266
2 The EPR-Situation……Page 270
3 Some Causal Influences Do Not Propagate……Page 275
4 Non-Separable Physical Entities Not Situated in Space……Page 279
5 The Creation-Discovery View……Page 280
6 Are Quantum Entities Individuals?……Page 287
7 Is The Creation-Discovery View a Scientific Realism?……Page 289
References……Page 291
2 The Mach-Zehnder interferometer considered as a unitary transformation……Page 294
3 Encoding protocol……Page 296
4 Decoding protocol……Page 297
5 A realistic variant of the technique……Page 298
References……Page 301
1 Introduction……Page 303
2 Quantum Cryptography……Page 304
3 Some Technological Limitations of the Quantum Technique……Page 308
4 A Semi-Classical Technique……Page 310
5 Comparison of the Quantum and Semi-Classical Protocols……Page 318
6 Generalisations of the Protocol……Page 323
References……Page 329
1 Introduction……Page 331
2 A Systematic Method to Generate Darboux-Invariant Lax Pairs……Page 333
3 Examples of Darboux-Invariant Equations……Page 336
4 A Nonisospectral Case……Page 338
5 The Darboux-Backlund Transformation……Page 339
6 Conclusions……Page 340
References……Page 341
1 Introduction……Page 342
2 Darboux-Integrable Equations……Page 345
3 Examples……Page 347
4 Binary Darboux Transformation……Page 350
5 The Main Theorem……Page 353
6 Conclusions……Page 358
References……Page 359
1 Introduction……Page 361
2 Darboux Transformations in Associative Ring with Automorphism……Page 362
3 Stationary Equations as Eigenvalue Problems and Chains……Page 364
4 Joint Covariance of Equations and Nonlinear Problems……Page 366
5 Non-Abelian Hirota System……Page 368
6 Nahm Equations……Page 371
References……Page 373
1 Introduction……Page 375
2 Classical Electromagnetism……Page 378
3 Quantum Description……Page 383
4 Fock Representation……Page 387
5 Poincare Invariance……Page 388
6 Conclusions……Page 394
Appendix A: Covariance Systems……Page 396
Appendix B: Smeared-out Field Operators……Page 397
Appendix D: Existence of the Vacuum State……Page 398
Appendix E: Unitary Representation of the Group of Shifts……Page 399
References……Page 400