Probing the structure of quantum mechanics

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