Quantum Processes

Contents......Page 14
Foreword......Page 6
1.1. Classical Description......Page 22
1.2. Schrödinger’s Equations......Page 23
1.2.1. Operator Treatment of Schrödinger’s Equation......Page 25
1.2.2. Momentum Representation......Page 26
1.3. Uncertainty Relations......Page 28
1.4. Individuals......Page 30
Remark......Page 33
1.6.1. The Principle of Complementarity......Page 35
1.7. Remarks on the Superposition Principle......Page 37
1.8.1. General Remarks......Page 41
1.8.2. Conclusion......Page 44
2.1. Preliminary Remarks......Page 46
2.2.1. The Elements of Space and Time......Page 48
2.2.2. Relationship between Matter and Space-Time......Page 49
Feature 2......Page 50
Remarks concerning feature 2......Page 51
2.2.5. Perception Processes......Page 52
2.2.6. Inside World and Outside World......Page 56
2.2.7. The Influence of Evolution......Page 57
2.2.8. Information in the Picture versus Information in Basic Reality (Outside Reality)......Page 59
2.2.9. Other Biological Systems......Page 60
2.3.1. Principal Remarks......Page 63
2.3.2. Mach’s Principle......Page 65
2.3.4.1. Fourier-space......Page 66
2.3.4.2. The influence of Planck’s constant......Page 67
2.3.4.3. Reality and its picture......Page 69
2.3.4.4. Remark......Page 71
2.3.5.1. Operators......Page 72
2.3.5.2. Conclusion......Page 74
2.3.6.1. Particles......Page 76
2.3.6.2. Role of time t......Page 77
2.3.6.3. Non-local effects......Page 78
2.3.6.4. Conclusion......Page 79
2.3.7.1. Determination of  (r, t) and  (p, E)......Page 80
2.3.7.2. Remarks......Page 81
2.3.7.3. Space-specific formulation......Page 82
Comparison with Schrödinger’s equation......Page 85
(r, E)-space representation......Page 86
2.3.7.5. Other representations......Page 88
The general case......Page 91
Conclusion......Page 94
2.3.8.1. General remarks......Page 95
2.3.8.2. Description of properties and appearances......Page 96
2.3.8.3. The meaning of the wave function......Page 99
2.3.8.4. Properties of probability distributions......Page 102
2.3.9. Time......Page 104
Principal remarks......Page 105
Introduction of the reference system......Page 106
2.3.9.2. Structure of reference time......Page 107
Convolution integral......Page 109
Rectangular form for the reference time distribution......Page 112
Effect of motion......Page 114
2.3.9.4. Information inside, information outside......Page 116
2.3.9.6. Constancy phenomena......Page 117
Derivation of Schrödinger’s equation from the principles of projection theory......Page 118
Space-time information......Page 121
Information in connection with usual quantum theory......Page 124
Summary......Page 125
Aspects......Page 126
2.3.9.9.  -Dependent systems......Page 128
2.3.9.10. Some additional remarks......Page 129
Block universe......Page 131
Feynman diagrams......Page 134
2.4. Summary......Page 136
3.1. General Remarks......Page 138
3.2. The Behaviour of the Basic Equations......Page 140
3.2.1. The Case f (p , E )     =......Page 142
3.2.2. On the Relationship Between p  and E......Page 143
3.2.3. The Case f (p , E )......Page 146
3.3. Classical and Quantum-Theoretical Elements......Page 149
3.4. Behaviour of the Wave Function in (r, t )-Space and (p, E)-Space......Page 150
Remark......Page 152
3.5. Probability Considerations in Connection with  (p , E )......Page 154
3.6. Normalization Condition......Page 155
3.7. Mean Values for the Momentum and the Energy......Page 158
3.8. The p, E-Pool......Page 161
3.9. Free, Elementary Systems do not Exist......Page 163
3.10.1. Additional Physically Relevant Conditions?......Page 165
3.10.2. Multi-valuedness of the Wave Function  (p , E )......Page 166
3.10.3. Existence and Non-Existence......Page 167
3.11. Principle of Usefulness......Page 168
3.12. Further General Remarks......Page 169
3.13. Rest Mass Effect......Page 170
3.14. Summary......Page 173
3.A.1. Superposition Ansatz......Page 174
3.A.2. Mean Momentum for a Free System......Page 176
3.A.3. Usual Quantum Theory and Projection Theory......Page 177
Appendix 3.B.......Page 181
Appendix 3.C.......Page 184
3.D.1. Definition......Page 187
3.D.2. Relevant Properties......Page 188
3.D.3.1. Singularities......Page 191
3.D.3.2. The probability argument......Page 193
3.D.3.3. More details concerning the potential V (x, y, z)......Page 194
3.D.3.4. Mean value for the energy......Page 198
3.D.3.5. Normalization condition......Page 200
3.D.4. Stationary Systems do not Exist......Page 201
3.D.5. Final Remarks......Page 203
Dependence of Mass on Velocity......Page 204
4.1. Interactions within Projection Theory......Page 210
4.2. What does Interaction Mean within Projection Theory?......Page 211
4.2.1. Relationships......Page 212
4.2.2. Fourier-Effects......Page 213
4.3.1. Classical Force Laws......Page 215
2. Proximity effect......Page 216
4.3.2. Equivalent Conceptions......Page 217
4.3.3. Further Remarks......Page 218
4.3.5. Delocalised Systems in (p, E)-Space......Page 219
4.3.6. Summary......Page 220
4.4.1. Space-Time Limiting Interactions......Page 221
4.4.2. Mutual (Distance-Dependent) Interactions......Page 224
General remark......Page 227
Conventional physics......Page 230
Projection theory......Page 231
4.4.4. The p, E-Concert......Page 235
4.4.5. Individual Processes......Page 238
4.4.6. Analogy to Conventional Physics......Page 240
4.4.7. Total Momentum and Total Energy......Page 241
4.5. Pair Distributions......Page 242
4.5.1. Information About the Interaction......Page 243
Dependency of the number of subsystems......Page 245
4.5.3. Analysis in (r, t )-Space......Page 246
4.5.4. Example for N = 4......Page 251
4.5.5. Further Discussions......Page 254
4.6.1. The Main Features......Page 255
Analysis in (p, E)-space......Page 256
Analysis in (r, t )-space......Page 257
Remark......Page 259
4.6.2. Some Additional Statements......Page 260
A brief summary concerning p, E-fluctuations......Page 261
Further remarks......Page 262
System with two subsystems......Page 263
Relationships......Page 264
The situation without initial conditions......Page 265
Situation in projection theory......Page 266
4.6.4. Introduction of Pair Potentials for Certain Configurations......Page 267
Discussion......Page 269
System with two subsystems......Page 271
Systems with two types of subsystems or more......Page 272
4.6.5. Interaction Effects......Page 273
4.7. Energy Levels......Page 275
4.7.1. Treatment of the Problem......Page 277
4.7.2. Specific Properties......Page 279
4.7.3. Conditional Wave Functions......Page 280
1. Energy shift......Page 283
2. Specific interaction mechanisms......Page 285
3. Discussion......Page 287
4. Conditional wave functions for φ(Eα)......Page 289
4.7.5. Extension to N Subsystems......Page 290
4.8. Distance-Independent Interactions......Page 292
4.8.1. Principal Remarks......Page 293
4.8.2. Some Minor Changes......Page 294
4.8.3. Some Basic Features of Distance-Independent Interactions......Page 295
4.8.4. Absolute Space-Time Positions......Page 297
4.8.5. Arbitrary Jumps......Page 299
Remark......Page 300
4.8.6. Effective Velocities......Page 301
Remark......Page 305
Conventional physics......Page 306
Conclusion......Page 307
Motion relative to nothing......Page 308
Remarks in connection with Newton’s theory......Page 309
4.8.9. Resting and Moving Frames......Page 311
4.8.10. Arbitrary Jumps within Single Systems......Page 315
Situation within projection theory......Page 316
2. Measurement at time    >......Page 317
Situation within usual quantum theory......Page 319
Conclusion......Page 320
4.9. The Meaning of the Potential Functions......Page 321
4.9.1. Introduction of a Potential Function in the Case of Distance-Independent Interactions (Form Interactions)......Page 322
4.9.2. Interaction within Conventional Physics......Page 323
4.9.3. Interaction Potentials are Auxiliary Elements......Page 324
4.9.4. Conventional Physics: What Mechanism is Behind Interaction?......Page 325
4.9.5. “Gravity . . . an Occult Quality”......Page 326
4.9.6. Phenomena in Usual Quantum Theory......Page 327
4.9.7. Summary......Page 328
4.10.1. Can Systems be Elementary in Character?......Page 329
4.10.2. Self-Creating Interaction Processes......Page 330
4.11.1. Mach’s Principle......Page 333
4.11.2. The Effect of Inertia within Newton’s Theory......Page 334
Special theory of relativity......Page 335
1. De Sitter’s Solution for a Lone Body......Page 336
2. Empty Space within General Theory of Relativity......Page 337
3. Gödel’s Solution......Page 338
Conclusion......Page 339
Further comments......Page 340
4.11.4. Final Remarks......Page 341
4.12.1. General Remarks......Page 342
4.12.2. Frames of Reference within Projection Theory......Page 343
4.12.3. Transformation Formulas......Page 346
4.12.4. Arbitrary Jumps of the Entire Complex in Space-Time......Page 348
4.13. Hierarchy of the Parts in a Part......Page 349
4.13.1. Conventional Physics......Page 350
4.13.2. Is this Principle Realizable within Projection Theory?......Page 351
4.13.2.1. Pictures and p, E-fluctuations......Page 352
4.13.2.2. No static building blocks......Page 353
Summary......Page 355
4.13.2.3. No fluctuations of fluctuations!......Page 356
4.13.2.4. Independent p, E-fluctuations......Page 358
4.13.2.5. Conclusion......Page 360
4.14. Granular Space-Time Structures......Page 361
4.14.1. Combined Interactions......Page 362
4.14.2. Selections......Page 364
4.14.3. The Unified Whole......Page 365
4.14.4. Simple Cosmological Considerations......Page 368
4.14.5. Arbitrary Motions through Space and Time......Page 369
4.15. Summary and Final Remarks......Page 373
5.1. The Particle-Wave Question......Page 382
5.1.1. No Need for an Experimental Arrangement......Page 383
Born’s Interpretation......Page 386
Double-Slit Experiment......Page 387
Material Objects in Space?......Page 389
1. Motion without Inertia......Page 390
2. Paradoxical Situation......Page 391
5.1.2.2. Situation in projection theory......Page 392
5.2.1. Compatible with the Principles of Evolution......Page 393
5.2.2. Configurations in Space-Time......Page 396
Conventional Quantum Theory......Page 399
Projection Theory......Page 400
6. Summary......Page 402
Situation in Conventional Quantum Theory......Page 405
Situation in Projection Theory......Page 408
Bibliography......Page 414
Index......Page 416