The world according to quantum mechanics: why the laws of physics make perfect sense after all
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| Main Author: | |
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| Format: | Book |
| Language: | English |
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New Jersey [u.a.]
World Scientific
2011
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 277 - 281 |
| Physical Description: | XVII, 298 S. graph. Darst. |
| ISBN: | 9814293377 9789814293372 |
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| adam_text | Titel: The world according to quantum mechanics
Autor: Mohrhoff, Ulrich
Jahr: 2011
Contents
Preface v
Overview 1
1. Probability: Basic concepts and theorems 3
1.1 The principle of indifference................. 3
1.2 Subjective probabilities versus objective probabilities ... 4
1.3 Relative frequencies ..................... 4
1.4 Adding and multiplying probabilities............ 5
1.5 Conditional probabilities and correlations......... 7
1.6 Expectation value and Standard deviation......... 8
2. A (very) brief history of the old theory 9
2.1 Planck............................. 9
2.2 Rutherford .......................... 9
2.3 Bohr.............................. 10
2.4 de Broglie........................... 12
3. Mathematical interlude 15
3.1 Vectors ............................ 15
3.2 Definite integrals....................... 17
3.3 Derivatives.......................... 19
3.4 Taylor series.......................... 23
3.5 Exponential function..................... 23
3.6 Sine and cosine........................ 24
3.7 Integrals............................ 25
xii The World According to Quantum Mechanics
3.8 Complex numbers ...................... 27
4. A (very) brief history of the new theory 31
4.1 Schrödinger.......................... 31
4.2 Born.............................. 33
4.3 Heisenberg and uncertainty ................ 35
4.4 Why energy is quantized................... 38
5. The Feynman route to Schrödinger (stage 1) 41
5.1 The rules of the game.................... 41
5.2 Two slits ........................... 41
5.2.1 Whyproduct?.................... 42
5.2.2 Why inverse proportional to BAI......... 43
5.2.3 Why proportional to UÄ1 ............. 43
5.3 Interference.......................... 44
5.3.1 Limits to the visibility of interference fringes ... 45
5.4 The propagator as a path integral ............. 47
5.5 The time-dependent propagator............... 48
5.6 A free particle......................... 50
5.7 A free and stable particle.................. 50
6. Special relativity in a nutshell 53
6.1 The principle of relativity.................. 53
6.2 Lorentz transformations: General form........... 54
6.3 Composition of velocities .................. 58
6.4 The case against positive K................. 59
6.5 An invariant speed...................... 61
6.6 Proper time.......................... 62
6.7 The meaning of mass..................... 63
6.8 The case against K = 0................... 64
6.9 Lorentz transformations: Some implications........ 65
6.10 4-vectors............................ 68
7. The Feynman route to Schrödinger (stage 2) 69
7.1 Action............................. 69
7.2 How to influence a stable particle?............. 70
7.3 Enter the wave function................... 71
7.4 The Schrödinger equation.................. 71
Contents xiii
A Closer Look 75
8. Why quantum mechanics? 77
8.1 The classical probability calculus.............. 77
8.2 Why nontrivial probabilities?................ 79
8.3 Upgrading from classical to quantum............ 80
8.4 Vector Spaces......................... 80
8.4.1 Why complex numbers?............... 82
8.4.2 Subspaces and projectors.............. 82
8.4.3 Commuting and non-commuting projectors .... 84
8.5 Compatible and incompatible elementary tests...... 86
8-6 Noncontextuality....................... 88
8.7 The core postulates...................... 90
8.8 The trace rule......................... 90
8.9 Self-adjoint Operators and the spectral theorem...... 92
8.10 Pure states and mixed states................ 93
8.11 How probabilities depend on measurement outcomes ... 94
8.12 How probabilities depend on the times of measurements . 95
8.12.1 Unitary Operators.................. 96
8.12.2 Continuous variables ................ 99
8.13 The rules of the game derived at last............ 100
9. The classical forces: Effects 101
9.1 The principle of least action ............... 101
9.2 Geodesic equations for flat spacetime............ 104
9-3 Energy and momentum................... 105
9.4 Vector analysis: Some basic concepts............ 107
9.4.1 Curl and Stokes s theorem............. 108
9.4.2 Divergence and Gauss s theorem.......... 110
9.5 The Lorentz force....................... 111
9.5.1 How the electromagnetic field bends geodesics . . 113
9.6 Curved spacetime....................... 115
9.6.1 Geodesic equations for curved spacetime..... 116
9.6.2 Raising and lowering indices............ 116
9.6.3 Curvature...................... 117
9.6.4 Parallel transport.................. 118
9.7 Gravity............................ 120
10. The classical forces: Causes 123
xiv The World According to Quantum Mechanics
10.1 Gauge invariance....................... 123
10.2 Fuzzy potentials ....................... 124
10.2.1 Lagrange function and Lagrange density ..... 125
10.3 Maxwell s equations..................... 126
10.3.1 Charge conservation................. 128
10.4 A fuzzy metric........................ 129
10.4.1 Meaning of the curvature tensor.......... 130
10.4.2 Cosmological constant................ 131
10.5 Einstein s equation...................... 131
10.5.1 The energy-momentum tensor........... 132
10.6 Aharonov-Bohm effect.................... 132
10.7 Fact and fiction in the world of classical physics...... 134
10.7.1 Retardation of effects and the invariant speed . . 136
11. Quantum mechanics resumed 139
11.1 The experiment of Elitzur and Vaidman.......... 139
11.2 Observables.......................... 141
11.3 The continuous case..................... 142
11.4 Commutators......................... 143
11.5 The Heisenberg equation................... 144
11.6 Operators for energy and momentum............ 144
11.7 Angular momentum..................... 145
11.8 The hydrogen atom in brief................. 147
12. Spin 153
12.1 Spin 1/2............................ 153
12.1.1 Other bases ..................... 155
12.1.2 Rotations as 2 x 2 matrices............. 156
12.1.3 Pauli spin matrices................. 159
12.2 A Stern-Gerlach relay.................... 160
12.3 Why spin?........................... 162
12.4 Beyond hydrogen....................... 163
12.5 Spin precession........................ 166
12.6 The quantum Zeno effect .................. 167
13. Composite systems 169
13.1 Bell s theorem: The simplest version............ 169
13.2 Entangled spins ...................... 171
Contents xv
13.2.1 The singlet state................... 172
13.3 Reduced density Operator.................. 173
13.4 Contextuality......................... 174
13.5 The experiment of Greenberger, Hörne, and Zeilinger . . . 177
13.5.1 A game........................ 177
13.5.2 A fail-safe strategy ................. 178
13.6 Uses and abuses of counterfactual reasoning........ 179
13.7 The experiment of Englert, Scully, and Walther...... 184
13.7.1 The experiment with shutters closed........ 185
13.7.2 The experiment with shutters opened....... 186
13.7.3 Influencing the past................. 187
13.8 Time-symmetric probability assignments.......... 190
13.8.1 A three-hole experiment .............. 192
14. Quantum statistics 195
14.1 Scattering billiard balls ................... 195
14.2 Scattering particles...................... 195
14.2.1 Indistinguishable macroscopic objects? ...... 197
14.3 Symmetrization........................ 198
14.4 Bosons are gregarious.................... 198
14.5 Fermions are solitary..................... 199
14.6 Quantum coins and quantum dice ............. 200
14.7 Measuring Sirius....................... 201
15. Relativistic particles 205
15.1 The Klein-Gordon equation................. 205
15.2 Antiparticles......................... 206
15.3 The Dirac equation...................... 207
15.4 The Euler-Lagrange equation................ 208
15.5 Noether s theorem...................... 210
15.6 Scattering amplitudes.................... 211
15.7 QED.............................. 212
15.8 A few words about renormalization............. 212
15.8.1 ... and about Feynman diagrams.......... 215
15.9 Beyond QED......................... 216
15.9.1 QED revisited.................... 217
15.9.2 Groups........................ 217
15.9.3 Generalizing QED.................. 218
xvi The World According to Quantum Mechanics
15.9.4 QCD......................... 219
15.9.5 Electroweak interactions.............. 220
15.9.6 Higgs mechanism .................. 221
Making Sense 223
16. Pitfalls 225
16.1 Standard axioms: A critique................. 225
16.2 The principle of evolution.................. 227
16.3 The eigenstate-eigenvalue link ............... 229
17. Interpretational strategy 231
18. Spatial aspects of the quantum world 233
18.1 The two-slit experiment revisited.............. 233
18.1.1 Bohmian mechanics................. 234
18.1.2 The meaning of both ............... 235
18.2 The importance of unperformed measurements...... 235
18.3 Spatial distinctions: Relative and contingent ....... 237
18.4 The importance of detectors................. 237
18.4.1 A possible objection................. 238
18.5 Spatiotemporal distinctions: Not all the way down .... 238
18.6 The shapes of things..................... 240
18.7 Space............................. 240
19. The macroworld 243
20. Questions of substance 247
20.1 Particles............................ 247
20.2 Scattering experiment revisited............... 247
20.3 How many constituents?................... 248
20.4 An ancient conundrum.................... 249
20.5 A fundamental particle by itself............... 250
21. Manifestation 251
21.1 Creation in a nutshell................... 251
21.2 The Coming into being of form............... 251
Contents xvii
21.3 Bottom-up or top-down?................... 252
21.4 Whence the quantum-mechanical correlation laws? .... 253
21.5 How are spooky actions at a distance possible?..... 254
22. Why the laws of physics are just so 257
22.1 The stability of matter.................... 257
22.2 Why quantum mechanics (summary)............ 258
22.3 Why special relativity (summary).............. 260
22.4 Why quantum mechanics (summary continued)...... 260
22.5 The classical or long-range forces.............. 261
22.6 The nuclear or short-range forces.............. 262
22.7 Fine tuning.......................... 264
23. Quanta and Vedanta 267
23.1 The central affirmation.................... 268
23.2 The poises of creative consciousness ............ 269
Appendix A. Solutions to selected problems 271
Bibliography 277
Index 283
|
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| language | English |
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| spelling | Mohrhoff, Ulrich Verfasser (DE-588)1013446046 aut The world according to quantum mechanics why the laws of physics make perfect sense after all Ulrich Mohrhoff New Jersey [u.a.] World Scientific 2011 XVII, 298 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 277 - 281 Quantentheorie Quantum theory Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 s DE-604 DE-601 pdf/application http://www.gbv.de/dms/bowker/toc/9789814293372.pdf Inhaltsverzeichnis HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025110681&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mohrhoff, Ulrich The world according to quantum mechanics why the laws of physics make perfect sense after all Quantentheorie Quantum theory Quantenmechanik (DE-588)4047989-4 gnd |
| subject_GND | (DE-588)4047989-4 |
| title | The world according to quantum mechanics why the laws of physics make perfect sense after all |
| title_auth | The world according to quantum mechanics why the laws of physics make perfect sense after all |
| title_exact_search | The world according to quantum mechanics why the laws of physics make perfect sense after all |
| title_full | The world according to quantum mechanics why the laws of physics make perfect sense after all Ulrich Mohrhoff |
| title_fullStr | The world according to quantum mechanics why the laws of physics make perfect sense after all Ulrich Mohrhoff |
| title_full_unstemmed | The world according to quantum mechanics why the laws of physics make perfect sense after all Ulrich Mohrhoff |
| title_short | The world according to quantum mechanics |
| title_sort | the world according to quantum mechanics why the laws of physics make perfect sense after all |
| title_sub | why the laws of physics make perfect sense after all |
| topic | Quantentheorie Quantum theory Quantenmechanik (DE-588)4047989-4 gnd |
| topic_facet | Quantentheorie Quantum theory Quantenmechanik |
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