Independent axioms for Minkowski space-time:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Harlow
Longman
1997
|
| Series: | Pitman research notes in mathematics series
373 |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 241 S. |
| ISBN: | 0582317606 |
Staff View
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Record in the Search Index
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| adam_text | Contents
Preface
1 Introduction 1
1.1 Axiomatic systems 1
1.2 Independence and consistency of the set of axioms 1
1.3 Axiomatic systems for geometries 2
1.4 Axiomatic systems for space-times 3
1.5 A brief introduction to the present axiomatic system 6
2 Primitive notions and axioms 9
2.1 Primitive undefined basis 9
2.2 Axioms of order 10
2.3 Axioms of independence 12
2.4 Axiom of isotropy or symmetry 16
2.5 Axiom of continuity 17
3 Temporal order on a path 18
3.1 Order on a finite chain 18
3.2 First collinearity theorem 20
3.3 Boundedness of the unreachable set 20
3.4 Prolongation 21
3.5 Second collinearity theorem 21
3.6 Order on a path 22
3.7 Continuity and monotonic sequence property 27
3.8 Connectedness of the unreachable set 29
4 Collinearity and temporal order 31
4.1 Third collinearity theorem 31
4.2 There is no fastest path 35
4.3 Each path is dense in itself 36
4.4 Compact collinear set 36
4.5 Optical line and record function theorems 38
4.6 Causality theorem 50
5 Existence and properties of collinear sets 53
5.1 Order properties of unreachable sets 53
5.2 Partial order on a compact collinear set 57
5.3 Order properties which imply coincidence 60
5.4 Collinear paths which meet at a single event 63
5.5 The collinear set theorem 71
6 Paths and optical lines in a collinear set 78
6.1 The crossing theorem 79
6.2 Order properties of signal functions 82
6.3 The signal theorem 91
6.4 Optical lines in a collinear set 97
6.5 Reflection in a path 99
6.6 Generalized triangle inequalities 102
6.7 Events at which paths cross 102
6.8 Modified signal and record functions 103
6.9 Mid-way and reflected paths 105
6.10 Existence theorem for paths in a collinear set 110
7 Theory of parallels 113
7.1 Divergent and convergent parallels 113
7.2 The parallel relations are equivalence relations 116
7.3 Coordinate systems on a collinear set 119
7.4 Automorphisms of a collinear set of paths 129
7.5 Uniqueness of parallelism and linearity of modified signal functions 134
8 One-dimensional kinematics 144
8.1 Rapidity is a natural measure for speed 144
8.2 Congruence of a collinear set of paths 147
8.3 Partitioning a collinear set into synchronous equivalence classes 149
8.4 Kinematic relations and coordinate transformations 151
9 Three-dimensional theorems 154
9.1 Each 3-SPRAY is a three-dimensional ordered geometry 154
9.2 The line bundle model of a 3-SPRAY 161
9.3 Each 3-SPRAY is a three-dimensional hyperbolic space 164
9.4 Coordinatization theorem 169
9.5 Isomorphism with the standard model 173
10 Standard model of Minkowski space-time 179
10.1 Induced isotropy mappings are Lorentz transformations 179
10.2 The indefinite metric 184
10.3 The orthochronous Lorentz group 186
10.4 The orthochronous Poincare group of motions 189
10.5 Transformations between coordinate frames 192
10.6 Consistency of the system of axioms 193
11 Independence models 194
11.1 Independence models MO and M OI 195
11.2 Independence model M02 195
11.3 Independence model M03 195
11.4 Independence models Mo* and M Oi 196
11.5 Independence model MO5 200
11.6 Independence model Mo 203
11.7 Independence model Mn 205
11.8 Independence model M/2 206
11.9 Independence model M/3 206
11.10 Independence models M/4 and M I4 207
11.11 Independence model MI5 207
11.12 Independence model M/6 207
11.13 Independence model M/7 208
11.14 Independence model Ms 208
11.15 Independence models Mcx , Mc2 and Mc3 208
|
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| author_facet | Schutz, John W. |
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| dewey-ones | 516 - Geometry |
| dewey-raw | 516.374 |
| dewey-search | 516.374 |
| dewey-sort | 3516.374 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| isbn | 0582317606 |
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| publishDate | 1997 |
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| series | Pitman research notes in mathematics series |
| series2 | Pitman research notes in mathematics series |
| spelling | Schutz, John W. Verfasser aut Independent axioms for Minkowski space-time John W. Schutz Harlow Longman 1997 241 S. txt rdacontent n rdamedia nc rdacarrier Pitman research notes in mathematics series 373 Pitman research notes in mathematics series 373 (DE-604)BV000022845 373 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019642740&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schutz, John W. Independent axioms for Minkowski space-time Pitman research notes in mathematics series |
| title | Independent axioms for Minkowski space-time |
| title_auth | Independent axioms for Minkowski space-time |
| title_exact_search | Independent axioms for Minkowski space-time |
| title_full | Independent axioms for Minkowski space-time John W. Schutz |
| title_fullStr | Independent axioms for Minkowski space-time John W. Schutz |
| title_full_unstemmed | Independent axioms for Minkowski space-time John W. Schutz |
| title_short | Independent axioms for Minkowski space-time |
| title_sort | independent axioms for minkowski space time |
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