Laws of Nature

Front Cover
Springer Science & Business Media, Jul 6, 2005 - Science - 376 pages
Thisbook isnotatextbook tobecomeacquainted with thelaws ofnature. An elementaryknowledgeaboutlawsofnature,inparticularthelawsofphysics,is presupposed. Thebookisratherintendedtoprovideaclari?cationofconcepts and properties of the laws of nature. The authors would like to emphasise that this book has been developed – created – as a real teamwork. Although the chapters (and in some cases parts of the chapters) were originally written by one of the two authors, all of them were discussed thoroughly and in detail and have been revised and complemented afterwards. Even if both authors were in agreement on most of the foundational issues discussed in the book, they did not feel it necessary to balance every viewpoint. Thus some individual and personal di?erence or emphasis will still be recognisable from the chapters written by the di?erent authors. In this sense the authors feel speci?cally responsible for the chapters as follows: Mittelstaedt for Chaps. 4, 9. 3, 10, 11. 2, 12, 13 and Weingartner for Chaps. 1, 2, 3, 5, 7, 8. 2, 9. 2, 9. 4. The remaining parts are joint sections. Most of the chapters are formulated as questions and they begin with arguments pro and contra. Then a detailed answer is proposed which contains a systematic discussion of the question. This is the respective main part of the chapter. It sometimes begins with a survey of the problem by giving some important answers to it from history (cf. Chaps. 6 and 9).
 

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Contents

Are there Laws of Nature at All?
5
13 Proposed Answer
6
Are there Laws of Nature at All?
10
14 Answer Commentary to the Objections
11
Can the Laws of Nature be Genuine Laws?
13
22 Arguments Pro
14
232 Commentary to the Conditions G1G8
15
24 Answer to the Arguments
25
814 Is the Separation into Laws and Boundary Conditions Necessary?
178
816 Are the Laws of Nature Valid also in Other Universes which Differ from Our Universe only with Respect to Initial Conditions?
181
817 Answer to the Objections
185
821 Arguments Pro and Contra
186
822 Proposed Answer
187
823 Answer to the Objections
196
Causality and Predictability
199
912 Thomas Aquinas
201

Are the Laws of Logic Laws of Nature?
27
32 Arguments Contra
29
331 The Domain of Problems
30
332 The Domain of Application
31
333 The Proper Domain
37
334 No Laws of Logic are Laws of Nature and no Laws of Nature are Laws of Logic
41
34 Answer to the Objections
42
Are the Laws of Mathematics Laws of Nature?
49
41 Arithmetic
50
412 Proposed Answer
52
414 Final Answer
53
43 Probability
56
44 Concluding Answer
61
Properties of Laws
63
Does Every Law of Nature Express an Invariance Symmetry?
65
52 What a Law Is
68
521 Our Understanding of What a Law Is
69
53 Invariance and Symmetry
71
532 Groups of Symmetries Invariances
76
533 Symmetry and SymmetryBreaking
82
Answer to the Objections
85
542 Symmetrical Laws and NonSymmetrical Phenomena to Objections 512 and 513
88
543 Explicit SymmetryBreaking to Objections 514 and 515
91
544 Higher and Lower Symmetries to Objections 516 and 517
92
Is Every Law of Nature Spacetime Invariant?
95
62 Concepts of Space and Time in History
97
622 Some Highlights of the Concept of Time
104
63 The Concept of Spacetime
112
Space can be Understood in a Twofold Way
113
Time can be Understood in a Twofold Way
114
64 Is Every Law of Nature Spacetime Invariant?
116
642 Spacetime Invariance is Concerned with Real Continuous Movements of the Reference Frame
118
644 Invariance Under Inertial Movement
119
Galilean Movement
120
Special Relativity
121
General Relativity
124
65 Reply to the Objections
136
Dynamical and Statistical Laws
141
712 Arguments Pro
142
714 Reply to the Objections
143
72 Is One Type of Law Reducible to the Other?
145
722 Argument Contra
147
724 Answer to the Objections
172
Laws Boundary Conditions and Constants of Nature
175
812 The Problem of the Separation of Boundary Conditions and Constants from Laws of Nature
176
813 The Separation of Boundary Conditions and Constants from Laws of Nature is Possible
177
913 Leibniz
202
Causes Interpreted as Forces
203
915 Newton Lagrange Laplace Hamilton Maxwell
204
917 Kant
205
918 von Helmholtz
207
Properties of the Causal Relation
209
921 Logical Properties
210
922 Intrinsic Properties
217
Regularity and Counterfactuality
226
924 Principles of Causality
230
925 Answer to the Objections
234
931 Causality in Classical Physics
235
932 Causality in Quantum Physics
246
94 Do all Laws of Nature Imply Predictability?
254
942 Arguments Contra
255
944 Answer to the Objections
264
Laws and Objects
265
1012 Arguments Contra
267
1014 Arguments Contra 1013
268
102 Objects and Laws of Nature in Classical Physics
269
103 The Constitution of Objects in Quantum Physics
275
1032 Objects in Quantum Mechanics
276
1033 Individual Quantum Systems
278
1034 Proposed Answer to Question 101 for the Quantum World
279
Completeness and Reliability
281
1112 Arguments Contra
282
1114 Answer to the Objections
297
112 Are the Laws of Nature Reliable?
298
1123 Answer to the Objections What does it Mean that a Law of Nature Holds?
302
1124 Summary
304
Why are Laws of Nature Valid?
307
Statistical Laws
309
1212 Why are Laws of Nature Valid?
310
122 Are Statistical Laws Based on Individual Laws?
312
123 Are there Statistical Laws without Individual Laws?
313
1231 Classical Statistics
314
1232 Quantum Statistics
317
Quantum Logic
329
1312 Objections Against 1311
333
1313 Preliminary Answer
338
1322 Objections Against 1321
345
1323 Answer to Question 132
346
References
347
Index
369
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