## Laws of NatureThisbook 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

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 |

347 | |

369 | |

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### Common terms and phrases

according Arguments Aristotle arithmetic axioms causal causal relation cause Chap classical logic classical mechanics complete concept Concerning consequence constants of nature coordinate system covariance defined described discussed domain dynamical laws Einstein empirical entropy equation of motion example expressed finite formulated Galilean genuine laws Hence hold inertial systems initial conditions interpretation invariant with respect Kant large number lattice Lq law statement laws of logic laws of nature laws of physics laws of quantum Leibniz light cone Lorentz Lorentz transformation mathematics means measurement microstates Minkowski spacetime Mittelstaedt natural numbers Newton's objects observable orthomodular lattice parameters particle physical laws physical system predictability principle priori probability processes properties propositions quantum logic quantum mechanics question reason reference frame reference system relative frequency restricted satisfied Sect sense sequence space spacetime invariant special relativity statistical laws structure symmetry theory Thomas Aquinas tion trajectory transformations true universe valid values velocity

### References to this book

Particle Metaphysics: A Critical Account of Subatomic Reality Brigitte Falkenburg Limited preview - 2007 |