Laws of Nature

376 Pages·2005·3.078 MB·English

by  Prof. Dr. Peter Mittelstaedt, Prof. Dr. Paul A. Weingartner (auth.)

Laws ofNature
P. Mittelstaedt P.A. Weingartner
Laws of Nature
ABC
Prof.Dr.PeterMittelstaedt Prof.Dr.PaulA.Weingartner
InstitutfürTheoretischePhysik InstitutfürPhilosophie
UniversitätzuKöln UniversitätSalzburg
ZülpicherStr.77 Franziskanergasse1
50937Köln 5020Salzburg
Germany Austria
e-mail:[email protected] e-mail:[email protected]
LibraryofCongressControlNumber:2005927735
ISBN-10 3-540-24079-9 SpringerBerlinHeidelbergNewYork
ISBN-13 978-3-540-24079-2 SpringerBerlinHeidelbergNewYork
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Preface
Thisbookisnotatextbooktobecomeacquaintedwiththelawsofnature.An
elementaryknowledgeaboutlawsofnature,inparticularthelawsofphysics,is
presupposed.Thebookisratherintendedtoprovideaclarificationofconcepts
and properties of the laws of nature.
The authors would like to emphasise that this book has been developed –
created–asarealteamwork.Althoughthechapters(andinsomecasesparts
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
ofthefoundationalissuesdiscussedinthebook,theydidnotfeelitnecessary
to balance every viewpoint. Thus some individual and personal difference or
emphasis will still be recognisable from the chapters written by the different
authors. In this sense the authors feel specifically responsible for the chapters
asfollows:MittelstaedtforChaps.4,9.3,10,11.2,12,13andWeingartnerfor
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
argumentsproandcontra.Thenadetailedanswerisproposedwhichcontains
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). However the
main part of each chapter is not historical and the authors do not identify
themselves with a historical position. The main part of the chapters tries to
give some systematic answer to basic questions in the light of our knowledge
today. The method to begin with arguments pro and contra was chosen in
ordertostimulateandtodrawthereader’sattentionalsotospecificproblems
connected with the question of the chapter. Since the problems of the pros
and contras are not always central they are discussed and clarified in the
commentaries (answers) to the objections at the ends of the chapters; first
because these commentaries presuppose what has been said in the main part
ofthechapter;secondtheyarenotincludedinthemainpartofthechapterin
order not to distract. It has to be emphasised however that what is expressed
VI Preface
in the pros and contras is not the opinion of the authors. It is sometimes the
opinion of other scholars as shown by quotations. The opinion of the authors
is expressed in the main part of the chapters and in the commentary to the
objections.
Acknowledgements
The authors want to thank Ursula Stranzinger, Eva Stieringer and Beate
Neugebauerfortypingpartsofthemanuscript.FurtherthanksgotoSpringer,
especially to Professor Beiglb¨ock and his team, for the effective cooperation.
October 2004 Peter Mittelstaedt
Paul Weingartner
Contents
Introduction................................................... 1
Part I What is a Law of Nature?
1 Are there Laws of Nature at All?.......................... 5
1.1 Arguments Contra (Objections) ........................... 5
1.2 Argument Pro .......................................... 5
1.3 Proposed Answer........................................ 6
1.3.1 Wide Concept of Law.............................. 6
1.3.2 Clarification of the Concept “Law of Nature” ......... 6
1.3.3 Answer to the Question:
Are there Laws of Nature at All?.................... 10
1.4 Answer (Commentary) to the Objections ................... 11
2 Can the Laws of Nature be Genuine Laws? ................ 13
2.1 Arguments Contra....................................... 13
2.2 Arguments Pro.......................................... 14
2.3 Proposed Answer........................................ 14
2.3.1 Genuine Law ..................................... 14
2.3.2 Commentary to the Conditions G1–G8............... 15
2.4 Answer to the Arguments ................................ 25
3 Are the Laws of Logic Laws of Nature? .................... 27
3.1 Arguments Pro.......................................... 27
3.2 Arguments Contra....................................... 29
3.3 Proposed Answer........................................ 29
3.3.1 The Domain of Problems........................... 30
3.3.2 The Domain of Application......................... 31
3.3.3 The Proper Domain ............................... 37
VIII Contents
3.3.4 No Laws of Logic are Laws of Nature
and no Laws of Nature are Laws of Logic............. 41
3.4 Answer to the Objections................................. 42
4 Are the Laws of Mathematics Laws of Nature? ............ 49
4.1 Arithmetic ............................................. 50
4.1.1 Question: Is Arithmetic a priori Valid? ............... 50
4.1.2 Proposed Answer.................................. 52
4.1.3 Question: Is Arithmetic Valid in the Real World?...... 52
4.1.4 Final Answer ..................................... 53
4.1.5 Reservation....................................... 53
4.2 Geometry .............................................. 53
4.3 Probability ............................................. 56
4.4 Concluding Answer ...................................... 61
Part II Properties of Laws
5 Does Every Law of Nature Express
an Invariance (Symmetry)? ................................ 65
5.1 Introduction. Arguments Pro and Contra................... 65
5.2 What a Law Is .......................................... 68
5.2.1 Our Understanding of What a Law Is ................ 69
5.2.2 The Beginning of Time............................. 69
5.3 Invariance and Symmetry ................................ 71
5.3.1 Different Meanings of “Invariance”
and “Symmetry” and their Context.................. 71
5.3.2 Groups of Symmetries (Invariances) ................. 76
5.3.3 Symmetry and Symmetry-Breaking.................. 82
5.4 Laws, Constants, Symmetries: Answer
to the Objections........................................ 85
5.4.1 Selection of Parameters Entering Laws
(to Objection 5.1.1)................................ 85
5.4.2 Symmetrical Laws and Non-Symmetrical Phenomena
(to Objections 5.1.2 and 5.1.3) ...................... 88
5.4.3 Explicit Symmetry-Breaking (to Objections 5.1.4
and 5.1.5) ........................................ 91
5.4.4 Higher and Lower Symmetries
(to Objections 5.1.6 and 5.1.7) ...................... 92
6 Is Every Law of Nature Spacetime Invariant?.............. 95
6.1 Introduction. Arguments Pro and Contra................... 95
6.2 Concepts of Space and Time in History .................... 97
6.2.1 Some Highlights of the Concept of Space and Place.... 97
6.2.2 Some Highlights of the Concept of Time..............104
Contents IX
6.3 The Concept of Spacetime................................112
6.3.1 Coordinate System and Reference System ............112
6.3.2 Space: Space can be Understood in a Twofold Way ....113
6.3.3 Time: Time can be Understood in a Twofold Way .....114
6.4 Is Every Law of Nature Spacetime Invariant? ...............116
6.4.1 General Remarks on Invariance .....................116
6.4.2 Spacetime Invariance is Concerned
with Real Continuous Movements
of the Reference Frame.............................118
6.4.3 Invariance Under Internal Transformations ...........118
6.4.4 Invariance Under Inertial Movement .................119
6.4.5 Invariance Under Inertial Movement I:
Galilean Movement ................................120
6.4.6 Invariance Under Inertial Movement II:
Special Relativity .................................121
6.4.7 Invariance Under Arbitrary Spacetime
Transformations: General Relativity .................124
6.5 Reply to the Objections ..................................136
7 Dynamical and Statistical Laws............................141
7.1 Are all Laws of Nature Either Dynamical
or Statistical Laws?......................................141
7.1.1 Arguments Contra.................................141
7.1.2 Arguments Pro....................................142
7.1.3 Proposed Answer..................................142
7.1.4 Reply to the Objections............................143
7.2 Is One Type of Law Reducible to the Other?................145
7.2.1 Arguments Pro....................................145
7.2.2 Argument Contra .................................147
7.2.3 Proposed Answer..................................147
7.2.4 Answer to the Objections ..........................172
8 Laws, Boundary Conditions, and Constants of Nature .....175
8.1 Are Boundary Conditions Independent
of Laws of Nature? ......................................175
8.1.1 Arguments Contra and Pro .........................175
8.1.2 The Problem of the Separation
of Boundary Conditions and Constants from Laws
of Nature.........................................176
8.1.3 The Separation of Boundary Conditions
and Constants from Laws of Nature is Possible........177
8.1.4 Is the Separation into Laws
and Boundary Conditions Necessary? ................178
8.1.5 Classification of Different Kinds
of Boundary Conditions – The Propagation of Fields...178
X Contents
8.1.6 Are the Laws
of Nature Valid also in Other Universes which Differ
from Our Universe only with Respect
to Initial Conditions? ..............................181
8.1.7 Answer to the Objections ..........................185
8.2 Are the Constants of Nature Independent
of the Laws of Nature? ...................................185
8.2.1 Arguments Pro and Contra .........................186
8.2.2 Proposed Answer..................................187
8.2.3 Answer to the Objections ..........................196
9 Causality and Predictability ...............................199
9.1 Do all Laws of Nature Represent a Causal Relation? .........199
9.1.1 Aristotle .........................................199
9.1.2 Thomas Aquinas ..................................201
9.1.3 Leibniz...........................................202
9.1.4 Newton: Causes Interpreted as Forces................203
9.1.5 Newton, Lagrange, Laplace, Hamilton, Maxwell .......204
9.1.6 Hume............................................204
9.1.7 Kant.............................................205
9.1.8 von Helmholtz ....................................207
9.2 Proposed Answer – General Part: Properties
of the Causal Relation ...................................209
9.2.1 Logical Properties .................................210
9.2.2 Intrinsic Properties ................................217
9.2.3 Two Recent Views: Regularity and Counterfactuality ..226
9.2.4 Principles of Causality .............................230
9.2.5 Answer to the Objections ..........................234
9.3 Proposed Answer – Special Part: Causality
in Different Areas of Physics ..............................234
9.3.1 Causality in Classical Physics .......................235
9.3.2 Causality in Quantum Physics ......................246
9.4 Do all Laws of Nature Imply Predictability? ................254
9.4.1 Arguments Pro....................................254
9.4.2 Arguments Contra.................................255
9.4.3 Proposed Answer..................................255
9.4.4 Answer to the Objections ..........................264
10 Laws and Objects..........................................265
10.1 Are Objects of Experience Governed by Laws of Nature? .....265
10.1.1 Arguments Pro....................................265
10.1.2 Arguments Contra.................................267
10.1.3 Arguments Contra Hume’s Scepticism................267
10.1.4 Arguments Contra 10.1.3...........................268
10.2 Objects and Laws of Nature in Classical Physics.............269
Contents XI
10.2.1 The Constitution of Objects in Classical Physics ......269
10.3 The Constitution of Objects in Quantum Physics............275
10.3.1 What is a Quantum System? .......................275
10.3.2 Objects in Quantum Mechanics .....................276
10.3.3 Individual Quantum Systems .......................278
10.3.4 Proposed Answer to Question 10.1
for the Quantum World ............................279
11 Completeness and Reliability ..............................281
11.1 Can the Laws of Nature (Physics) be Complete?.............281
11.1.1 Arguments Pro....................................281
11.1.2 Arguments Contra.................................282
11.1.3 Proposed Answer..................................282
11.1.4 Answer to the Objections ..........................297
11.2 Are the Laws of Nature Reliable?..........................298
11.2.1 What does it Mean that a Law of Nature is Reliable? ..298
11.2.2 Arguments Contra – “How the Laws of Physics Lie” ...298
11.2.3 Answer to the Objections – What does it Mean
that a Law of Nature Holds?........................302
11.2.4 Summary.........................................304
Part III Why are Laws of Nature Valid?
12 Statistical Laws............................................309
12.1 General Preliminaries ....................................309
12.1.1 Regularity and Necessity ...........................309
12.1.2 Why are Laws of Nature Valid? .....................310
12.2 Are Statistical Laws Based on Individual Laws? .............312
12.3 Are there Statistical Laws
without Individual Laws?.................................313
12.3.1 Classical Statistics.................................314
12.3.2 Quantum Statistics ................................317
13 Quantum Logic ............................................329
13.1 Are the Laws of Quantum Logic Laws of Nature?............329
13.1.1 Arguments Pro – What is Quantum Logic? ...........329
13.1.2 Objections Against 13.1.1 ..........................333
13.1.3 Preliminary Answer ...............................338
13.2 Are the Laws of Quantum Logic a priori Valid? .............338
13.2.1 Arguments Pro – On the a priori Justification
of Quantum Logic .................................338
13.2.2 Objections Against 13.2.1 ..........................345
13.2.3 Answer to Question 13.2 ...........................346
13.3 Concluding Answer to Question 13.1.......................346