Interactions: Mathematics, Physics and Philosophy, 1860–1930

344 Pages·2006·2.63 MB·English

by  David Hyder (auth.)

INTERACTIONS
BOSTON STUDIES IN THE PHILOSOPHY OF SCIENCE
Editors
ROBERT S. COHEN. Boston University
JÜRGEN RENN. Max-Planck-Institute for the History of Science
KOSTAS GAVROGLU, University of Athens
Editorial Advisory Board
THOMAS F. GLICK, Boston University
ADOLF GRÜNBAUM, University of Pittsburgh
SYLVAN S. SCHWEBER, Brandeis University
JOHN H. STACHEL, Boston University
MARX W. WARTOFSKY†, (Editor 1960–1997)
VOLUME 251
INTERACTIONS
Mathematics, Physics and
Philosophy, 1860-1930
Edited by
VINCENT F. HENDRICKS
Department of Philosophy and Science Studies,
Roskilde University, Denmark
KLAUS FROVIN JØRGENSEN
Department of Philosophy and Science Studies,
Roskilde University, Denmark
JESPER LÜTZEN
Institute for Mathematical Sciences,
University of Copenhagen, Denmark
and
STIG ANDUR PEDERSEN
Department of Philosophy and Science Studies,
Roskilde University, Denmark
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN-10 1-4020-5194-8 (HB)
ISBN-13 978-1-4020-5194-4 (HB)
ISBN-10 1-4020-5195-6 (e-book)
ISBN-13 978-1-4020-5195-1 (e-book)
Published by Springer,
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© 2006 Springer
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REVIEWS
This stimulating volume covers a wide range of topics which are of direct
interest to anyone who thinks about the curious relation between mathemat-
ics and the natural world. Philosophers often pose interesting questions about
the “dispensability” of mathematics to science. But they too often overlook
the wealth of philosophical perplexities that can arise in detailed examples
and case studies, both contemporary and historical. This volume refocuses
our attention by addressing a number of topics connected to applied mathe-
matics, any one of which is worthy of every philosopherís attention.
—James Robert Brown, University of Toronto
What to make of neo-Kantianism in its hey-day, from 1840–1940? It was the
most prolific of times and the most seminal, it was the most muddled and
confused, it is philosophy working at its hardest with science and most dam-
agingly against science.
It is examined here episodically, as it engaged individual scientists:
Helmholtz, Hertz, Poincare, Minkowski, Hilbert, Eddington and Weyl. If
Einstein is not in their number, he had to contend with their influence, and
anyway he transformed their agenda. The essays on these figures are glinting
in their focus and scholarship. Whatever one thinks of neo-Kantianism, this
book is history and philosophy of science at its best: mathematically and
physically informed, historically engaged, and philosophically driven.
—Simon Saunders, University of Oxford
Ten first-rate philosopher-historians probe insightfully into key conceptual
questions of pre-quantum mathematical physics, from Helmholtz and
Boltzmann, through Hertz and Lorentz, to Einstein, Weyl and Eddington,
with an interesting aside on the rarely studied philosophy of Federigo
Enriques. A rich and effective display of what the critical history of science
can do for our understanding of scientific thought and its achievements.
—Roberto Torretti, University of Puerto Rico
CONTENTS
Preface ........................................................... xi
Contributing Authors.............................................. xiii
DAVID HYDER/Kant, Helmholtz and the Determinacy of Physical
Theory............................................................ 1
Abstract ....................................................... 1
Introduction ................................................... 1
1. Helmholtz’s ProofoftheCentralityofForces ................... 3
2. TheKo¨nigsberg Connection ................................. 15
3. Helmholtz’s LaterCriticismsofhisDeterminacyArgument ..... 28
4. EmpiricalDeterminacyandGeometry ........................ 32
5. Conclusion ................................................. 36
Notes ........................................................ 39
References ................................................... 42
JESPER LU¨TZEN / A Mechanical Image: Heinrich Hertz’s Principles of
Mechanics ....................................................... 45
1. Introduction ................................................ 45
2. AStrugglewithMechanics .................................. 45
3. WhyTheoretical ResearchonMechanics? .................... 46
4. Hertz’sMechanicalSystems ................................. 53
5. Hertz’sImageTheory ....................................... 53
6. Images,Colorless Theories,andtheGayGarment .............. 55
7. Conclusion ................................................. 61
8. Postscript aboutPhilosophy, PhysicsandMathematics .......... 61
Notes ........................................................ 62
References ................................................... 62
MICHELJANSSENANDMATTHEWMECKLENBURG/FromClassical
toRelativistic Mechanics: Electromagnetic ModelsoftheElectron .... 65
1. Introduction ................................................ 65
2. Energy-Momentum-Mass-Velocity Relations .................. 68
3. Lorentz’sTheoremofCorresponding States,theGeneralized
Contraction Hypothesis, andtheVelocityDependence
ofElectronMass ........................................... 75
4. Electromagnetic Energy,Momentum,andMassofaMoving
vii
viii CONTENTS
Electron ................................................... 80
5. Poincare´ Pressure ........................................... 90
6. TheRelativistic TreatmentoftheElectronModelofLorentzas
AmendedbyPoincare´ ....................................... 99
7. FromtheElectromagnetic ViewofNaturetoRelativistic
Continuum Mechanics ..................................... 105
Notes ....................................................... 115
References .................................................. 123
JEREMYGRAY/Enriques: Popularising ScienceandtheProblemsof
Geometry ...................................................... 135
Abstract ..................................................... 135
1. Introduction ............................................... 135
2. Enriques’ ProblemsofScience .............................. 139
3. EnriquesasaPhilosopher .................................. 144
4. TheAmericanReception ................................... 148
5. Conclusion ................................................ 149
Notes ....................................................... 150
References .................................................. 151
ULRICH MAJER / Hilbert’s Axiomatic Approach to the Foundations of
Science—aFailedResearchProgram? ............................. 155
1. Introduction ............................................... 155
2. Hilbert’sAxiomaticPointofViewandtheFoundations
ofGeometry .............................................. 156
3. Hilbert’sWorkinPhysicsBetween1900and1930 ............ 162
4. Hilbert’s‘Silent’PeriodFrom1898to1911 .................. 163
5. Hilbert’sMostEffectivePeriodsinPhysics ................... 171
6. TheLegitimacyofanAxiomaticPointofViewinScience ..... 174
Notes ....................................................... 177
References .................................................. 181
HELMUT PULTE / The Space between Helmholtz and Einstein: Moritz
SchlickonSpatialIntuition andtheFoundations ofGeometry ........ 185
1. Biographical Introduction .................................. 185
2. Schlick’sBasicEpistemological Problem: Intuition, Evidenceand
CertaintyofKnowledge .................................... 187
CONTENTS ix
3. Intuitive SpacesandConceptual Space: Einstein’sGeneralTheory
andSchlick’sReception .................................... 194
4. SpatialIntuition andtheProcessofConceptualization:
Schlick’sCriticism ofHelmholtz’sApproach ................. 197
5. Concluding Remark ........................................ 200
Notes ....................................................... 200
References .................................................. 202
ROBERT DISALLE / Mathematical Structure, “World Structure,” and the
Philosophical Turning-point inModernPhysics ..................... 207
1. Introduction ............................................... 207
2. Theproblem ofInterpretation inHistoricalPerspective ........ 208
3. Relativityand“World-structure” ............................ 213
4. Conclusion ................................................ 226
Notes ....................................................... 227
References .................................................. 227
DAVID E. ROWE / Einstein’s Allies and Enemies: Debating Relativity in
Germany,1916–1920 ............................................ 231
1. PublicityandFame ........................................ 232
2. ArnoldBerliner’sDieNaturwissenschaften ................... 235
3. ErnstGehrckeandtheRootsoftheAnti-Relativist Movement .. 242
4. Einstein’s “DialogueonArgumentsagainstRelativityTheory” . 248
5. TheAnti-Relativity Campaignof1920 ....................... 251
6. TheLenard-Einstein DebateinBadNauheim ................. 257
7. OnRelativityinWeimarGermany ........................... 263
8. Appendix ................................................. 266
Notes ....................................................... 267
References .................................................. 271
ERHARDSCHOLZ/TheChangingConceptofMatterinH.Weyl’sThought,
1918–1930 ...................................................... 281
Abstract ..................................................... 281
1. Introduction ............................................... 281
2. Adherence toMie’sDynamisticApproachtoMatter .......... 283
3. AGeometricalExtensionofMie’sTheory ................... 287
4. BreakwithMie’sTheory ................................... 289
5. AShort-livedSingularity TheoryofMatter ................... 292
x CONTENTS
6. TheAgencyConceptofMatterasanOpenResearchField ..... 295
7. AViewBackin1930 ...................................... 297
8. Acknowledgment .......................................... 300
Notes ....................................................... 300
References .................................................. 302
LAWRENCESKLAR/WhyDoestheStandardMeasureWorkinStatistical
Mechanics? ..................................................... 307
1. TheFoundational ProbabilityPositandItsJustification ........ 307
2. Measuring theStirring-UpofaShiftWithoutIntroducing a
Measure .................................................. 310
3. InitialProbability OutofNon-StandardQuantumMechanics ... 311
4. Molecular RouletteWheelsandWeakAPrioriPosits ......... 314
5. Summary ................................................. 317
6. Suggested FurtherReading ................................. 318
Index .......................................................... 321