Reflections on the Practice of Physics: James Clerk Maxwell’s Methodological Odyssey in Electromagne

Methodology: framing scientific knowledgeAn overview of Maxwell’s approach to methodologyMaxwell’s initial publication of 1856 (an abstract)—placing methodology at the forefrontMethodology as an essential feature of scientific practice: the case of MaxwellThe argumentNotesMaxwell’s choice: Faraday vs. AmpèreMichael Faraday (1791–1867) and James Clerk Maxwell: a unique relationAndré-Marie Ampère (1775–1836): the contrastNotesThomson, Stokes, Rankine, and Thomson and TaitIntroduction: methodology in electromagnetismWilliam Thomson (1824–1907): from analogy to representationGeorge Stokes (1819–1903): idealizationWilliam J. M. Rankine (1820–1872): energy—a novel unifying conceptW. Thomson and Peter Tait (1831–1901): abstract dynamicsConclusionNotesStation 1 (1856–1858): On Faraday’s lines of forceA novel methodology: modifying the methodology of analogyThe structure of Maxwell’s argumentFrom the general to the specificConfronting Ampère’s theoryConclusionAppendix: a bibliographical note on Maxwell 1858NotesStation 2 (1861–1862): On physical lines of forceIntroductionPreliminary: from instrumentalism to causalityThe methodology: linking hypothesis to representationApplying the methodology: assumptions and their consequencesIII: a landmark in the history of physicsConclusionNotesStation 3 (1865): A dynamical theory of the electromagnetic fieldIntroductionI: marking the goal—the construction of a formal theory consisting of a set of general equationsII: the flywheel analogyHow does the analogy work?Illustration vs. analogyThe methodology of reversing the argumentIntermediate summaryA physical theory in symbolic languageAn example—the case of electric elasticityConclusionNotesStation 4 (1873): A treatise on electricity and magnetismIntroductionFrameworkNovel methodologiesEnergy as a key concept in electrodynamicsMathematical tools in the treatment of electrodynamicsDimensionality of unitsAnalogies, illustrations, and working models as mechanical representationsMental imageryThe impact of the new methodologies on the construction of the theoryThe electric displacement and the displacement currentGeneral equations of the electromagneticFrom mathematics to physics: vortices and mechanismConclusionNotesPhilosophical reflections on Maxwell’s methodological odysseyCommitmentModifications of methodologiesStation 1: analogyStation 2: hypothesisStation 3: textual descriptionStation 4: abstract dynamicsTransitions from one methodology to the nextMethodologies in Maxwell’s practiceThe role of mathematicsReciprocity of formulation: translationMental imageryAnalogyHypothesis: the micro-level and explanatory claimsModel and modelingConcluding remarksNotes
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