FN11) Thomas S. Kuhn, The Structure of Scientific Revolutions. 3rd edition (orig. 1962). University of Chicago Press, 1996, p. 1.
FN22) Oxford University Press, 2007. Gauge theories are theories with ‘local symmetries’, that is, theories that remain invariant under transformation of a variable quantity that is ‘local’ (‘infinitesimal’ would be more exact) in the sense that its value expressly depends on the space and time coordinates. The quantum field theories that comprise the so-called Standard Model of elementary particles – the current best understanding of the non-¬gravitational fundamental interaction – are quantized gauge theories, also known as Yang-Mills ¬theories.
FN33) I have in mind historical studies of physics by James Cushing, Mara Beller, John Heilbron, Sam Schweber, Arthur Miller, the Einstein Studies volumes, and others.
FN44) Steven Weinberg, “Effective Field Theories, Past and Future”, arXiv:0908.1964v1 [hep-th] 13 Aug 2009.
FN55) Kuhn, SSR “Postscript – 1969”, p. 206.
FN66) James Ladyman and Don Ross, Every Thing Must Go: Metaphysics Naturalized. Oxford University Press, 2007, p. 37.
FN77) “The Sentiment of Rationality”, in Selected Essays (Reprinted in William James; Writings 1878–1899, Library of America, 1992, p. 951).
FN88) “The philosophical significance of Bell’s inequalities, in my opinion, is that they permit a near decisive test of those world views which are contrary to quantum mechanics. Bell’s work made possible, therefore, some near decisive results in experimental metaphysics.” “Contextual Hidden Variable Theories and Bell’s Inequalities”, British Journal for the Philosophy of Science 35 (1984), pp. 25–45, p. 36.
FN99) “Die Grundlagen der allgemeinen Relativitätstheorie”, Annalen der Physik (Vierte Folge) 49, pp. 769–822; reprinted in The Collected Papers of Albert Einstein v.6, Princeton University Press, 1996, pp. 284–339, p. 287 and p. 291.
FN1010) Albert Einstein: Creator and Rebel. NY, Viking Press, 1972, p. 127.
FN1111) Katherine Brading and Thomas Ryckman, “Hilbert’s ‘Foundations of Physics’: Gravitation and Electromagnetism within the Axiomatic Method”, Studies in History and Philosophy of Modern Physics 39 (2009), 102–53.
FN1212) Harvey Brown and Katherine Brading, “General Covariance from the Perspective of Noether’s Theorems”, Diálogos 79 (Festschrift for Roberto Torretti), 59–86.
FN1313) “Einstein’s Search for General Covariance, 1912–1915”, in Don Howard and John Stachel (eds.), Einstein and the History of General Relativity (Einstein Studies, v.1). Birkhäuser, 1989, 63–100 (circulated privately since 1980).
FN1414) S.W. Hawking and G.F.R. Ellis, The Large Scale Structure of Space-Time. Cambridge University Press, 1973.
FN1515) For example, in the Heisenberg representation, wave functions are independent of time but operators are time-dependent; whereas in the Schrödinger representation the time-dependences are reversed. Heisenberg’s version, with its emphasis on manipulation of operators appears very different from the Schrödinger equation, which is a differential equation in configuration space. In any case, the two representations are equivalent for all empirical predictions.
FN1616) “Preface” to Many Worlds: Everett, Quantum Theory & Reality, edited by Simon Saunders, Jonathan Barrett, Adrian Kent, and David Wallace. Oxford University Press, 2010.
FN1717) Mathematical Foundations of Quantum Mechanics, translated from the German (1932) by Robert T. Beyer. Princeton University Press, 1955.
FN1818) “Thus with each succeeding observation (or interaction), the observer state ‘branches’ into a number of different states. Each branch represents a different outcome of the measurement and the corresponding eigenstate for the object-system state [our S – TR]. All branches exist simultaneously in the superposition after any given sequence of observations.” “ ‘Relative State’ Formulation of Quantum Mechanics”, Reviews of Modern Physics, 29 (1957), 454–62; p. 459.
FN1919) Everett himself had only the crudest idea of an observer in quantum mechanics: the observer is a “servomechanism” possessing a memory tape and capable of responding to its environment.
FN2020) “Quantum Mechanics for Cosmologists”, in John S. Bell, Speakable and Unspeakable in Quantum Mechanics. 2nd ed. Cambridge University Press, 2004, p. 136.
FN2121) See e.g., Craig Callender, “Taking Thermodynamics Too Seriously”, Studies in History and Philosophy of Modern Physics 32 (2001), 539–553; Lawrence Sklar, Physics and Chance: Philosophical Issues in the Foundations of Statistical Mechanics. Cambridge University Press, 1993.
FN2222) Quotations that follow are from John Earman and John Norton, “Exorcist XIV: The Wrath of Maxwell’s Demon. Part I”, Studies in History and Philosophy of Modern Physics 29 (1998), pp. 435–71.
FN2323) “A Discussion with Thomas S. Kuhn”, in James Conant and John Haugeland (eds.) The Road Since Structure: Philosophical Essays 1970–1993, with an Autobiographical Interview; Thomas S. Kuhn. University of Chicago Press, 2000, p. 311.
FN2424) Kuhn’s Black-Body Theory and the Quantum Discontinuity, 1894–1912 (University of Chicago Press, 1978) is a stellar example of such an internal history.