Cassirer and Dirac on the Symbolic Method in Quantum Mechanics: A Confluence of Opposites
DOI:
https://doi.org/10.15173/jhap.v6i3.3440Abstract
Determinismus und Indeterminismus in der modernen Physik (DI) is one of Cassirer’s least known and studied works, despite his own assessment as “one of his most important achievements” (Gawronsky 1949, 29). A prominent theme locates quantum mechanics as a yet further step of the tendency within physical theory towards the purely functional theory of the concept and functional characterization of objectivity. In this respect DI can be considered an “update”, like the earlier monograph Zur Einsteinschen Relativitätstheorie: Erkenntnistheoretische Betrachtungen (1921), to Substanzbegriff und Funktionsbegriff (1910), a seminal work considering only classical and pre-relativistic physics. But how does DI cohere with the three volumes of The Philosophy of Symbolic Forms (1923–29) providing a systematic survey of symbolic meanings in diverse aspects of culture, each with its own mode of “objectification” via self-created signs and images? Cassirer’s “phenomenology of cognition” via distinct types of symbolic form locates Dirac’s Principles of Quantum Mechanics (1930) as an exemplar within physical theory of purely symbolic thought, a realm of pure relations and their correlated meanings. In particular, Dirac’s characterization of the new notion of “physical state” in quantum mechanics by a “symbolic algebra of observables” severed from particular representations points to a limiting pole of the Bedeutungsfunktion, the third and highest mode of symbolic formation.References
Baker, Henry F., 1922–1925. Principles of Geometry, 6 vols. Cambridge: Cambridge University Press.
Bohr, Niels, 1928. “The Quantum Postulate and the Recent Development of Atomic Theory.” Nature 121: 580–90. Reprinted in Wheeler and Zurek (1981), pp. 87–126.
Bokulich, Alisa, 2004. “Open or Closed? Dirac, Heisenberg, and the Relation between Classical and Quantum Mechanics.” Studies in History and Philosophy of Modern Physics 35: 377–96.
———, 2008. “Paul Dirac and the Einstein-Bohr Debate.” Perspectives on Science 16: 103–14.
Born, Max, 1926. “Zur Quantenmechanik der Stoßvorgänge.” Zeitschrift für Physik 37: 863–67. Translated into English as “On the Quantum Mechanics of Collisions,” in Wheeler and Zurek (1981), pp. 52–55.
Born, Max and Pascual Jordan, 1925. “Zur Quantenmechanik.” Zeitschrift für Physik 34: 858–88.
Born, Max, Werner Heisenberg and Pascual Jordan, 1925. “Zur Quantenmechanik II.” Zeitschrift für Physik 35: 557–615. Translated into English in van der Waerden (1967), pp. 321–85.
Cassirer, Ernst, 1910. Substanzbegriff und Funktionsbegriff. Berlin: Bruno Cassirer.
———, 1921. Zur Einsteins’chen Relativitätstheorie: erkenntnistheoretische Betrachtungen. Berlin: Bruno Cassirer Verlag. Reprinted as Cassirer (2001). Translated as Einstein’s Theory of Relativity Considered from the Epistemological Standpoint. Chicago: Open Court, 1923; reprinted in Cassirer (1953), pp. 347–465.
———, 1923a. “Der Begriff der symbolischen Form im Aufbau der Geisteswissenschaften,” vol. I. Vorträge der Bibliothek Warburg 1: 11–39. Reprinted in Gesammelte Werke, Hamburg Ausgabe, vol. 16, Aufsätze und Kleine Schriften (1922–26), pp. 75–104. Hamburg: Felix Meiner Verlag, 2003.
———, 1923b. Philosophie der symbolischen Formen, part 1, Die Sprache. Berlin: Bruno Cassirer. Reprinted in Gesammelte Werke, Hamburg Ausgabe, vol. 11. Hamburg: Felix Meiner Verlag, 2001. Translated into English as Cassirer (1955).
———, 1925. Philosophie der symbolischen Formen, part 2, Das mythische Denken. Berlin: Bruno Cassirer. Reprinted in Gesammelte Werke, Hamburg Ausgabe, vol. 12. Hamburg: Felix Meiner Verlag, 2002. Translated into English as The Philosophy of Symbolic Forms, vol. 2, Mythical Thought. New Haven: Yale University Press, 1955.
———, 1927. “Das Symbolproblem und seine Stellung im System der Philosophie.” Zeitschrift für Ästhetik und allgemeine Kunstwissenschaft 21: 295–315. Reprinted in Gesammelte Werke, Hamburg Ausgabe, vol. 17, Aufsätze und Kleine Schriften (1927–1931), pp. 253–82. Hamburg: Felix Meiner Verlag, 2004.
———, 1929. Philosophie der symbolischen Formen, part 3, Phänomenologie der Erkenntnis. Berlin: Bruno Cassirer. Reprinted in Gesammelte Werke, Hamburg Ausgabe, vol. 13. Hamburg: Felix Meiner Verlag, 2002. Translated into English as Cassirer (1957).
———, 1936–1937. Determinismus und Indeterminismus in der modernen Physik. Historische und systematische Studien zum Kausalproblem. Göteborg: Göteborgs Högskolas Årsskrift/Elanders Boktryckeri Aktiebolag. Reprinted as Cassirer (2004). Translated into English as Cassirer (1956).
———, 1944. An Essay on Man. New Haven: Yale University Press.
———, 1945. “Reflections on the Concept of Group and the Theory of Perception.” In Symbol, Myth and Culture: Essays and Lectures of Ernst Cassirer 1935–1945, edited by D. Verene, pp. 271–91. New Haven: Yale University Press.
———, 1953. Substance and Function & Einstein’s Theory of Relativity. New York: Dover.
———, 1955. The Philosophy of Symbolic Forms, vol. 1, Language. New Haven: Yale University Press.
———, 1956. Determinism and Indeterminism in Modern Physics. Historical and Systematic Studies of the Problem of Causality. New Haven: Yale University Press.
———, 1957. The Philosophy of Symbolic Forms, vol. 3, Phenomenology of Knowledge. New Haven: Yale University Press.
———, 2001. Gesammelte Werke, Hamburg Ausgabe, vol. 10, Zur Einsteins’chen Relativitätstheorie: erkenntnistheoretische Betrachtungen. Hamburg: Felix Meiner Verlag.
———, 2004. Gesammelte Werke, Hamburg Ausgabe, vol. 19, Determinismus und Indeterminismus in der modernen Physik. Hamburg: Felix Meiner Verlag.
———, 2009. Nachgelassene Manuskripte und Texte, Hamburg Ausgabe, vol. 18, Ausgewählter wissenschaftlicher Briefwechsel, edited by K. C. Köhnke, J. M. Krois, and O. Schwemmer. Hamburg: Felix Meiner Verlag.
Cassirer, Toni, 1981. Mein Leben mit Ernst Cassirer. Hildesheim: Gerstenberg.
Darrigol, Olivier, 1992. From c-Numbers to q-Numbers: The Classical Analogy in the History of Quantum Theory. Berkeley and Los Angeles: University of California Press.
De la Madrid, Rafael, 2005. “The Role of the Rigged Hilbert Space in Quantum Mechanics,” arXiv:quant-ph/0502053v1.
Dirac, Paul Adrien Maurice, 1925. “The Fundamental Equations of Quantum Mechanics.” Proceedings of the Royal Society of London series A, 106: 642–53. Reprinted in Dirac (1995), pp. 67–78.
———, 1926. “The Physical Interpretation of Quantum Dynamics.” Proceedings of the Royal Society of London series A, 113: 621–41. Reprinted in Dirac (1995), pp. 207–29.
———, 1930. The Principles of Quantum Mechanics. Oxford: Oxford University Press.
———, 1939. “A New Notation for Quantum Mechanics.” Mathematical Proceedings of the Cambridge Philosophical Society 35: 416–18.
———, 1963. “The Evolution of the Physicist’s Picture of Nature.” Scientific American 208: 45–54. Reprinted in Mathematics in the Modern World: Readings from Scientific American, pp. 239–48. San Francisco and London: W. H. Freeman and Company, 1968.
———, 1973. “Relativity and Quantum Mechanics.” In The Past Decade in Particle Theory, edited by E. C. G. Sudarshan and Y. Ne’eman, pp. 747–72. London and New York: Gordon and Breach.
———, 1977. “Recollections of an Exciting Era.” In History of Twentieth Century Physics (Italian Physical Society, Proceedings of the International School of Physics ‘Enrico Fermi’, Course LVII), edited by C. Weiner, pp. 109–57. New York and London: Academic Press.
———, 1995. The Collected Works of P. A. M. Dirac 1923–1948, edited by R. H. Dalitz. Cambridge: Cambridge University Press.
Einstein, Albert, 1931. “Maxwell’s Influence on the Development of the Conception of Physical Reality.” In James Clerk Maxwell: A Commemoration Volume 1831–1931, pp. 66–74. Cambridge: Cambridge University Press.
Farmelo, Graham, 2009. The Strangest Man: The Hidden Life of Paul Dirac, Mystic of the Atom. New York: Basic Books.
Gawronsky, Dimitri, 1949. “Ernst Cassirer: His Life and Works.” In The Philosophy of Ernst Cassirer, edited by P. A. Schilpp, pp. 3–37. Evanston, IL: Northwestern University Press.
Gordon, Peter E., 2010. Continental Divide: Heidegger, Cassirer, Davos. Cambridge, MA: Harvard University Press.
Gottfried, Kurt, 2003. “P. A. M. Dirac and the Discovery of Quantum Mechanics,” arXiv:quant-ph/0302041v1.
Hamburg, Carl H., 1964. “A Cassirer-Heidegger Seminar.” Philosophy and Phenomenological Research 25: 208–22.
Heisenberg, Werner, 1925. “Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen.” Zeitschrift für Physik 33: 879–93. Translated into English as “Quantum-Theoretical Re-Interpretation of Kinematic and Mechanical Relations,” in van der Waerden (1967), pp. 261–76.
———, 1927. “Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik.” Zeitschrift für Physik 43: 172–98. Translated into English as “The Physical Content of Quantum Kinematics and Mechanics,” in Wheeler and Zurek (1981), pp. 60–84.
———, 1969. Der Teil und das Ganze. Gespräche im Umkreis der Atomphysik. Munich: R. Piper Verlag.
Hilbert, David, 1899. Grundlagen der Geometrie. Leipzig: Teubner. Reprinted in David Hilbert’s Lectures on the Foundations of Geometry 1891–1902, edited by M. Hallett and U. Majer, pp. 436–523. Berlin-Heidelberg: Springer, 2004.
Hodge, William Vallace Douglas, 1956. “Henry Frederick Baker.” Biographical Memoirs of Fellows of the Royal Society 2: 49–68.
Kant, Immanuel, 1998. Critique of Pure Reason, edited and translated by P. Guyer and A. Wood. Cambridge: Cambridge University Press.
Kragh, Helge, 1990. Dirac: A Scientific Biography. New York: Cambridge University Press.
———, 2013. “Paul Dirac and The Principles of Quantum Mechanics.” In Research and Pedagogy: A History of Quantum Physics Through its Textbooks, edited by M. Badino and J. Navarro, pp. 249–64. Berlin: Edition Open Access.
Krois, John, 2011. “The Priority of ‘Symbolism’ over Language in Cassirer’s Philosophy.” Synthese 179: 9–20.
Kuhn, Thomas, 1963. Interview with P. A. M. Dirac, Session II, 6 May 1963. American Institute of Physics; Oral History Interviews. https://www.aip.org/history-programs/niels-bohr-library/oral-histories/4575--2, accessed 27 December 2017.
Longair, Malcolm, 2013. Quantum Concepts in Physics. Cambridge: Cambridge University Press.
Mormann, Thomas, 2015. “Mathematics to Quantum Mechanics: On the Conceptual Unity of Cassirer’s Philosophy of Science (1907–1937).” In The Philosophy of Ernst Cassirer: A Novel Assessment, edited by J. T. Friedman and S. Luft, pp. 31–64. Berlin: De Gruyter.
O’Connor, John J. and Edmund F. Robertson, 2003. “Henry Frederick Baker.” In MacTutor History of Mathematics, University of St. Andrews, Scotland, http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Baker.html, accessed 28 December 2017.
Pashby, Thomas, 2012. “Dirac’s Prediction of the Positron: A Case Study for the Current Realism Debate.” Perspectives on Science 20: 440–74.
Russell, Bertrand, 1901. “Recent Work on the Principles of Mathematics.” International Monthly 4: 83–101. Reprinted in The Collected Papers of Bertrand Russell, vol. 3, edited by G. H. Moore, pp. 366–79. London: Routledge, 1993.
Schaffner, Kenneth, 1970. “Outlines of a Logic of Comparative Theory Evaluation with Special Attention to Pre- and Post-Relativistic Electrodynamics.” In Historical and Philosophical Perspectives on Science, edited by R. Steuwer, pp. 311–64. Minneapolis: University of Minnesota Press.
Scholz, Erhard, 2008. “Weyl Entering the ‘New’ Quantum Mechanical Discourse.” In HQ 1: Conference on the History of Quantum Physics, edited by C. Joas, C. Lehner and J. Renn, pp. 249–64. Berlin: Max Planck Institut für Wissenschaftsgeschichte.
Schrödinger, Erwin, 1926. “Über das Verhältnis der Heisenberg-Born-Jordanschen Quantenmechanik zu der meinen.” Annalen der Physik 79: 734–56. Translated into English in Collected Papers on Wave Mechanics, pp. 45–61. New York: Chelsea Publishing, 1982.
Van der Waerden, Bartel, ed., 1967. Sources of Quantum Mechanics. Amsterdam: North Holland.
Von Meyenn, Karl, ed., 1985. Wolfgang Pauli: Wissenschaftlicher Briefwechsel, vol. 2. Berlin: Springer-Verlag.
Von Neumann, John, 1927. “Mathematische Begründung der Quantenmechanik.” Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen 1927: 1–57. Reprinted in John von Neumann: Collected Works, vol. 1, edited by A. H. Taub, pp. 151–207. New York: Pergamon Press, 1961.
———, 1932. Mathematische Grundlagen der Quantenmechanik. Berlin: Springer.
Weyl, Hermann, 1928. Gruppentheorie und Quantenmechanik. Leipzig: Verlag von S. Hirzel.
Wheeler, John A. and Wojciech Zurek, eds., 1981. Quantum Theory and Measurement. Princeton: Princeton University Press.
Wilczek, Frank, 2002. “A Piece of Magic: The Dirac Equation.” In It Must be Beautiful: Great Equations of Modern Science, edited by G. Farmelo, pp. 132–60. London: Granta Publications.
Wright, Aaron, 2016. “A Beautiful Sea: P. A. M. Dirac’s Epistemology and Ontology of the Vacuum.” Annals of Science 73: 225–56.
Zalaletdinov, Roustam, Reza Tavakol and George F. Ellis, 1996. “On General and Restricted Covariance in General Relativity.” General Relativity and Gravitation 28: 1251–67.
Zalamea, Federico, 2016. Chasing Individuation: Mathematical Description of Physical Systems. Ph.D. Dissertation, Paris-Sorbonne University.
Bohr, Niels, 1928. “The Quantum Postulate and the Recent Development of Atomic Theory.” Nature 121: 580–90. Reprinted in Wheeler and Zurek (1981), pp. 87–126.
Bokulich, Alisa, 2004. “Open or Closed? Dirac, Heisenberg, and the Relation between Classical and Quantum Mechanics.” Studies in History and Philosophy of Modern Physics 35: 377–96.
———, 2008. “Paul Dirac and the Einstein-Bohr Debate.” Perspectives on Science 16: 103–14.
Born, Max, 1926. “Zur Quantenmechanik der Stoßvorgänge.” Zeitschrift für Physik 37: 863–67. Translated into English as “On the Quantum Mechanics of Collisions,” in Wheeler and Zurek (1981), pp. 52–55.
Born, Max and Pascual Jordan, 1925. “Zur Quantenmechanik.” Zeitschrift für Physik 34: 858–88.
Born, Max, Werner Heisenberg and Pascual Jordan, 1925. “Zur Quantenmechanik II.” Zeitschrift für Physik 35: 557–615. Translated into English in van der Waerden (1967), pp. 321–85.
Cassirer, Ernst, 1910. Substanzbegriff und Funktionsbegriff. Berlin: Bruno Cassirer.
———, 1921. Zur Einsteins’chen Relativitätstheorie: erkenntnistheoretische Betrachtungen. Berlin: Bruno Cassirer Verlag. Reprinted as Cassirer (2001). Translated as Einstein’s Theory of Relativity Considered from the Epistemological Standpoint. Chicago: Open Court, 1923; reprinted in Cassirer (1953), pp. 347–465.
———, 1923a. “Der Begriff der symbolischen Form im Aufbau der Geisteswissenschaften,” vol. I. Vorträge der Bibliothek Warburg 1: 11–39. Reprinted in Gesammelte Werke, Hamburg Ausgabe, vol. 16, Aufsätze und Kleine Schriften (1922–26), pp. 75–104. Hamburg: Felix Meiner Verlag, 2003.
———, 1923b. Philosophie der symbolischen Formen, part 1, Die Sprache. Berlin: Bruno Cassirer. Reprinted in Gesammelte Werke, Hamburg Ausgabe, vol. 11. Hamburg: Felix Meiner Verlag, 2001. Translated into English as Cassirer (1955).
———, 1925. Philosophie der symbolischen Formen, part 2, Das mythische Denken. Berlin: Bruno Cassirer. Reprinted in Gesammelte Werke, Hamburg Ausgabe, vol. 12. Hamburg: Felix Meiner Verlag, 2002. Translated into English as The Philosophy of Symbolic Forms, vol. 2, Mythical Thought. New Haven: Yale University Press, 1955.
———, 1927. “Das Symbolproblem und seine Stellung im System der Philosophie.” Zeitschrift für Ästhetik und allgemeine Kunstwissenschaft 21: 295–315. Reprinted in Gesammelte Werke, Hamburg Ausgabe, vol. 17, Aufsätze und Kleine Schriften (1927–1931), pp. 253–82. Hamburg: Felix Meiner Verlag, 2004.
———, 1929. Philosophie der symbolischen Formen, part 3, Phänomenologie der Erkenntnis. Berlin: Bruno Cassirer. Reprinted in Gesammelte Werke, Hamburg Ausgabe, vol. 13. Hamburg: Felix Meiner Verlag, 2002. Translated into English as Cassirer (1957).
———, 1936–1937. Determinismus und Indeterminismus in der modernen Physik. Historische und systematische Studien zum Kausalproblem. Göteborg: Göteborgs Högskolas Årsskrift/Elanders Boktryckeri Aktiebolag. Reprinted as Cassirer (2004). Translated into English as Cassirer (1956).
———, 1944. An Essay on Man. New Haven: Yale University Press.
———, 1945. “Reflections on the Concept of Group and the Theory of Perception.” In Symbol, Myth and Culture: Essays and Lectures of Ernst Cassirer 1935–1945, edited by D. Verene, pp. 271–91. New Haven: Yale University Press.
———, 1953. Substance and Function & Einstein’s Theory of Relativity. New York: Dover.
———, 1955. The Philosophy of Symbolic Forms, vol. 1, Language. New Haven: Yale University Press.
———, 1956. Determinism and Indeterminism in Modern Physics. Historical and Systematic Studies of the Problem of Causality. New Haven: Yale University Press.
———, 1957. The Philosophy of Symbolic Forms, vol. 3, Phenomenology of Knowledge. New Haven: Yale University Press.
———, 2001. Gesammelte Werke, Hamburg Ausgabe, vol. 10, Zur Einsteins’chen Relativitätstheorie: erkenntnistheoretische Betrachtungen. Hamburg: Felix Meiner Verlag.
———, 2004. Gesammelte Werke, Hamburg Ausgabe, vol. 19, Determinismus und Indeterminismus in der modernen Physik. Hamburg: Felix Meiner Verlag.
———, 2009. Nachgelassene Manuskripte und Texte, Hamburg Ausgabe, vol. 18, Ausgewählter wissenschaftlicher Briefwechsel, edited by K. C. Köhnke, J. M. Krois, and O. Schwemmer. Hamburg: Felix Meiner Verlag.
Cassirer, Toni, 1981. Mein Leben mit Ernst Cassirer. Hildesheim: Gerstenberg.
Darrigol, Olivier, 1992. From c-Numbers to q-Numbers: The Classical Analogy in the History of Quantum Theory. Berkeley and Los Angeles: University of California Press.
De la Madrid, Rafael, 2005. “The Role of the Rigged Hilbert Space in Quantum Mechanics,” arXiv:quant-ph/0502053v1.
Dirac, Paul Adrien Maurice, 1925. “The Fundamental Equations of Quantum Mechanics.” Proceedings of the Royal Society of London series A, 106: 642–53. Reprinted in Dirac (1995), pp. 67–78.
———, 1926. “The Physical Interpretation of Quantum Dynamics.” Proceedings of the Royal Society of London series A, 113: 621–41. Reprinted in Dirac (1995), pp. 207–29.
———, 1930. The Principles of Quantum Mechanics. Oxford: Oxford University Press.
———, 1939. “A New Notation for Quantum Mechanics.” Mathematical Proceedings of the Cambridge Philosophical Society 35: 416–18.
———, 1963. “The Evolution of the Physicist’s Picture of Nature.” Scientific American 208: 45–54. Reprinted in Mathematics in the Modern World: Readings from Scientific American, pp. 239–48. San Francisco and London: W. H. Freeman and Company, 1968.
———, 1973. “Relativity and Quantum Mechanics.” In The Past Decade in Particle Theory, edited by E. C. G. Sudarshan and Y. Ne’eman, pp. 747–72. London and New York: Gordon and Breach.
———, 1977. “Recollections of an Exciting Era.” In History of Twentieth Century Physics (Italian Physical Society, Proceedings of the International School of Physics ‘Enrico Fermi’, Course LVII), edited by C. Weiner, pp. 109–57. New York and London: Academic Press.
———, 1995. The Collected Works of P. A. M. Dirac 1923–1948, edited by R. H. Dalitz. Cambridge: Cambridge University Press.
Einstein, Albert, 1931. “Maxwell’s Influence on the Development of the Conception of Physical Reality.” In James Clerk Maxwell: A Commemoration Volume 1831–1931, pp. 66–74. Cambridge: Cambridge University Press.
Farmelo, Graham, 2009. The Strangest Man: The Hidden Life of Paul Dirac, Mystic of the Atom. New York: Basic Books.
Gawronsky, Dimitri, 1949. “Ernst Cassirer: His Life and Works.” In The Philosophy of Ernst Cassirer, edited by P. A. Schilpp, pp. 3–37. Evanston, IL: Northwestern University Press.
Gordon, Peter E., 2010. Continental Divide: Heidegger, Cassirer, Davos. Cambridge, MA: Harvard University Press.
Gottfried, Kurt, 2003. “P. A. M. Dirac and the Discovery of Quantum Mechanics,” arXiv:quant-ph/0302041v1.
Hamburg, Carl H., 1964. “A Cassirer-Heidegger Seminar.” Philosophy and Phenomenological Research 25: 208–22.
Heisenberg, Werner, 1925. “Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen.” Zeitschrift für Physik 33: 879–93. Translated into English as “Quantum-Theoretical Re-Interpretation of Kinematic and Mechanical Relations,” in van der Waerden (1967), pp. 261–76.
———, 1927. “Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik.” Zeitschrift für Physik 43: 172–98. Translated into English as “The Physical Content of Quantum Kinematics and Mechanics,” in Wheeler and Zurek (1981), pp. 60–84.
———, 1969. Der Teil und das Ganze. Gespräche im Umkreis der Atomphysik. Munich: R. Piper Verlag.
Hilbert, David, 1899. Grundlagen der Geometrie. Leipzig: Teubner. Reprinted in David Hilbert’s Lectures on the Foundations of Geometry 1891–1902, edited by M. Hallett and U. Majer, pp. 436–523. Berlin-Heidelberg: Springer, 2004.
Hodge, William Vallace Douglas, 1956. “Henry Frederick Baker.” Biographical Memoirs of Fellows of the Royal Society 2: 49–68.
Kant, Immanuel, 1998. Critique of Pure Reason, edited and translated by P. Guyer and A. Wood. Cambridge: Cambridge University Press.
Kragh, Helge, 1990. Dirac: A Scientific Biography. New York: Cambridge University Press.
———, 2013. “Paul Dirac and The Principles of Quantum Mechanics.” In Research and Pedagogy: A History of Quantum Physics Through its Textbooks, edited by M. Badino and J. Navarro, pp. 249–64. Berlin: Edition Open Access.
Krois, John, 2011. “The Priority of ‘Symbolism’ over Language in Cassirer’s Philosophy.” Synthese 179: 9–20.
Kuhn, Thomas, 1963. Interview with P. A. M. Dirac, Session II, 6 May 1963. American Institute of Physics; Oral History Interviews. https://www.aip.org/history-programs/niels-bohr-library/oral-histories/4575--2, accessed 27 December 2017.
Longair, Malcolm, 2013. Quantum Concepts in Physics. Cambridge: Cambridge University Press.
Mormann, Thomas, 2015. “Mathematics to Quantum Mechanics: On the Conceptual Unity of Cassirer’s Philosophy of Science (1907–1937).” In The Philosophy of Ernst Cassirer: A Novel Assessment, edited by J. T. Friedman and S. Luft, pp. 31–64. Berlin: De Gruyter.
O’Connor, John J. and Edmund F. Robertson, 2003. “Henry Frederick Baker.” In MacTutor History of Mathematics, University of St. Andrews, Scotland, http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Baker.html, accessed 28 December 2017.
Pashby, Thomas, 2012. “Dirac’s Prediction of the Positron: A Case Study for the Current Realism Debate.” Perspectives on Science 20: 440–74.
Russell, Bertrand, 1901. “Recent Work on the Principles of Mathematics.” International Monthly 4: 83–101. Reprinted in The Collected Papers of Bertrand Russell, vol. 3, edited by G. H. Moore, pp. 366–79. London: Routledge, 1993.
Schaffner, Kenneth, 1970. “Outlines of a Logic of Comparative Theory Evaluation with Special Attention to Pre- and Post-Relativistic Electrodynamics.” In Historical and Philosophical Perspectives on Science, edited by R. Steuwer, pp. 311–64. Minneapolis: University of Minnesota Press.
Scholz, Erhard, 2008. “Weyl Entering the ‘New’ Quantum Mechanical Discourse.” In HQ 1: Conference on the History of Quantum Physics, edited by C. Joas, C. Lehner and J. Renn, pp. 249–64. Berlin: Max Planck Institut für Wissenschaftsgeschichte.
Schrödinger, Erwin, 1926. “Über das Verhältnis der Heisenberg-Born-Jordanschen Quantenmechanik zu der meinen.” Annalen der Physik 79: 734–56. Translated into English in Collected Papers on Wave Mechanics, pp. 45–61. New York: Chelsea Publishing, 1982.
Van der Waerden, Bartel, ed., 1967. Sources of Quantum Mechanics. Amsterdam: North Holland.
Von Meyenn, Karl, ed., 1985. Wolfgang Pauli: Wissenschaftlicher Briefwechsel, vol. 2. Berlin: Springer-Verlag.
Von Neumann, John, 1927. “Mathematische Begründung der Quantenmechanik.” Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen 1927: 1–57. Reprinted in John von Neumann: Collected Works, vol. 1, edited by A. H. Taub, pp. 151–207. New York: Pergamon Press, 1961.
———, 1932. Mathematische Grundlagen der Quantenmechanik. Berlin: Springer.
Weyl, Hermann, 1928. Gruppentheorie und Quantenmechanik. Leipzig: Verlag von S. Hirzel.
Wheeler, John A. and Wojciech Zurek, eds., 1981. Quantum Theory and Measurement. Princeton: Princeton University Press.
Wilczek, Frank, 2002. “A Piece of Magic: The Dirac Equation.” In It Must be Beautiful: Great Equations of Modern Science, edited by G. Farmelo, pp. 132–60. London: Granta Publications.
Wright, Aaron, 2016. “A Beautiful Sea: P. A. M. Dirac’s Epistemology and Ontology of the Vacuum.” Annals of Science 73: 225–56.
Zalaletdinov, Roustam, Reza Tavakol and George F. Ellis, 1996. “On General and Restricted Covariance in General Relativity.” General Relativity and Gravitation 28: 1251–67.
Zalamea, Federico, 2016. Chasing Individuation: Mathematical Description of Physical Systems. Ph.D. Dissertation, Paris-Sorbonne University.
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