Cassirer’s Functional-Based Approach in the Reconstruction of the Early Quantum Theory
Keywords:
Functional-based approach, Neo-kantism, Planck, Einstein, Bohr
Abstract
I propose a rational reconstruction of the early quantum theory (1900-1913) in terms of the ideas presented by Ernst Cassirer. Specifically, I propose to reconsider the early quantum theory through the lens of the method of conceptual functionalization that Ernst Cassirer laid down in his Substance and Function (1910) and he later refined in Determinism and Indeterminism in Modern Physics (1937). Following Cassirer’s functional interpretation of natural sciences, it is my primary concern to reconsider the conceptual evolution of Planck’s quantum of action from 1900 to 1913. In this regard, I shall emphasize the importance of the quantum of action (Planck’s constant) in the architectonic structure of the early quantum theory, in the role of an element of fundamental continuity between the first quantum theory and the formulation by Niels Bohr of the first atomic theory.
References
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Boltzmann, Ludwig (1877). “Über die Beziehung zwischen dem zweiten Hauptsatze der mechanischen Wärmetheorie und der Wahrscheinlichkeitsrechnung, 20 espective den Sätzen über das Wärmegleichgewicht”, Sitz.ber. Akad. Wiss. (Wien) 76, pp. 373-435 (submitted to the meeting of 11 October 1877); reprinted in Wissenschftliche Abhandlungen II, pp. 164-223.
Cassirer, Ernst (1937). Determinismus und Indeterminismus in der modernen Physik: Historische und systematische Studien zum Kausalproblem. Göteborgs Högskolas Årsskrift, Bd. 42, No.3. Reprinted in Ernst Cassirer, Zur modernen Physik. Darmstadt: Wissenschaftliche Buchgesellschaft, 1957, pp.127-376. English translation by O. T. Benfey, Determinism and Indeterminism in modern Physics: Historical and Systematic Studies of the Problem of Causality. With a Preface by Henry Margenau. New Haven: Yale University Press, 1956.
Cassirer, Ernst (1957). The Philosophy of Symbolic Forms, Vol. 3: The Phenomenology of Knowledge. Yale University Press.
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Darrigol, Olivier (2000). “Continuities and discontinuities in Planck’s Akt der Verzweiflung”, Ann. d. Phys., 9: pp. 951-960. https://doi.org/10.1002/1521-3889(200011)9:11/12<951::AID-ANDP951>3.0.CO;2-W
Darrigol, Olivier (1992). From c-numbers to q-numbers. The Classical Analogy in the History of Quantum Theory. Berkeley: University of California Press.
Darrigol, Olivier (1991). “Statistics and Combinatorics in Early Quantum Theory, II: Early Symptoma of Indistinguishability and Holism”, Studies in History and Philosophy of Biological Sciences, 21 (2), pp. 237- 298. https://doi.org/10.2307/27757664
Dirichlet, Peter Gustav Lejeune (1837). “Über die Darstellung ganz willkiirliche Funktionen durch Sinus- und Cosinusreihen”, reprinted in L. Kronecker (hg.), Gesammelte Werke, Bd. I., Berlin, 1889, pp. 133-160.
Dulong, Pierre Louis and Petit, Alexis-Thérèse (1819). “Sur quelques points importants de la théorie de la chaleur”, Ann. Chim. et Phys., 10, pp. 395-413.
Ehrenfest, Paul (1906). “Zur Planckschen Strahlungstheorie”, Phys. Zs., 7, pp. 528-532.
Einstein, Albert (1916). “Strahlungs-Emission und –Absorption nach der Quantentheorie”, Deutsche Physikalische Gesellschaft, Verhandlungen, 18, pp. 318–323.
Einstein, Albert (1909). “Zum gegenwärtigen Stand des Strahlungsproblems”, Phys. Zs., 10, 185-193.
Einstein, Albert (1906a). “Die Plancksche Theorie der Strahlung und die Theorie der spezifischen Wärme”, Ann. d. Phys., 22, pp. 180-190.
Einstein, Albert (1906b). “Zur Theorie der Lichterzeugung und Lichtabsorption “, Ann. d. Phys., 20, pp. 199-206. https://doi.org/10.1002/andp.19063250613
Einstein, Albert (1905). “Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt”, Ann. d. Phys. 17, pp. 132-148. English transl. in H. A. Boorse and L. Motz (Ed.), The World of the Atom, Vol. 1. Oxford: Pergamon, 1966, pp. 544-557.
Friedman, Michael (2016). “Ernst Cassirer”, The Stanford Encyclopedia of Philosophy (Fall 2016 Edition), Edward N. Zalta (ed.), URL =
Friedman, Michael (2000). A Parting of the Ways. Carnap, Cassirer, and Heidegger. Chicago: Open Court Publishing.
Kant, Immanuel (1781). Critique of Pure Reason. P. Guyer and A. Wood (transl.), P. Guyer (Ed.). Cambridge University Press, 1998.
Klein, Martin J. (1962). “Max Planck and the Beginnings of the Quantum Theory”, Archive for History of Exact Sciences, Vol. 1, n. 5, pp. 459-479. https://doi.org/10.1007/BF00327765
Kuhn, Thomas Samuel (1978). Black-Body Theory and the Quantum Discontinuity, 1894-1912. Oxford: Oxford University Press.
Jammer, Max (1966). The Conceptual Development of Quantum Mechanics. New York: MacGraw-Hill.
Mormann, Thomas (2015). “Mathematics to Quantum Mechanics On the Conceptual Unity of Cassirer’s Philosophy of Science (1907-1937)”. In T.J. Friedman and S. Luft (Eds.), The Philosophy of Ernst Cassirer: A Novel Assessment (pp. 31-63). Berlin/Boston: De Gruyter. https://doi.org/10.1515/9783110421811-003
Nernst, Walther and Lindemann, Frederick A. (1911). “Spezifische Wärme und Quantentheorie”, Zeitsch. f. Elektrochemie, 17, pp. 817-827.
Pais, Abraham (1982). Subtle is the Lord. The science and the life of Albert Einstein. Oxford and New York: Oxford University Press.
Planck, Max (1910). “Zur Theorie der Wärmestrahlung”, in Physikalische Abhandlungen und Vorträge, Braunschweig, Vieweg, 1958, vol. II, pp. 237-247.
Planck, Max (1906). Vorlesungen über die Theorie der Wärmestrahlung, 1st ed. Leipzig: Barth.
Planck, Max (1900). “Zur Theorie des Gesetzes der Energieverteilung im Normalspectrum”, Verh. d. D. Phys. Ges., 2, pp. 237-245, presented 14 December 1900. English transl. Ter Haar 1967 and Kangro 1972.
Rosenfeld, Leon and Rud Nielsen, Jens (eds.) (1976). Niels Bohr Collected Works, Vol. 3: The Correspondence Principle, 1918-1923. Amsterdam: North-Holland Publishing Company.
Ryckman, Thomas (2015). “A Retrospective View of Determinism and Indeterminism in Modern Physics”. In T.J. Friedman and S. Luft (Eds.), The Philosophy of Ernst Cassirer: A Novel Assessment (pp. 65-102). Berlin/Boston: De Gruyter. https://doi.org/10.1515/9783110421811-004
Ryckman, Thomas (1991). “Conditio Sine Qua Non? Zuordnung in the Early Epistemologies of Cassirer and Schlick”, Synthese, 88, pp. 57-95. https://doi.org/10.1007/BF00540093
Stark, Johannes (1908). “Zur Energetik und Chemie der Bandenspektra”, Phys Zs., 9, pp. 85-94.
Stark, Johannes (1907). “Beziehung des Doppler-Effektes bei Kanaldstrahlen zur Planckschen Strahlungstherorie”, Phys. Zs., 8, pp. 913-919.
Stark, Johannes and Steubing, Wilhelm (1908). “Fluoreszenz und lichtelektrische Empfindlichkeit organischer Substanzen”, Phys. Zs., 9, pp. 481-495.
Sundaram, K. (1972). “Kant or Cassirer: A Study in Complementarity”, Journal for General Philosophy of Science, 3 (1): pp. 40-48.
Boltzmann, Ludwig (1877). “Über die Beziehung zwischen dem zweiten Hauptsatze der mechanischen Wärmetheorie und der Wahrscheinlichkeitsrechnung, 20 espective den Sätzen über das Wärmegleichgewicht”, Sitz.ber. Akad. Wiss. (Wien) 76, pp. 373-435 (submitted to the meeting of 11 October 1877); reprinted in Wissenschftliche Abhandlungen II, pp. 164-223.
Cassirer, Ernst (1937). Determinismus und Indeterminismus in der modernen Physik: Historische und systematische Studien zum Kausalproblem. Göteborgs Högskolas Årsskrift, Bd. 42, No.3. Reprinted in Ernst Cassirer, Zur modernen Physik. Darmstadt: Wissenschaftliche Buchgesellschaft, 1957, pp.127-376. English translation by O. T. Benfey, Determinism and Indeterminism in modern Physics: Historical and Systematic Studies of the Problem of Causality. With a Preface by Henry Margenau. New Haven: Yale University Press, 1956.
Cassirer, Ernst (1957). The Philosophy of Symbolic Forms, Vol. 3: The Phenomenology of Knowledge. Yale University Press.
Cassirer, Ernst (1910). Substanzbegriff und Funktionsbegriff; Untersuchungengiberdie Grundfragen der Erkenntniskritik, B. Cassirer, Berlin. English translation by William Curtis Swabey and Marie Collins Swabey, Substance and Function and Einstein’s Theory of Relativity. Chicago-London: The Open Court Publishing Company, 1923.
Darrigol, Olivier (2000). “Continuities and discontinuities in Planck’s Akt der Verzweiflung”, Ann. d. Phys., 9: pp. 951-960. https://doi.org/10.1002/1521-3889(200011)9:11/12<951::AID-ANDP951>3.0.CO;2-W
Darrigol, Olivier (1992). From c-numbers to q-numbers. The Classical Analogy in the History of Quantum Theory. Berkeley: University of California Press.
Darrigol, Olivier (1991). “Statistics and Combinatorics in Early Quantum Theory, II: Early Symptoma of Indistinguishability and Holism”, Studies in History and Philosophy of Biological Sciences, 21 (2), pp. 237- 298. https://doi.org/10.2307/27757664
Dirichlet, Peter Gustav Lejeune (1837). “Über die Darstellung ganz willkiirliche Funktionen durch Sinus- und Cosinusreihen”, reprinted in L. Kronecker (hg.), Gesammelte Werke, Bd. I., Berlin, 1889, pp. 133-160.
Dulong, Pierre Louis and Petit, Alexis-Thérèse (1819). “Sur quelques points importants de la théorie de la chaleur”, Ann. Chim. et Phys., 10, pp. 395-413.
Ehrenfest, Paul (1906). “Zur Planckschen Strahlungstheorie”, Phys. Zs., 7, pp. 528-532.
Einstein, Albert (1916). “Strahlungs-Emission und –Absorption nach der Quantentheorie”, Deutsche Physikalische Gesellschaft, Verhandlungen, 18, pp. 318–323.
Einstein, Albert (1909). “Zum gegenwärtigen Stand des Strahlungsproblems”, Phys. Zs., 10, 185-193.
Einstein, Albert (1906a). “Die Plancksche Theorie der Strahlung und die Theorie der spezifischen Wärme”, Ann. d. Phys., 22, pp. 180-190.
Einstein, Albert (1906b). “Zur Theorie der Lichterzeugung und Lichtabsorption “, Ann. d. Phys., 20, pp. 199-206. https://doi.org/10.1002/andp.19063250613
Einstein, Albert (1905). “Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt”, Ann. d. Phys. 17, pp. 132-148. English transl. in H. A. Boorse and L. Motz (Ed.), The World of the Atom, Vol. 1. Oxford: Pergamon, 1966, pp. 544-557.
Friedman, Michael (2016). “Ernst Cassirer”, The Stanford Encyclopedia of Philosophy (Fall 2016 Edition), Edward N. Zalta (ed.), URL =
Friedman, Michael (2000). A Parting of the Ways. Carnap, Cassirer, and Heidegger. Chicago: Open Court Publishing.
Kant, Immanuel (1781). Critique of Pure Reason. P. Guyer and A. Wood (transl.), P. Guyer (Ed.). Cambridge University Press, 1998.
Klein, Martin J. (1962). “Max Planck and the Beginnings of the Quantum Theory”, Archive for History of Exact Sciences, Vol. 1, n. 5, pp. 459-479. https://doi.org/10.1007/BF00327765
Kuhn, Thomas Samuel (1978). Black-Body Theory and the Quantum Discontinuity, 1894-1912. Oxford: Oxford University Press.
Jammer, Max (1966). The Conceptual Development of Quantum Mechanics. New York: MacGraw-Hill.
Mormann, Thomas (2015). “Mathematics to Quantum Mechanics On the Conceptual Unity of Cassirer’s Philosophy of Science (1907-1937)”. In T.J. Friedman and S. Luft (Eds.), The Philosophy of Ernst Cassirer: A Novel Assessment (pp. 31-63). Berlin/Boston: De Gruyter. https://doi.org/10.1515/9783110421811-003
Nernst, Walther and Lindemann, Frederick A. (1911). “Spezifische Wärme und Quantentheorie”, Zeitsch. f. Elektrochemie, 17, pp. 817-827.
Pais, Abraham (1982). Subtle is the Lord. The science and the life of Albert Einstein. Oxford and New York: Oxford University Press.
Planck, Max (1910). “Zur Theorie der Wärmestrahlung”, in Physikalische Abhandlungen und Vorträge, Braunschweig, Vieweg, 1958, vol. II, pp. 237-247.
Planck, Max (1906). Vorlesungen über die Theorie der Wärmestrahlung, 1st ed. Leipzig: Barth.
Planck, Max (1900). “Zur Theorie des Gesetzes der Energieverteilung im Normalspectrum”, Verh. d. D. Phys. Ges., 2, pp. 237-245, presented 14 December 1900. English transl. Ter Haar 1967 and Kangro 1972.
Rosenfeld, Leon and Rud Nielsen, Jens (eds.) (1976). Niels Bohr Collected Works, Vol. 3: The Correspondence Principle, 1918-1923. Amsterdam: North-Holland Publishing Company.
Ryckman, Thomas (2015). “A Retrospective View of Determinism and Indeterminism in Modern Physics”. In T.J. Friedman and S. Luft (Eds.), The Philosophy of Ernst Cassirer: A Novel Assessment (pp. 65-102). Berlin/Boston: De Gruyter. https://doi.org/10.1515/9783110421811-004
Ryckman, Thomas (1991). “Conditio Sine Qua Non? Zuordnung in the Early Epistemologies of Cassirer and Schlick”, Synthese, 88, pp. 57-95. https://doi.org/10.1007/BF00540093
Stark, Johannes (1908). “Zur Energetik und Chemie der Bandenspektra”, Phys Zs., 9, pp. 85-94.
Stark, Johannes (1907). “Beziehung des Doppler-Effektes bei Kanaldstrahlen zur Planckschen Strahlungstherorie”, Phys. Zs., 8, pp. 913-919.
Stark, Johannes and Steubing, Wilhelm (1908). “Fluoreszenz und lichtelektrische Empfindlichkeit organischer Substanzen”, Phys. Zs., 9, pp. 481-495.
Sundaram, K. (1972). “Kant or Cassirer: A Study in Complementarity”, Journal for General Philosophy of Science, 3 (1): pp. 40-48.
Published
2018-12-31
How to Cite
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Angeloni, R. 2018. Cassirer’s Functional-Based Approach in the Reconstruction of the Early Quantum Theory. Disputatio. 7, 8 (Dec. 2018), a012. DOI:https://doi.org/10.5281/zenodo.2552851.
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