Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-20T04:10:04.009Z Has data issue: false hasContentIssue false
  • English
  • Français

Einstein, Cassirer, and General Covariance — Then and Now

Published online by Cambridge University Press:  26 September 2008

T. A. Ryckman
T. A. Ryckman
Affiliation:
University of California, Berkeley
Get access Rights & Permissions [Opens in a new window]

Abstract

Recent archival research has brought about a new understanding of the import of Einstein's puzzling remarks (1916) attributing a physical meaning to general covariance. Debates over the scope and meaning of general covariance still persist, even within physics. But already in 1921 Cassirer identified the significance of general covariance as a novel stage in the development of the criterion of objectivity within physics; an account of this development, and its implications, is the primary task undertaken in his monograph of “epistemological considerations” on the theory of relativity. Cassirer's assessment is correct: general covariance, understood as an injunction against dynamical theories with background elements, is a “limiting heuristic principle” guiding Einstein's fundamental conception of a “complete field theory”; as such, it underlies a “separation principle” built into the conceptual framework of the EPR criticism of quantum mechanics. In conclusion, a further parallel is noted: mutual recognition that the principle of general covariance is but a form of “anthropomorphism.”

Type
Article
Information
Science in Context , Volume 12 , Issue 4 , winter 1999 , pp. 585 - 619
Copyright
Copyright © Cambridge University Press 1999

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Anderson, John L. 1964. “Relativity Principles and the Role of Coordinates in Physics.” In Gravitation and Relativity, edited by Chiu, H. and Hoffman, W., 175–94. New York: W.A. Benjamin.Google Scholar
Auyang, Suny. 1995. How is Quantum Field Theory Possible? New York and London: Oxford University Press.CrossRefGoogle Scholar
Beller, Mara. n. d. “Kant's Impact on Einstein's Thought.” Manuscript. Hebrew University, Jerusalem.Google Scholar
Born, Max. 1971. The Born-Einstein Letters. New York: Walker.Google Scholar
Cassirer, Ernst. 1902. Leibniz' System in seinen wissenschaftlichen Grundlagen. Marburg: N. G. Elwert'sche Verlagsbuchhandlung.Google Scholar
Cassirer, Ernst. 1906. Das Erkenntnisproblem in der Philosophie und Wissenschaft der neueren Zeit I. Berlin: Bruno Cassirer.Google Scholar
Cassirer, Ernst. 1907. “Zur Frage nach der Methode der Erkenntniskritik: Eine Entgegnung.” Vierteljahrsschrift für wissenschaftliche Philosophie und Soziologie 31: 441–65.Google Scholar
Cassirer, Ernst. 1910. Substanzbegriff und Funktionsbegriff: Untersuchungen über der Grundfragen der Erkenntniskritik. Berlin: Bruno Cassirer.Google Scholar
Cassirer, Ernst. 1916. Freiheit und Form. Berlin: Bruno Cassirer.Google Scholar
Cassirer, Ernst. 1920. Das Erkenntnisproblem in der Philosophie und Wissenschaft der neueren Zeit III. Berlin: Bruno Cassirer.Google Scholar
Cassirer, Ernst. [1921] 1957. Zur Einsteinschen Relativitätstheorie. Berlin: Bruno Cassirer. In Cassirer 1957.Google Scholar
Cassirer, Ernst. 1921a. “Goethe und die mathematische Physik.” In Idee und Gestalt, 37–76. Berlin: Bruno Cassirer.Google Scholar
Cassirer, Ernst. [1923] 1953. Substance and Function and Einstein's Theory of Relativity. Cassirer 1910 and [1921] 1957. Translated by W., and Swabey, M.. New York: Dover.Google Scholar
Cassirer, Ernst. 1928. “Zur Theorie des Begriffs.” Kant-Studien 33: 129–36.CrossRefGoogle Scholar
Cassirer, Ernst. [1929] 1957. The Philosophy of Symbolic Forms 3. Translated by Manheim, R.. New Haven: Yale University Press. Originally published as Philosophie der Symbolische Formen III. Berlin: Bruno Cassirer.Google Scholar
Cassirer, Ernst. [1931] 1985. “Mythischer, Aesthetischer und Theoretischer Raum.” In Ernst Cassirer: Symbol, Technik, Sprache, edited by Orth, E. and Krois, J. M., 93–111. Hamburg: Felix Meiner. Originally published in Zeitschrift für Aesthetik und Allgemeine Kunstwissenschaft 25: 21–36.Google Scholar
Cassirer, Ernst. 1950. The Problem of Knowledge. New Haven: Yale University Press.Google Scholar
Cassirer, Ernst. [1957] 1994. Zur modernen Physik. Darmstadt: Wissenschaftliche Buchgesellschaft.Google Scholar
Cohen, Hermann. 1883. Das Princip der Infinitesimal Methode. Berlin: F. Dümmler.Google Scholar
Cohen, Herman. [1902] 1922. Logik der reinen Erkenntnis. Berlin: Bruno Cassirer.Google Scholar
Ciufolini, Ignazio, , and Wheeler, John Archibald. 1995. Gravitation and Inertia. Princeton: Princeton University Press.CrossRefGoogle Scholar
Cushing, James T., and McMullin, Ernan, eds. 1989. Philosophical Consequences of Quantum Theory: Reflections on Bell's Theorem. Notre Dame, Ind.: University of Notre Dame Press.Google Scholar
Dosch, H. G. 1991. “Renormalized Quantum Field Theory and Cassirer's Epistemological System.” Philosophia Naturalis 28: 97–114.Google Scholar
Earman, John, , and Glymour, Clark. 1978. “Lost in the Tensors: Einstein's Struggles with Covariance Principles, 1912–1916.” Studies in the History and Philosophy of Science 9: 251–78.CrossRefGoogle Scholar
Eddington, Arthur Stanley. 1920. Space, Time and Gravitation. Cambridge: Cambridge University Press.Google Scholar
Ehlers, Jürgen. 1995. “Machian Ideas and General Relativity.” In Mach's Principle; From Newton's Bucket to Quantum Gravity, edited by Barbour, J. and Pfister, H., 458–73. Boston: Birkhäuser.Google Scholar
Einstein, Albert. [1914] 1996. “Die formale Grundlage der allgemeinen Relativitätstheorie.” In Einstein 1996. Originally published in Sitzungsberichte der Preußischen Akad. d. Wissenschaft, Math.-Physik, Kl. 34.Google Scholar
Einstein, Albert. [1916] 1952. “The Foundation of the General Theory of Relativity.” Translated by W. Perrett and G. B. Jeffrey. In The Principle of Relativity, edited by Lorentz, H. A., Einstein, A., Minkowski, H., and Weyl, H., 111–64. New York: Dover. Originally published as Die Grundlagen der allgemeinen Relativitätstheorie. Leipzig: J. Barth.CrossRefGoogle Scholar
Einstein, Albert. [1917] 1988. Über die spezielle und die allgemeine Relativitätstheorie. 23rd ed. Braunschweig, Vieweg.Google Scholar
Einstein, Albert. 1918. “Prinzipielles zur allgemeinen Relativitätstheorie.” Annalen der Physik 55: 241–44.CrossRefGoogle Scholar
Einstein, Albert. 1925. “Die Relativitätstheorie.” In Die Kultur der Gegenwart: Ihre Entwicklung und ihre Ziele. 2nd rev. ed., edited by Lecher, E., 794–97. Leipzig: Teubner.Google Scholar
Einstein, Albert. [1936] 1983. “Physics and Reality.” In Einstein 1983, 290–323.Google Scholar
Einstein, Albert. [1940] 1983. “The Fundaments of Theoretical Physics.” In Einstein 1983, 323–37.Google Scholar
Einstein, Albert. 1948. “Quanten-Mechanik und Wirklichkeit.” Dialectica 2: 320–24.Google Scholar
Einstein, Albert. 1949. “Autobiographical Notes” and “Replies to Criticisms.” In Albert Einstein: Philosopher-Scientist, edited by Schilpp, P. A., 2–97, 663–88. Evanston: Northwestern University Press.Google Scholar
Einstein, Albert. [1950] 1983. “On the Generalized Theory of Gravitation.” In Einstein 1983, 341–56.Google Scholar
Einstein, Albert. [1952] 1961. “Relativity and the Problem of Space.” In Einstein 1961, Appendix V. 135–57.Google Scholar
Einstein, Albert. 1956. The Meaning of Relativity. 5th ed. Princeton: Princeton University Press.Google Scholar
Einstein, Albert. 1961. Relativity: The Special and General Theory. 15th ed New York: Crown.Google Scholar
Einstein, Albert. 1983. Ideas and Opinion. New York: Crown.Google Scholar
Einstein, Albert. 1996. The Collected Papers of Albert Einstein. Princeton: Princeton University Press.Google Scholar
Einstein, Albert, , Podolsky, Boris, and Rosen, Nathan. 1935. “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” Physical Review 47: 777–80.CrossRefGoogle Scholar
Fine, Arthur. [1985] 1996. The Shaky Game: Einstein Realism and the Quantum Theory. Chicago: University of Chicago Press.Google Scholar
Frankel, Theodore. 1998. The Geometry of Physics. New York: Cambridge University Press.Google Scholar
Frege, Gottlob. [1885] 1984. Review of Cohen 1883. In Collected Papers on Mathematics, Logic, and Philosophy, edited by McGuiness, B., 108–11. Oxford: Blackwell. Originally published in Zeitschrift für Philosophie und philosophische Kritik 87: 324–29.Google Scholar
Friedman, Michael. 1983. Foundations of Space-Time Theories: Relativistic Physics and Philosophy of Science. Princeton: Princeton University Press.Google Scholar
Funkenstein, Amos. 1986. “The Persecution of Absolutes: On the Kantian and Neo-Kantian Theories of Science.” In The Kaleidoscope of Science, edited by Ullman-Margalit, E., 39–63. Dordrecht: D. Reidel.CrossRefGoogle Scholar
Göckeler, M., and Schücker, T.. 1987. Differential Geometry, Gauge Theories, and Gravity. Cambridge: Cambridge University Press.Google Scholar
Haag, Rudolf. 1988. “Quantum Physics and Gravitation.” In Quantum Theories and Geometry, edited by Cahen, M. and Flato, M., 103–112. Dordrecht: Kluwer.Google Scholar
Haag, Rudolf. 1992. Local Quantum Physics: Fields, Particles, Algebras. Berlin: Springer Verlag.CrossRefGoogle Scholar
Hoffmann, Banesh, , with Dukas, Helen. 1972. Albert Einstein: Creator and Rebel. New York: Viking Press.Google Scholar
Howard, Don. 1984. “Realism and Conventionalism in Einstein's Philosophy of Science: The Einstein-Schlick Correspondence.” Philosophia Naturalis 21: 616–29.Google Scholar
Howard, Don. 1985. “Einstein on Separability and Locality.” Studies in History and Philosophy of Science 16: 171–201.Google Scholar
Howard, Don. 1989. “Holism, Separability, and the Metaphysical Implications of the Bell Experiments.” In Philosophical Consequences of Quantum Theory, edited by Cushing, J. and McMullin, E., 224–53. Notre Dame, Ind.: University of Notre Dame Press.Google Scholar
Howard, Don. 1994. “Einstein, Kant, and the Origins of Logical Empiricism.” In Logic, Language, and the Structure of Scientific Theories, edited by Salmon, W. and Wolters, G., 45–105. Pittsburgh: University of Pittsburgh Press.CrossRefGoogle Scholar
Hübner, Kurt. 1963. “Beiträge zur Philosophic der Physik.” Philosophische Rundschau 11: 2–27.Google Scholar
Kretschmann, Erich. 1917. “Über den physikalischen Sinn der Relativitätspostulate: A. Einstein's neue und seine ursprüngliche Relativitätstheorie.” Annalen der Physik 53: 575–614Google Scholar
Maxwell, James Clerk. [1876] 1953. Matter and Motion. New York: Dover. Originally published by the London Society for Promoting Christian Knowledge.Google Scholar
Majer, Ulrich. 1995. “Geometry, Intuition and Experience: From Kant to Husserl.” Erkenntnis 42: 261–85.Google Scholar
Maidens, Anna. 1998. “Symmetry Groups, Absolute Objects and Action Principles in General Relativity.” Studies in the History and Philosophy of Modern Physics 29: 245–72.Google Scholar
Mould, Richard. 1994. Basic Relativity. New York: Springer Verlag.CrossRefGoogle Scholar
Norton, John D. 1989. “How Einstein Found His Field Equations, 1912–1915.” In Einstein and the History of General Relativity, edited by Howard, D. and Stachel, J., 101–59. Boston: Birkhäuser.Google Scholar
Norton, John D. 1992. “The Physical Content of General Covariance.” In Studies in the History of General Relativity, edited by Eisenstaedt, J. and Kox, A., 281–315. Boston: Birkhäuser.Google Scholar
Norton, John D. 1993. “General Covariance and the Foundations of General Relativity: Eight Decades of Dispute.” Reports on Progress in Physics 56: 791–858.CrossRefGoogle Scholar
Ohanian, Hans C., and Ruffini, Remo. 1994. Gravitation and Spacetime. 2nd ed. New York: Norton.Google Scholar
Pais, Abraham. 1982. “Subtle Is the Lord…”; The Science and the Life of Albert Einstein. New York: Oxford University Press.Google Scholar
Pauli, Wolfgang Jr., [1921] 1958. The Theory of Relativity. New York: Pergamon Press.Google Scholar
Planck, Max. 1908. “Die Einheit des physikalisches Weltbild.” In Wege zur physikalischen Erkenntnis, 1–32. Leipzig: S. Hirzel.Google Scholar
Planck, Max. 1910. Acht Vorlesungen über Theoretische Physik. Leipzig: S. Hirzel.Google Scholar
Prugovečki, Eduard. 1995. Principles of Quantum General Relativity. Singapore: World Scientific Publishers.Google Scholar
Reichenbach, Hans. 1920. Relativitätstheorie und Erkenntnis A Priori. Berlin: J. Springer.Google Scholar
Rovelli, Carlo. 1997. “Halfway through the Woods: Contemporary Research on Space and Time.” In The Cosmos of Science: Essays of Exploration, edited by Earman, J. and Norton, J., 180–223. Pittsburgh: University of Pittsburgh Press.Google Scholar
Ryckman, T. A. 1991. “Conditio Sine Qua Non: Zuordnung in the Early Epistemologies of Cassirer and Schlick.” Synthese. 88: 57–95.Google Scholar
Ryckman, T. A. 1992. “(P)oint-(Coincidence Thinking,” Studies in History and Philosophy of Science 23: 471–97.CrossRefGoogle Scholar
Schlick, Moritz. [1920] 1979. “Philosophical Reflections on the Causal Principle.” Translated by P. Heath. In Moritz Schlick: Philosophical Papers 1, edited by Mulder, H. L. and van de Velde-Schlick, B., 295–321. Dordrecht: D. Reidel. Originally published as “Naturphilosophische Betrachtungen über das Kausalprinzip.” Die Naturwissenschaften 8: 461–74.Google Scholar
Schlick, Moritz [1921] 1979. “Critical or Empiricist Interpretation of Modern Physics.” Translated by Heath, P.. In Schlick, Philosophical Papers 1: 322–34. Originally published as “Kritizistische oder Empiristische Deutung der neuen Physik.” Kant-Studien 26: 96–111.Google Scholar
Smolin, Lee. 1992. “Space and Time in the Quantum Universe.” In Conceptual Problems of Quantum Gravity, edited by Ashtekar, A. and Stachel, J., 228–88. Boston: Birkhäuser.Google Scholar
Speziali, P., ed. 1972. Albert Einstein-Michele Besso Correspondance, 1903–1955. Paris: Hermann.Google Scholar
Stachel, John. 1986. “What a Physicist Can Learn from the Discovery of General Relativity.” In Proceedings of the Fourth Marcel Grossmann Meeting on General Relativity, edited by Ruffini, R., 1857–1862. Amsterdam: Elsevier Science Publishers.Google Scholar
Stachel, John. 1989. “Einstein's Search for General Covariance, 1912–1915.” In Einstein and the History of General Relativity, edited by Howard, D. and Stachel, J., 63–100. Boston: Birkhäuser. Based on a paper circulating privately since 1980.Google Scholar
Stachel, John. 1992. “Einstein and Quantum Mechanics.” In Conceptual Problems of Quantum Gravity, edited by Ashtekar, A. and Stachel, J., 13–42. Boston: Birkhäuser.Google Scholar
Stachel, John. 1993a. “The Meaning of General Covariance: The Hole Story.” In Philosophical Problems of the Internal and External Worlds: Essays on the Philosophy of Adopf Grünbaum, edited by Earman, J. et al. , 129–60. Pittsburgh: University of Pittsburgh Press.Google Scholar
Stachel, John. 1993b. “The Other Einstein: Einstein Contra the Field Theory.” Science in Context 6: 275–90.CrossRefGoogle Scholar
Stachel, John. 1996. “Introduction.” In Einstein 1996.CrossRefGoogle Scholar
Trautman, Andrzej. 1966. “The General Theory of Relativity.” Soviet Physics Uspekhi 89: 319–36.Google Scholar
Weinberg, Steven. 1972. Gravitation and Cosmology. New York: Wiley.Google Scholar
Weyl, Hermann. 1923. Raum-Zeit-Materie 5th ed. Berlin: J. Springer.CrossRefGoogle Scholar
Weyl, Hermann. 1927. Philosophie der Mathematik und Naturwissenschaft. Munich: R. Oldenbourg.Google Scholar