Abstract
In this paper I put forward a suggestion for identifying causality in micro-systems with the specific quantum field theoretic interactions that occur in such systems. I first argue — along the lines of general transference theories — that such a physicalistic account is essential to an understanding of causation; I then proceed to sketch the concept of interaction as it occurs in quantum field theory and I do so from both a formal and an informal point of view. Finally, I present reasons for thinking that only a quantum field theoretic account can do the job — in particular I rely on a theorem by D. Currie and to the effect that interaction cannot be described in (a Hamiltonian formulation of) Classical Mechanics. Throughout the paper I attempt to suggest that the widespread scepticism about the ability of quantum theory to support a theory of causality is mistaken and rests on several misunderstandings.
Similar content being viewed by others
References
Aronson, J. L.: 1971a, ‘The Legacy of Hume's Analysis of Causation’,Studies in the History and Philosophy of Science 7, 135–56.
Aronson, J. L.: 1971b, ‘On the Grammer of ‘Cause’’,Synthese 22, 414–30.
Aronson, J. L.: 1982, ‘Untangling Ontology from Epistemology in Causation’,Erkenntnis 18, 293–305.
Ascoli, R., G. Epiphanio and A. Restivo: 1970, ‘On the Mathematical Description of Quantized Fields’,Commun. Math. Phys. 18, 291–300.
Balaban, T. and A. Jaffe: 1984, ‘Constructive Gauge Theory’, preprint.
Beauchamp, T. L. and A. Rosenberg: 1981,Hume and the Problem of Causation, Oxford University Press, New York.
Brydges, D. C.: 1983, ‘What is a Quantum Field Theory’,Bull. Amer. Math. Soc. 8, 31–40.
Currie, D.: 1963, ‘Interactioncontra Classical Relativistic Hamiltonian Particle Mechanics’,J. Math. Phys. 4, 1470–88.
Cook, J. M.: 1953, ‘The Mathematics of Second Quantization’,Trans. Am. Math. Soc. 74, 222–45.
Dieks, D.: 1981, ‘A Note on Causation and the Flow of Energy’,Erkenntnis 16, 103–08.
Dieks, D.: 1986, ‘Physics and the Direction of Causation’,Erkenntnis 25, 85–110.
Dirac, P. A. M.: 1958,The Principles of Quantum Mechanics, 4th Edition, Oxford University Press, Oxford.
Dimock, J.: 1980, ‘Algebras of Local Observables on a Manifold’,Commun. Math. Phys. 77, 219–228.
Dyson, F. J.: 1972, ‘Missed Opportunities’,Bull. Amer. Math. Soc. 78, 635–652.
Earman, J.: 1976, ‘Causation: a Matter of Life and Death’,Journal of Philosophy 73, 23–35.
Ellis, B.: 1965, ‘The Origin and Nature of Newton's Laws of Motion’, in R. G. Colodny (ed.),Beyond the Edge of Certainty, Pittsburgh University Press, Pittsburgh.
Emch, G.: 1972,Algebraic Methods in Statistical Mechanics and Quantum Field Theory, Interscience, New York.
Friedrichs, K.: 1953,Mathematical Aspects of the Quantum Theory of Fields, Interscience, New York.
Fair, D.: 1979, ‘Causation as Flow of Energy’,Erkenntnis 14, 219–50.
Friedman, M.: 1983,Foundations of Space-Time Theories, Princeton University Press, Princeton.
Gillespie, D.: 1973,A Quantum Mechanics Primer, International Textbook Company, London.
Glimm, J.: 1969, ‘The Foundations of Quantum Field Theory’,Advances in Math. 3, 101–25.
Glimm, J. and A. Jaffe: 1971, ‘Quantum Field Theory Models’, reprinted in Glimm and Jaffe (1985).
Glimm, J. and A. Jaffe: 1972, ‘Boson Quantum Field Theories’, reprinted in Glimm and Jaffe (1985).
Glimm, J. and A. Jaffe: 1981,Quantum Physics: a Functional Integral Point of View, Reidel, New York.
Glimm, J. and A. Jaffe: 1985,Quantum Field Theory and Statistical Mechanics, Birkhauser, Boston.
Guenin, M.: 1966, ‘On the Interaction Picture’,Commun. Math. Phys. 3, 120–132.
Haag, R.: 1970, ‘Observables and Fields’ 1970 Brandeis University Summer Institute in Theoretical Physics, Vol. 2.
Haag, R. and D. Kastler: 1964, ‘An Algebraic Approach to Quantum Field Theory’,J. Math. Phys. 5, 848–61.
Hume, D.: 1977,An Enquiry Concerning Human Understanding, Hackett, Indianapolis.
Jost, R.: 1965,A General Theory of Quantized Fields, Amer. Math. Soc., Providence, Rhode Island.
Jauch, J. M.: 1968,Foundations of Quantum Mechanics, Addison-Wesley, Reading.
Jauch, J. M.: 1972, ‘On Bras and Kets’ in Abdus Salam and E. P. Wigner (eds.),Aspects of Quantum Theory, Cambridge University Press, Cambridge.
Kline, A. D.: 1985, ‘Transference and the Direction of Causation’,Erkenntnis 23, 51–54.
Merzbacher, E.: 1961,Quantum Mechanics, Wiley, New York.
von Neumann, J.: 1955,Mathematical Foundations of Quantum Mechanics, Princeton University Press, Princeton.
Roberts, J. E.: 1966, ‘Rigged Hilbert Spaces in Quantum Mechanics’,Commun. Math. Phys. 3, 98–119.
Roberts, J. E.: 1982, ‘Localization in Algebraic Field Theory’,Commun. Math. Phys. 85, 87–98.
Russel, B.: 1913, ‘On the Notion of Cause’,Proc. of the Aristotelian Soc. 13, 1–26.
Ryder, L. H.: 1985,Quantum Field Theory, Cambridge University Press, Cambridge.
Schweber, S.: 1961,An Introduction to Relativistic Quantum Field Theory, Row and Peterson and Co., New York.
Simon, B.: 1974,The P(ϕ) 2 Euclidean (Quantum) Field Theory, Princeton University Press, Princeton.
Streater, R.: 1975, ‘An Outline of Axiomatic Quantum Field Theory’,Rep. Prog. Phys. 38, 771–846.
Streater, R. and A. Wightman: 1964,PCT, Spin and Statistics, and all that, Benjamin, New York.
Wightman, A.: 1976, ‘Hilbert's Sixth Problem: Mathematical Treatment of the Axioms of Physics’,Proc. Symp. In Pure Mathematics, Vol. 28, pp. 147–240.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Heathcote, A. A theory of causality: Causality=interaction (as defined by a suitable quantum field theory). Erkenntnis 31, 77–108 (1989). https://doi.org/10.1007/BF01239130
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01239130