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Experimental Tests of the Sum Rule

Published online by Cambridge University Press:  01 April 2022

M.L.G. Redhead
M.L.G. Redhead*
Affiliation:
Chelsea College, University of London
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Abstract

Recent discussions of experimental tests of the Sum Rule have been carried out in the context of the special circumstances attending the Cross-Ramsey experiment. A more general analysis of possible tests is presented. A technical mistake of Fine and Glymour concerned with a misunderstanding of the physics of the Cross-Ramsey experiment is explained and a detailed analysis of a thought experiment based on the Einstein-Podolsky-Rosen wave function is given. It is concluded, in agreement with Fine, that scattering experiments do not test the Sum Rule as a principle which supplements standard quantum mechanics.

Type
Research Article
Information
Philosophy of Science , Volume 48 , Issue 1 , March 1981 , pp. 50 - 64
Copyright
Copyright © 1981 by the Philosophy of Science Association

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Footnotes

†

Earlier drafts of this paper were presented at the 6th International Congress of Logic, Methodology and Philosophy of Science held at Hanover in August 1979, and at the Symposium on Philosophical Aspects of Quantum Theory held at Dubrovnik in April 1980. I am grateful for helpful comments from Jon Dorling, Richard Healey, Arthur Fine and Nancy Cartwright. They are not, however, to be held responsible for any of the opinions expressed.

References

Amrein, W. O., Jauch, J. M. and Sinha, K. B. (1977), Scattering Theory in Quantum Mechanics: Physical Principles and Mathematical Methods. Reading, Mass: Benjamin.Google Scholar
Ashkin, A., Page, L. A. and Woodward, W. M. (1954), “Electron-Electron and Positron-Electron Scattering Measurements.” Physical Review 94: 357–362.CrossRefGoogle Scholar
Bell, J. S. (1966), “On the Problem of Hidden Variables in Quantum Mechanics.” Reviews of Modern Physics 38: 447–475.CrossRefGoogle Scholar
Berestetskii, V. B., Lifschitz, E. M. and Pitaevskii, L. P. (1971), Relativistic Quantum Theory. New York: Pergamon.Google Scholar
Bloch, F. and Nordsieck, A. (1937), “Note on the Radiation Field of the Electron.” Physical Review 52: 54–59.CrossRefGoogle Scholar
Bohr, N. (1935), “Can Quantum-Mechanical Description of Physical Reality be Considered Complete?” Physical Review 48: 696–702.CrossRefGoogle Scholar
Bohr, N. (1949), “Discussion with Einstein on Epistemological Problems in Atomic Physics,” in Albert Einstein: Philosopher-Scientist. Edited by Schilpp, P. A. New York: Tudor, pp. 199–241.Google Scholar
Brown, L. M. and Feynman, R. P. (1952), “Radiative Corrections to Compton Scattering.” Physical Review 85: 231–244.CrossRefGoogle Scholar
Cartwright, N. (1977), “The Sum Rule Has Not Been Tested.” Philosophy of Science 44: 107–112.CrossRefGoogle Scholar
Champion, F. C. (1932), “On Some Close Collisions of Fast β-Particles, with Electrons, Photographed by the Expansion Method.” Proceedings of the Royal Society (London) A 136: 630–637.Google Scholar
Cross, W. and Ramsey, N. (1950), “The Conservation of Energy and Momentum in Compton Scattering.” Physical Review 80: 929–936.CrossRefGoogle Scholar
Einstein, A., Podolsky, B. and Rosen, N. (1935), “Can Quantum-Mechanical Description of Physical Reality be Considered Complete?” Physical Review 47: 777–780.CrossRefGoogle Scholar
Fine, A. (1974), “On the Completeness of Quantum Theory.” Synthese 29: 257–289. (Reprinted in Logic and Probability in Quantum Mechanics. Edited by Suppes, P. Dordrecht: D. Reidel, 1976, pp. 249–281.)CrossRefGoogle Scholar
Fine, A. (1977), “Conservation, the Sum Rule and Confirmation.” Philosophy of Science 44: 95–106.CrossRefGoogle Scholar
Fine, A. and Teller, P. (1978), “Algebraic Constraints on Hidden Variables.” Foundations of Physics 8: 629–637.CrossRefGoogle Scholar
Fine, A. (1979), “Counting Frequencies: A Primer for Quantum Realists.” Synthese 42: 145–154.CrossRefGoogle Scholar
Gardner, M. R. (1972), “Quantum-Theoretical Realism: Popper and Einstein v. Kochen and Specker.” The British Journal for the Philosophy of Science 23: 13–23.CrossRefGoogle Scholar
Glymour, C. (1977), “The Sum Rule is Well-Confirmed.” Philosophy of Science 44: 86–94.CrossRefGoogle Scholar
Healey, R., (1979), “Quantum Realism: Naïveté is No Excuse.” Synthese 42: 121–144.CrossRefGoogle Scholar
Kochen, S. and Specker, E. (1967), “The Problem of Hidden Variables in Quantum Mechanics.” Journal of Mathematics and Mechanics 17: 59–87. (Reprinted in The Logico-Algebraic Approach to Quantum Mechanics, Vol. I: Historical Evolution. Edited by Hooker, C. A., Dordrecht: D. Reidel, 1975, pp. 293–328.)Google Scholar
Maczynski, M. J. (1971), “Boolean Properties of Observables in Axiomatic Quantum Mechanics.” Reports on Mathematical Physics 2: 135–150.CrossRefGoogle Scholar
Massey, H. S. W. and Mohr, C. B. O. (1933), “Free Paths and Transport Phenomena in Gases and the Quantum Theory of Collisions. I—The Rigid Sphere Model.” Proceedings of the Royal Society (London) A 141: 434–453.Google Scholar
Messiah, A. (1965), Quantum Mechanics, vol. I. Amsterdam: North Holland.Google Scholar
Mott, N. F. and Massey, H. S. W. (1965), The Theory of Atomic Collisions, 3rd ed. Oxford: The Clarendon Press.Google Scholar
Redhead, M. L. G. (1953), “Radiative Corrections to the Scattering of Electrons and Positrons by Electrons.” Proceedings of the Royal Society (London) A: 219–239.Google Scholar
Redhead, M.L.G. (1972), “Radiative Corrections to Coincidence Experiments in High Energy Electron-Electron and Positron-Electron Scattering.” Journal of Physics A 5: 431–443.CrossRefGoogle Scholar
Schiff, L. I. (1968), Quantum Mechanics, 3rd ed. New York: McGraw Hill.Google Scholar
Scott, M. B., Hanson, A. O. and Lyman, F. M. (1951), “Electron-Electron Scattering at 14.7 Mev.” Physical Review 84: 638–643.CrossRefGoogle Scholar
Stairs, A. (1978), Quantum Mechanics, Logic and Reality. Unpublished PhD Thesis, University of Western Ontario.Google Scholar
Taylor, J. R. (1972), Scattering Theory. New York: John Wiley and Sons.Google Scholar
van Fraassen, B. (1973), “Semantic Analysis of Quantum Logic,” in Contemporary Research in the Foundations and Philosophy of Quantum Theory. Edited by Hooker, C. A. Dordrecht: D. Reidel, pp. 80–113.CrossRefGoogle Scholar