Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-25T17:19:24.433Z Has data issue: false hasContentIssue false

What is the Logical Interpretation of Quantum Mechanics?

Published online by Cambridge University Press:  28 February 2022

Extract

Let me begin by briefly explaining the concept of ‘interpretation’ relevant to this discussion.

Certain physical theories postulate abstract structural constraints which events are held to satisfy. Such theories are termed ‘principle theories’. Interpretations of principle theories aim to explain their relation to the theories they replace. Interpretations are therefore concerned with the nature of the transitions between theories.

Theories of space-time structure provide the most accessible illustration of principle theories. For example, Newtonian mechanics in the absence of gravitation represents the 4-dimensional geometry of space-time by the inhomogeneous Galilean group, which acts transitively in the class of free motions, i.e. the inhomogeneous Galilean group is the symmetry group of the free motions: it is a subgroup of the symmetry group of every mechanical system, and the largest such subgroup. Einstein’s special principle of relativity is the hypothesis that the symmetry group of the free motions is the Poincaré group.

Type
Contributed Papers: Session V
Copyright
Copyright © 1976 by D. Reidel Publishing Company, Dordrecht-Holland

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

Birkhoff, G. and J., Von Neumann: ‘The Logic of Quantum Mechanics’; , Annals of Mathematics 37 (1936), 823843.CrossRefGoogle Scholar
Born, M.: The Born-Einstein Letters: The Correspondence Between Albert Einstein and Max and Hedwig Born: 1916-1955, Walker and Company, 1971.Google Scholar
Bub, J.: The Interpretation of Quantum Mechanics, Reidel, 1974.CrossRefGoogle Scholar
Demopoulos, W.: ‘Contributions to the Interpretation of Quantum Mechanics’ in Hooker, C. (ed.), The Logico-Algebraic Approach to Quantum Mechanics, Reidel, 1975.Google Scholar
Einstein, A.: ‘Quantum Mechanics and Reality’ (1948), in The Born-Einstein Letters: The Correspondence Between Albert Einstein and Max and Hedwig Born: 1916-1955, Walker and Company, (1971) pp. 168173.Google Scholar
Finkelstein, D.: ‘Logic of Quantum Physics’; , Transactions of the New York Academy of Science 25 (1963), 621635.Google Scholar
Gleason, A.: ‘Measures on the Closed Subspaces of Hilbert Space’, Journal of Mathematics and Mechanics 6 (1957), 885893.Google Scholar
Kochen, S. and Specker, E. P.: ‘The Problem of Hidden Variables in Quantum Mechanics’, Journal of Mathematics and Mechanics 17 (1967), 5987.Google Scholar
von Neumann, J.: Mathematical Foundations of Quantum Mechanics, Princeton University Press, 1955.Google Scholar
Putnam, H.: ‘Is Logic Empirical?’, Boston Studies in the Philosophy of Science, Vol. V (ed. by Cohen, R. S. and Wartofsky, M. W.), Reidel, 1969.Google Scholar