Abstract
It is shown that the correlations predicted by relativistic quantum field theory in locally normal states between projections in local von Neumann algebras \({\cal A}\)(V 1),\({\cal A}\)(V 2) associated with spacelike separated spacetime regions V 1,V 2 have a (Reichenbachian) common cause located in the union of the backward light cones of V 1 and V 2. Further comments on causality and independence in quantum field theory are made.
Article PDF
References
Borchers, H.-J. (1965). On the vacuum state in quantum field theory, II. Communications in Mathematical Physics 1, 57–79.
Buchholz, D. and Verch, R. (1996). Scaling algebras and renormalization group in algebraic quantum field theory. Reviews in Mathematical Physics 7, 1195–1239.
Cirel’son, B. S. (1980). Quantum generalizations of Bell’s inequalities, Letters in Mathematical Physics 4, 93–100.
Florig, M. and Summers, S. J. (1997). On the statistical independence of algebras of observables, Journal of Mathematical Physics 38, 1318–1328.
Fredenhagen, K. (1985). On the modular structure of local algebras of observables, Communications in Mathematical Physics 97, 79–89.
Garber, W. D. (1975). The connexion of duality and causality properties for generalized free fields, Communications in Mathematical Physics 42, 195–208.
Glimm, J. and Jaffe, A. (1972). Boson quantum field models. In Mathematics in Contemporary Physics, Streater, R. F., ed., Academic Press, New York.
Haag, R. and Schroer, B. (1962). Postulates of quantum field theory, Journal of Mathematical Physics 3, 248–256.
Haag, R. (1992), Local Quantum Physics, Springer Verlag, Berlin.
Halvorson, H. and Clifton, R. (2000). Generic Bell correlation between arbitrary local algebras in quantum field theory, Journal of Mathematical Physics 41, 1711–1717.
Hamhalter, J. (1997). Statistical independence of operator algebras, Annales de l’Institut Henri Poincaré - Physique théorique 67, 447–462.
Hofer-Szabó, G., Rédei, M., and Szabó, L. E. (1999). On Reichenbach’s Common Cause Principle and Reichenbach’s notion of common cause, British Journal for the Philosophy of Science 50, 377–399.
Hofer-Szabó, G., Rédei, M., and Szabó, L. E. (2002). Common-Causes are not common common-causes, Philosophy of Science 69, 623–636.
Horuzhy, S. S. (1990), Introduction to Algebraic Quantum Field Theory, Kluwer Academic Publishers, Dordrecht.
Neumann, H. and Werner, R. (1983). Causality between preparation and registration processes in relativistic quantum theory, International Journal of Theoretical Physics 22, 781–802.
Rédei, M. (1995a). Logically independent von Neumann lattices, International Journal of Theoretical Physics 34, 1711–1718.
Rédei, M. (1995). Logical independence in quantum logic, Foundations of Physics 25, 411–422.
Rédei, M. (1997). Reichenbach’s common cause principle and quantum field theory, Foundations of Physics 27, 1309–1321.
Rédei, M. (1998), Quantum Logic in Algebraic Approach, Kluwer Academic Publishers, Dordrecht.
Rédei, M. and Summers, S. J. (2002). Local primitive causality and the Common Cause Principle in quantum field theory, Foundations of Physics 32, 335–355.
Reichenbach, H. (1956), The Direction of Time, University of California Press, Los Angeles.
Roos, H.-J. (1970). Independence of local algebras in quantum field theory, Communications in Mathematical Physics 16, 238–246.
Salmon, W. C. (1984) Scientific Explanation and the Causal Structure of the World, Princeton University Press, Princeton.
Summers, S. J. (1990). On the independence of local algebras in quantum field theory, Reviews in Mathematical Physics 2, 201–247.
Summers, S. J. and Werner, R. (1985). The vacuum violates Bell’s inequalities, Physics Letters A 110, 257–279.
Summers, S. J. and Werner, R. (1987a). Bell’s inequalities and quantum field theory, I, General setting, Journal of Mathematical Physics 28, 2440–2447.
Summers, S. J. and Werner, R. (1987b). Maximal violation of Bell’s inequalities is generic in quantum field theory, Communications in Mathematical Physics 110, 247–259.
Summers, S. J. and Werner, R. (1988). Maximal violation of Bell’s inequalities for algebras of observables in tangent spacetime regions, Annales de l’Institut Henri Poincaré - Physique théorique 49, 215–243.
van Fraassen, B. C. (1982). The Charybdis of realism: Epistemological implications of Bell’s inequalities, Synthese 52, 25–38.
Author information
Authors and Affiliations
Corresponding author
Additional information
Originally published in International Journal of Theoretical Physics, Vol. 44, No. 7, 2005,Due to a publishing error, authorship of the article was credited incorrectly. The corrected article is reprinted in its entirety here. The online version of the original article can be found at http://dx.doi.org/10.1007/s10773-005-7079-2
Rights and permissions
About this article
Cite this article
Rédei, M., Summers, S.J. Remarks on Causality in Relativistic Quantum Field Theory. Int J Theor Phys 46, 2053–2062 (2007). https://doi.org/10.1007/s10773-006-9299-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10773-006-9299-5