Abstract
This Chapter provides a brief overview of the interconnections between the various causality and locality concepts in algebraic quantum field theory such as causal dynamics, primitive causality, local primitive causality, no-signaling, selective and nonselective measurements, local determinism, stochastic Einstein locality.
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Notes
- 1.
The domain of dependence \(D(\mathcal{S})\) of a (piece of) a Cauchy surface \(\mathcal{S}\) consists of those points in \(\mathcal{M}\) for which any causal curve containing them intersects \(\mathcal{S}\).
- 2.
If \(V''\notin \mathcal{K}\) this requirement would mean that by extending \(\mathcal{K}\) by the globally hyperbolic bounded subspacetime regions \(V'', V\in \mathcal{K}\) and defining \(\mathcal{A}(V''):=\mathcal{A}(V)\) one obtains an extended net of local algebras satisfying isotony, microcausality, and covariance.
- 3.
Butterfield (1995, Eqs. 3.6 and 3.7) and Earman and Valente (2014, Sect. 7.2) called (3.6) and (3.9) parameter independence and outcome independence, respectively (Shimony 1986). For the difference between parameter independence, where \(\phi \) in (3.6) is conditioned on the common cause, and no-signaling, where \(\phi \) is unconditioned, see Maudlin (2002) and Norsen (2011).
References
R. Brunetti, K. Fredenhagen, Quantum field theory on curved backgrounds, in Quantum Field Theory on Curved Spacetimes, Concepts and Mathematical Foundations, vol. 786, Lecture Notes in Physics, ed. by C. Bär, K. Fredenhagen (Springer, Berlin, 2009)
J. Butterfield, Vacuum correlations and outcome independence in algebraic quantum field theory, in Fundamental Problems in Quantum Theory, Annals of the New York Academy of Sciences, Proceedings of a conference in honour of John Wheeler, ed. by D. Greenberger, A. Zeilinger (1995), pp. 768–785
R. Clifton, H. Halvorson, Entanglement and open systems in algebraic quantum field theory. Stud. Hist. Philos. Mod. Phys. 32(1), 1–31 (2001)
J. Earman, No superluminal propagation for classical relativistic quantum fields. Stud. Hist. Philos. Mod. Phys. 48, 102–108 (2014)
J. Earman, G. Valente, Relativistic causality in algebraic quantum field theory. Int. Stud. Philos. Sci. 28(1), 1–48 (2014)
R. Geroch, Faster than light? (2010). arXiv:1005.1614
G. Hofer-Szabó, P. Vecsernyés, On the concept of Bell’s local causality in local classical and quantum theory. J. Math. Phys. 56, 032303 (2015)
G. Lüders, Über die Zustandsänderung durch den Messprozess. Ann. Phys. 443, 322 (1950)
T. Maudlin, Quantum Non-Locality and Relativity (Malden, Massachusetts, 2002)
T. Norsen, J.S. Bell’s concept of local causality. Am. J. Phys. 79, 12 (2011)
M. Rédei, A categorial approach to relativistic locality. Stud. Hist. Philos. Mod. Phys. 48, 137–146 (2014)
L. Ruetsche, Interpreting Quantum Theories (Oxford University Press, Oxford, 2011)
S. Schlieder, Einige Bemerkungen über Projektionsoperatoren (Konsequenzen eines Theorems von Borchers). Commun. Math. Phys. 13, 216–225 (1969)
A. Shimony, Events and processes in the quantum world, in Quantum Concepts in Space and Time, ed. by R. Penrose, C. Isham (Oxford University Press, Oxford, 1986), pp. 182–203
R. Werner, Local preparability of states and the split property in quantum field theory. Lett. Math. Phys. 13, 325–329 (1987)
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Hofer-Szabó, G., Vecsernyés, P. (2018). Locality and Causality Principles. In: Quantum Theory and Local Causality. SpringerBriefs in Philosophy. Springer, Cham. https://doi.org/10.1007/978-3-319-73933-5_3
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