Abstract
In my commentary, I will argue that the conclusions drawn in the paper Noncommutative Causality in Algebraic Quantum Field Theory by Gábor Hofer-Szabó are incorrect. As proven by J.S. Bell, a local common causal explanation of correlations violating the Bell inequality is impossible.
Let me guess. He pulled a lost in translation on you?
– from the movie Oceans Twelve (2004)
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The only additional assumption is that the local candidate theories excluded by the theorem are supposed to be non-conspiratorial or not superdeterministic, meaning that certain parameter-choices involved in the experiments are assumed to be “free” or random and not predetermined in precisely such a way as to arrange for apparently non-local correlations. See Bell (1990) for details.
- 2.
A beautiful presentation of his analysis can be found in Bell (1981, 1990), the original version of the theorem is Bell (1964). For a more recent discussion, see Goldstein et al. (2011) or Maudlin (2011). The most common misunderstandings are addressed, for instance, in Norsen (2006) or Goldstein et al. (2011).
- 3.
Algebraic Quantum Field Theory is sometimes referred to as Local Quantum Field theory, but that is due to an unfortunate double-use of terminology. “Locality” in quantum field theory usually refers to the postulate of “microcausality” or “local commutativity” requiring that operators localized in space-like separated regions of space-time commute. This, however, is very different from the concept of Bell-locality as discussed above. In AQFT, local commutativity assures the impossibility of faster-than-light signaling, the theory nevertheless contains non-local correlations between space-like separated events due to the non-local nature of the quantum state (or most “states”), which is defined as a functional on the entire “net” of operator algebras all over space-time.
- 4.
About common controversies or misconceptions regarding the relevance of “quantum logic”, “quantum probabilities” or “noncommutativity” for the issue of non-locality, see also Goldstein et al. (2011).
References
Bell, J.S. 1964. On the Einstein-Podolsky-Rosen paradox. Reprinted In Bell, J.S. 2004. Speakable and unspeakable in quantum mechanics, 14–21. Cambridge: Cambridge University Press.
Bell, J.S. 1981. Bertlmann’s socks and the nature of reality. Reprinted In Bell, J.S. 2004. Speakable and unspeakable in quantum mechanics, 139–158. Cambridge: Cambridge University Press.
Bell, J.S. 1990. La Nouvelle cuisine. Reprinted In Bell, J.S. 2004. Speakable and unspeakable in quantum mechanics, 233–248. Cambridge: Cambridge University Press.
Goldstein, S., et al. 2011. Bell’s theorem. Scholarpedia 6(10): 8378. http://www.scholarpedia.org/article/Bell’s_theorem
Hofer-Szabó, G., and P. Vecsernyés. 2012, preprint. Bell inequality and common causal explanation in algebraic quantum field theory. http://philsci-archive.pitt.edu/id/eprint/9101.
Maudlin, T. 2011. Quantum non-locality and relativity, 3rd ed. Malden/Oxford: Wiley-Blackwell.
Norsen, T. 2006. Bell locality and the nonlocal character of nature. Foundations of Physics Letters 19(7): 633–655.
Rédei, M. 1997. Reichenbach’s common cause principle and quantum field theory. Foundations of Physics 27: 1309–1321.
Stapp, H.P. 1975. Bell’s theorem and world process. Il Nuovo Cimento 40B(29): 270–276.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Lazarovici, D. (2014). Lost in Translation: A Comment on “Noncommutative Causality in Algebraic Quantum Field Theory”. In: Galavotti, M., Dieks, D., Gonzalez, W., Hartmann, S., Uebel, T., Weber, M. (eds) New Directions in the Philosophy of Science. The Philosophy of Science in a European Perspective, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-319-04382-1_39
Download citation
DOI: https://doi.org/10.1007/978-3-319-04382-1_39
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-04381-4
Online ISBN: 978-3-319-04382-1
eBook Packages: Humanities, Social Sciences and LawPhilosophy and Religion (R0)