Not Throwing out the Baby with the Bathwater: Bell’s Condition of Local Causality Mathematically ‘Sharp and Clean’
The starting point of the present paper is Bell’s notion of local causality and his own sharpening of it so as to provide for mathematical formalisation. Starting with Norsen’s (2007 , 2009 ) analysis of this formalisation, it is subjected to a critique that reveals two crucial aspects that have so far not been properly taken into account. These are (i) the correct understanding of the notions of sufficiency, completeness and redundancy involved; and (ii) the fact that the apparatus settings and measurement outcomes have very different theoretical roles in the candidate theories under study. Both aspects are not adequately incorporated in the standard formalisation, and we will therefore do so. The upshot of our analysis is a more detailed, sharp and clean mathematical expression of the condition of local causality. A preliminary analysis of the repercussions of our proposal shows that it is able to locate exactly where and how the notions of locality and causality are involved in formalising Bell’s condition of local causality.
PACS numbers: 03.65.Ta, 03.65.Ud
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MPS acknowledges very fruitful conversations with Hans Westman and Eric Cavalcanti and thanks the Centre for Time, Sydney, Australia for hosting him as a guest researcher. JU acknowledges fruitful discussions with Joe Henson and thanks the Perimeter Institute, Waterloo, Canada for generous hospitality.
- Bell, J. S. (1964). On the Einstein-Podolski-Rosen Paradox, Physics 1, 195. Reprinted in , chapter 2.Google Scholar
- Bell, J. S. (1976). The theory of local beables, Epistemological Letters, vol. 9, March 1976. Reprinted in Dialectica 39, 85 (1985) and in , chapter 7.Google Scholar
- Bell, J. S. (1977). Free variables and local causality, Epistemological letters, February 1977. Reprinted in , chapter 12.Google Scholar
- Bell, J. S. (1980). Atomic-cascade photons and quantum-mechanical nonlocality. Comments on Atomic and Molecular Physics 9, 121. Reprinted in , chapter 13.Google Scholar
- Bell, J. S. (1981). Bertlmann’s socks and the nature of reality, Journal de Physique, Colloque C2 , suppl. au numero 3, Tome 42, 41. Reprinted in , chapter 16.Google Scholar
- Bell, J. S. (1984). Beables for quantum field theory, CERN-TH.4035/84. Reprinted in , chapter 19.Google Scholar
- Bell, J. S. (1986). EPR correlations and EPW distributions. In New Techniques and Ideas in Quantum Measurement Theory, New York Academy of Sciences. Reprinted in , chapter 21.Google Scholar
- Bell, J.S. (1987). Speakable and unspeakable in quantum mechanics. Cambridge: Cambridge University Press.Google Scholar
- Bell, J. S. (1990). La nouvelle cuisine. In A. Sarlemijn and P. Kroes (Eds.), Between Science and Technology (pp. 97-115). Elsevier (North-Holland).Google Scholar
- Cartwright, N., Jones, M. (1991). How to hunt quantum causes. Erkenntnis 35, 205-231.Google Scholar
- Cavalcanti, E. G. (2008). Reality, locality and all that: “experimental metaphysics” and the quantum foundations. PhD thesis, the University of Queensland. arXiv: 0810.4974 (v1, 28 Oct 2008)Google Scholar
- Fisher, R. A. (1922). On the mathematical foundations of theoretical statistics. Philosophical Transactions of the Royal Society, A, 222. p. 309368.Google Scholar
- Jarrett, J. P. (1984). On the Physical Significance of the Locality Conditions in the Bell Arguments, Noǔs 18, 569.Google Scholar
- Norsen, T. (2007). J.S. Bell’s Concept of Local Causality, arXiv:0707.0401 (v2, 6 Jan 2010)Google Scholar
- Norsen, T. (2009). Local Causality and Completeness: Bell vs. Jarrett, Found. Phys. 39, 273.Google Scholar
- Seevinck, M. P. (2008). Parts and Wholes, PhD thesis, University of Utrecht. arXiv:0811.1027. (v3, 23 Apr 2009)Google Scholar
- Seevinck, M. P., Uffink, J. (2010). In preparation.Google Scholar
- Shimony, A. in Proceedings of the International Symposium: Foundations of Quantum Mechanics in the light of New Technology, (Tokyo, 1984).Google Scholar