Robustness of an Experimental Result: The Example of the Tests of Bell’s Inequalities

  • Catherine Dufour†
  • Léna SolerEmail author
Part of the Boston Studies in the Philosophy of Science book series (BSPS, volume 292)


Bell’s inequalities provide a quantitative criterion to test experimentally the local hidden variables theories (LHVT) versus standard quantum mechanics (SQM). From the early 1970s to the present, a huge number of experimental tests have been performed. We will discuss their independence. The outcomes – except one – are consistent with SQM and inconsistent with LHVT. At a first glance, one can consider that the result of the experimental tests of Bell’s inequalities is robust if one follows the statement of Wimsatt (1981): “the robustness of a result is characterized by its invariance with respect to a great number of independent derivations”. This opinion is implicitly shared by many physicists. However, real experiments differ from the ideal experiment used to derive Bell’s theorem in several respects. Two kinds of problems are mainly emphasized. First, in all the experiments an additional assumption is used due to the fact that a part of the experimental set-up is not 100% efficient. This leads to the detection loophole. Second, the experiments do not fulfill one of the requirements of the theorem, for example the locality condition. This leads to the locality loophole. Consequently, one cannot strictly speaking conclude that the experimental tests have ruled out the LHVT. We argue that, for experimental tests of a given theoretical question to be robust, one has to consider the validity of the various independent derivations carefully. In order to find a way to increase robustness, we will discuss the following questions: Do both loopholes have the same importance? Are they both crucial? Is an ultimate experiment closing both loopholes simultaneously necessary to conclude that the result favouring SQM is robust? Or, are a couple of experiments, each one closing a given loophole, enough?


Experimental Test Bell Inequality Local Realism Standard Quantum Mechanic Optical Photon 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The author would like to thank Soler and Trizio for helpful comments.


  1. Aspect, A. 1999. “Bell’s Inequality Test: More Ideal than Ever.” Nature 398:189–90.CrossRefGoogle Scholar
  2. Aspect, A. 2004. “Bell’s Theorem: The Naive View of an Experimentalist.” ArX iv:quant-ph/0402001.Google Scholar
  3. Aspect, A., Ph. Grangier, and G. Roger. 1982. “Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedanken Experiment: A New Violation of Bell’s Inequalities.” Physical Review Letters 49:91–4.CrossRefGoogle Scholar
  4. Bell, J.S. 1964. “On the Einstein Podolsky Rosen Paradox.” Physics 1(3):195–200.Google Scholar
  5. Bell, J.S. 1987. Speakable and Unspeakable in Quantum Mechanics, 14–21. Cambridge: Cambridge University Press.Google Scholar
  6. Berche, B., C. Chatelain, C. Dufour, T. Gourieux, and D. Karevski. 2006. “Historical and Interpretative Aspects of Quantum Mechanics: A Physicists’ Naive Approach.” Condensed Matter Physics. 2(46):319.Google Scholar
  7. Collins, H. 1985, 2002. Changing Order: Replication and Induction in Scientific Practices. Chicago: University of Chicago Press.Google Scholar
  8. Einstein, A., B. Podolsky, and N. Rosen. 1935. “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” Physical Review 47:777–80.CrossRefGoogle Scholar
  9. Freedman, S.J., and J.F. Clauser. 1972. “Experimental Test of Local Hidden-Variable Theories.” Physical Review Letters 28:938.CrossRefGoogle Scholar
  10. Fry, E.S., et al. 1995. “Proposal for a Loophole-Free Test of the Bell Inequalities.” Physical Review A 52:4381–95.CrossRefGoogle Scholar
  11. Garcia-Patròn, R., et al. 2004. “Proposal for a Loophole-Free Bell Test Using Homodyne Detection.” Physical Review Letters 93(13):130409.CrossRefGoogle Scholar
  12. Genovese, M. 2005. “Research on Hidden Variable Theories: A Review of Recent Progresses.” Physics Reports 413:319.CrossRefGoogle Scholar
  13. Grangier, Ph. 2001. “Quantum Physics: Count Them All.” Nature 409:774.CrossRefGoogle Scholar
  14. Hong, F.Y., et al. 2008. “Proposal for a Loophole-Free Test of Nonlocal Realism with Electron Spins of Donors.”. Physical Review A 77:052113.CrossRefGoogle Scholar
  15. Huelga, S.F., et al. 1995. “Loophole-Free Test of the Bell Inequality.” Physical Review A 51:5008–11.CrossRefGoogle Scholar
  16. Kwiat, P.G., et al. 1994. “Proposal for a Loophole-Free Bell Inequality Experiment.” Physical Review A 49:3209–20.CrossRefGoogle Scholar
  17. Lakatos, I. 1980. “The Methodology of Scientific Research Programmes.” In Philosophical Papers, vol. 1, edited by J. Worrall and G. Currie. New York: Cambridge University Press.Google Scholar
  18. Les dossiers de la Recherche No. 29, 2007. “Le monde quantique”.Google Scholar
  19. Levins, R. 1966. “The Strategy of Model Building in Population Biology.” American Scientist 54:421.Google Scholar
  20. Matsukevich, D.N., P. Maunz, D.L. Moehring, S. Olmschenk, and C. Monroe. 2008. “Bell Inequality Violation With Two Remote Atomic Qubits.” Physical Review Letters 100:150404.CrossRefGoogle Scholar
  21. Percival, I.C. 2000a. Speakable and Unspeakable After John Bell. A talk given at the International Erwin Schrödinger Institute, Vienna (ESI) at the November 2000 Conference in commemoration of John Bell 2000 Dec 05.Google Scholar
  22. Percival, I.C. 2000b. “Why Do Bell Experiments?” Nature (submitted). arXiv:0008097v1.Google Scholar
  23. Rowe, M.A., et al. 2001. “Experimental Violation of a Bell’s Inequality with Efficient Detection.” Nature 409:791–4.CrossRefGoogle Scholar
  24. Salart, D., et al. 2008. “Space-like Separation in a Bell Test Assuming Gravitationally Induced Collapses.” Physical Review Letters 100:220404.CrossRefGoogle Scholar
  25. Santos, E. 1992. “Critical Analysis of the Empirical Tests of Local Hidden-Variable Theories.” Physical Review A 46:3646.CrossRefGoogle Scholar
  26. Santos, E. 2005. “Bell’s Theorem and the Experiments: Increasing Empirical Support for Local Realism?” Studies in History and Philosophy of Modern Physics 36:544–65.CrossRefGoogle Scholar
  27. Tapster, P.R., J.G. Rarity, and P.C.M. Owens. 1994. “Violation of Bell’s Inequality over 4 km of Optical Fiber.” Physical Review Letters 73:1923.CrossRefGoogle Scholar
  28. Tittel, W., J. Brendel, H. Zbinden, and N. Gisin. 1998. “Violation of Bell Inequalities by Photons More than 10 km Apart.” Physical Review Letters 81:3563.CrossRefGoogle Scholar
  29. Weihs, G., T. Jennewein, C. Simon, H. Weinfurter, and A. Zeilinger. 1998. “Violation of Bell’s Inequality Under Strict Einstein Locality Conditions.” Physical Review Letters 81:5039.CrossRefGoogle Scholar
  30. Wimsatt, W.C. 1981. “Robustness, Reliability and Overdetermination.” In Scientific Inquiry and the Social Sciences, edited by M.B. Brewer and B.E. Collins, 123–62. San Francisco, CA: Jossey-Bass Publishers.Google Scholar

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© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Archives H. Poincaré, Laboratoire d’Histoire des Sciences et de PhilosophieUMR 7117 CNRSNancyFrance

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