Relating Bell’s Local Causality to the Causal Markov Condition


The aim of the paper is to relate Bell’s notion of local causality to the Causal Markov Condition. To this end, first a framework, called local physical theory, will be introduced integrating spatiotemporal and probabilistic entities and the notions of local causality and Markovity will be defined. Then, illustrated in a simple stochastic model, it will be shown how a discrete local physical theory transforms into a Bayesian network and how the Causal Markov Condition arises as a special case of Bell’s local causality and Markovity.

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    For the sake of uniformity throughout the paper I slightly changed Bell’s notation and figures.

  2. 2.

    See also our remark in the last paragraph of Sect. 3.


  1. 1.

    Bell, J.S.: Speakable and Unspeakable in Quantum Mechanics. Cambridge University Press, Cambridge (2004)

    Google Scholar 

  2. 2.

    Glymour, C.: Markov properties and quantum experiments. In: Demopoulos, W., Pitowsky, I. (eds.) Physical Theory and its Interpretation, pp. 117–126. Springe, New York (2006)

    Google Scholar 

  3. 3.

    Glymour, C., Scheines, R., Spirtes, P.: Causation, Prediction, and Search. The MIT Press, Cambridge (2000)

    Google Scholar 

  4. 4.

    Haag, R.: Local Quantum Physics. Springer Verlag, Berlin (1992)

    Google Scholar 

  5. 5.

    Hausman, D., Woodward, J.: Independence, invariance and the causal Markov condition. Br. J. Philos. Sci. 50, 521–583 (1999)

    MATH  MathSciNet  Article  Google Scholar 

  6. 6.

    Henson, J.: Non-separability does not relieve the problem of Bell’s theorem. Found. Phys. 43, 1008–1038 (2013)

    MATH  MathSciNet  Article  ADS  Google Scholar 

  7. 7.

    Hofer-Szabó, G., Rédei, M., Szabó, L.E.: The Principle of the Common Cause. Cambridge University Press, Cambridge (2013)

    Google Scholar 

  8. 8.

    Hofer-Szabó, G., Vecsernyés, P.: On the concept of Bell’s local causality in local classical and quantum theory (submitted) (2015a)

  9. 9.

    Hofer-Szabó, G., Vecsernyés, P.: Bell’s local causality for philosophers (submitted) (2015b)

  10. 10.

    Hofer-Szabó, G.: Local causality and complete specification: a reply to Seevinck and Uffink (forthcoming in EPSA 2013 Proceedings) (2015)

  11. 11.

    Mann, C., Crease, R.: John Bell, particle physicist (Interview). Omni 10(8), 84–92 (1988)

    Google Scholar 

  12. 12.

    Norsen, T.: J.S. Bell’s concept of local causality. Am. J. Phys 79, 12 (2011)

    Article  Google Scholar 

  13. 13.

    Pearl, J.: Causality: Models, Reasoning, and Inference. Cambridge University Press, Cambridge (2000)

    Google Scholar 

  14. 14.

    Seevinck, M.P., Uffink, J.: Not throwing out the baby with the bathwater: Bell’s condition of local causality mathematically ‘sharp and clean’. In: Dieks, D., Gonzalez, W.J., Hartmann, S., Uebel, Th, Weber, M. (eds.) Explanation, Prediction, and Confirmation The Philosophy of Science in a European Perspective, vol. 2, pp. 425–450. Springer, Dordrecht (2011)

    Google Scholar 

  15. 15.

    Suárez, M., San Pedro. I.: ‘Causal Markov, robustness and the quantum correlations. In: Suarez, M. (ed.) Probabilities, Causes andPpropensities in Physics, pp. 173–193. Synthese Library, vol. 347. Springer, Dordrecht (2011)

  16. 16.

    Suárez, M.: Interventions and causality in quantum mechanics. Erkenntnis 78, 199–213 (2013)

    MATH  MathSciNet  Article  Google Scholar 

Download references


This work has been supported by the Hungarian Scientific Research Fund OTKA K-100715.

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Correspondence to Gábor Hofer-Szabó.

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Hofer-Szabó, G. Relating Bell’s Local Causality to the Causal Markov Condition. Found Phys 45, 1110–1136 (2015).

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  • Local causality
  • Causal Markov Condition
  • d-Separation