Skip to main content
SpringerLink
Log in

Bayesian Probabilities and the Histories Algebra

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

We attempt a justification of a generalisation of the consistent histories programme using a notion of probability that is valid for all complete sets of history propositions. This consists of introducing Cox's axioms of probability theory and showing that our candidate notion of probability obeys them. We also give a generalisation of Bayes' theorem and comment upon how Bayesianism should be useful for the quantum gravity/cosmology programmes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Aerts, D. (2002). Reality and probability: Introducing a new type of probability calculus. In Probing the Structure of Quantum Mechanics: Nonlocality, Computation and Axiomatics, D. Aerts, M. Czachor and T. Durt eds. World Scientific, Singapore, preprint: quant-ph/0205165.

  • Anastopoulos, C. (2004). On the relation between quantum mechanical probabilities and event frequencies. Annals Physics, 313, 368, preprint: quant-ph/0403207.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Anastopoulos, C. (2005). Classical vs quantum probability in sequential measurements. preprint: quant-ph/0509019.

  • Caticha, A. (1998). Consistency, amplitudes and probabilities in quantum theory. Physical Review A, 57, 1572, preprint: quant-ph/9804012.

    Article  ADS  Google Scholar 

  • Caticha, A. (2004). Relative entropy and inductive inference. AIP Conference Proceedings, 707, 75–96, preprint: physics/0311093.

    Article  ADS  MathSciNet  Google Scholar 

  • Caticha, A. (2005). The information geometry of space and time. Preprint: gr-qc/0508108 v1.

  • Cox, R. T. (1961). The Algebra of Probable Inference, The Johns Hopkins University Press.

  • Feynman, R. P. (1987). Negative probabilities. In Quantum Implications, B. J. Hiley and F. David Peat, eds., Routledge and Kegan Paul, p. 235.

  • Gell-Mann, M. and Hartle, J. B. (1990). Quantum mechanics in the light of quantum cosmology. In Proceedings of the Third International Symposium on the Foundations of Quantum Mechanics in the Light of New Technology, Physical Society of Japan, Tokyo, Japan, pp. 321–343.

  • Goldstein, S. and Page, D. N. (1995). Linearly positive history propositions: Probabilities for a robust family of sequences of quantum events. Physical Review Letters, 74, 3715–3719, preprint: gr-qc/9403055.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Griffiths, R. B. (1984). Consistent history propositions and the interpretation of quantum mechanics. Journal of Statistical Physics, 36, 219–273.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Hartle, J. B. (1991). Excess baggage. In Elementary Particles and the Universe, J. Schwarz, ed., Cambridge University Press, updated preprint: gr-qc/0508001.

  • Hartle, J. B. (2004). Linear positivity and virtual probability. Physical Review A, 70, 022104, preprint: quant-ph/0401108.

    Article  ADS  MathSciNet  Google Scholar 

  • Isham, C. J. (2003). Some reflections on the status of conventional quantum theory when applied to quantum gravity. In Proceedings of the Conference in Honour of Stephen Hawking's birthday, G. Gibbons ed., Cambridge University Press, preprint: quant-ph/0206090 v1.

  • Isham, C. J. (1994). Quantum logic and the history propositions approach to quantum theory. Journal of Mathematical Physics, 35, 2157–2185, preprint: gr-qc/9308006.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Jaynes, E. T. (2003). Probability Theory: The Logic of Science, Cambridge University Press.

  • Mana, P. G. L. (2004). Consistency of the Shannon entropy in quantum experiments. Physical Review A, 69, 062108, preprint: quant-ph/0302049 v5.

    Article  ADS  Google Scholar 

  • Marlow, T. (2006). A Bayesian account of quantum histories. Annales Physics 321, 1103–1125, preprint: quant-ph/0509149.

    Google Scholar 

  • Marlow, T. (2006b). Relationalism vs. Bayesianism. preprint: gr-qc/0603015 v1.

  • Omnés, R. (1988). Logical reformulation of quantum mechanics. I. Foundations. Journal of Statistical Physics, 53, 933–955.

    Article  ADS  MathSciNet  Google Scholar 

  • Poulin, D. (2005). Toy model for a relational formulation of quantum theory. preprint: quant-ph/0505081 v2.

  • Smolin, L. (2005). The case for background independence. preprint: hep-th/0507235.

  • Sorkin, R. D. (1997). Quantum measure theory and its interpretation. In Quantum Classical Correspondence: Proceedings of the 4th Drexel Symposium on Quantum Nonintegrability, D. H. Feng and B.L. Hu, eds., International Press, Cambridge Mass., preprint: gr-qc/9507057.

  • Youssef, S. (1994). Quantum mechanics as complex probability theory. Mod. Physics Lett A, 9, 2571.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Youssef, S. (2001). Physics with exotic probability theory. preprint: hep-th/0110253 v2. All preprints refer to the http://arxiv.org/ website

Download references

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK

    Thomas Marlow

Authors
  1. Thomas Marlow
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Thomas Marlow.

Additional information

PACS: 02.50.Cw;03.65.Ta;04.60.-m.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Marlow, T. Bayesian Probabilities and the Histories Algebra. Int J Theor Phys 45, 1247–1257 (2006). https://doi.org/10.1007/s10773-006-9122-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-006-9122-3

Keywords

Search

Navigation