Skip to main content
SpringerLink
Log in

Observables have No Value: A no-go Theorem for Position and Momentum Observables

  • Published:
Foundations of Physics Aims and scope Submit manuscript

The Bell–Kochen–Specker contradiction is presented using continuous observables in infinite dimensional Hilbert space. It is shown that the assumption of the existence of putative values for position and momentum observables for one single particle is incompatible with quantum mechanics.

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

  1. Einstein A., Podolsky B., Rosen N. (1935). Phys. Rev. 47: 777

    Article  MATH  ADS  Google Scholar 

  2. S. J. Freedman and J. F. Clauser, Phys. Rev. Lett. 28, 938 (1972). A. Aspect, J. Dalibard, and G. Roger, Phys. Rev. Lett. 49, 1804 (1982).

    Google Scholar 

  3. Bell J.S. (1964). Physics 1: 195

    Google Scholar 

  4. Bell J.S. (1966). Rev. Mod. Phys. 38: 447

    Article  MATH  ADS  Google Scholar 

  5. Kochen S., Specker E.P. (1967). J. Math. Mech. 17: 59

    MATH  Google Scholar 

  6. Peres A. (1991). J. Phys. A 24: L175

    Article  ADS  Google Scholar 

  7. R. Penrose, in Quantum Reflections, J. Ellis and D. Amati, eds. (Cambridge University Press, Cambridge, 2000), pp. 1–27.

  8. Kernaghan M., Peres A. (1995). Phys. Lett. A 198: 1

    Article  MATH  ADS  Google Scholar 

  9. Cabello A., Estebaranz J.M., García-Alcaine G. (1996). Phys. Lett. A 212: 283

    Article  Google Scholar 

  10. A. Galindo, in Algunas cuestiones de física teórica (G.I.F.T., Zaragoza, 1975) pp. 3; R. D. Gill and M. S. Keane, J. Phys. A 29, L289 (1996). This proof is reproduced in greater detail in A. Cassinello and A. Gallego, Am. J. Phys. 73, 273 (2005).

  11. Mermin N.D. (1993). Rev. Mod. Phys. 65: 803

    Article  ADS  Google Scholar 

  12. Bohm D. (1951). Quantum Theory. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  13. Zimba J. (1998). Found. Phys. Lett. 11: 503–533

    Article  Google Scholar 

  14. Fleming G.N. (1995). Ann.(NY) Acad. Sci. 755: 646

    Article  ADS  Google Scholar 

  15. R. Clifton, in Quantum Entanglements: Selected Papers of Rob Clifton, J. Butterfield and H. Halvorsen, eds. (Oxford University Press, Oxford, 2004); arXiv:quant-ph/9912108

  16. See, for instance, C. J. Isham, Lectures on Quantum Theory. Mathematical and Structural Foundations, Chap. 9 (Imperial College Press, London, (1995)

  17. A simple presentation of this mathematics can be found in Sec. 1.4 of L. E. Ballentine, Quantum Mechanics. A Modern Development (World Scientific, Singapore, 1998).

  18. Robinett R.W., Doncheski M.A., Bassett L.C. (2005). Found. Phys. Lett. 18: 455 [ArXiv: quant-ph/0502097]

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Física, Universidad Nacional de Mar del Plata, Funes 3350, 7600, Mar del Plata, Argentina

    Alberto C. de la Torre

Authors
  1. Alberto C. de la Torre
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alberto C. de la Torre.

Rights and permissions

Reprints and permissions

About this article

Cite this article

de la Torre, A.C. Observables have No Value: A no-go Theorem for Position and Momentum Observables. Found Phys 37, 1243–1252 (2007). https://doi.org/10.1007/s10701-007-9148-2

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10701-007-9148-2

Keywords

Search

Navigation