Skip to main content

Abstract

There were so many interesting points raised during this workshop, that I wonder whether I can still say anything new on quanuum logic. Therefore, I would like to make a confession. For thirteen years I have been fighting against quantum logic. Due to some paradoxes of sociology, my activities were finally noticed by somebody who said: “Mielnik? Ah, yes, he is doing something in quantum logic”.

The text is a combination of two talks delivered by the author at The Royal Institute of Technology, Stockholm, in October 1979, and at the Ettore Majorana Centre, Erice, in December 1979.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 109.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. C. Piron, Helv. Phys. Acta 37 (1964), p. 439; “Foundations of Quantum Physics”, W.A. Benjamin (1976).

    MathSciNet  MATH  Google Scholar 

  2. R. Giles, J. Math. Phys. 11 (1970), p. 2139; Anon-classical logic for physics, in “Selected Papers on Lukasiewicz Sentential Calculi”, R. Wojcicki ed., Ossolineum, Warsaw (1977); also Studia Logica 33 (1974), p. 397.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. B.C. van Fraassen, “Formal Semantics and Logic”, Macmillan, New York ( 1971 ); Semantic analysis of quantum logic, in “Contemporary Research cm the Foundations and Philosophy of Quantum Theory”, Reidel, Dordrecht (1973).

    MATH  Google Scholar 

  4. K. Bugajska, S. Bugajski, Ann. Inst. Henri Poincaré 19 (1973), p. 333.

    MathSciNet  Google Scholar 

  5. B. Mielnik, Quantum logic: is it necessarily orthocomplemented? in “Quantum Mechanics, Determinism, Causality and Particles”, Flato et al. eds., Reidel, Dordrecht (1976).

    Google Scholar 

  6. R. Haag, D. Kastler, J. Math. Phys. 5 (1964), p. 848.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. H. Araki, On characterization of the state space of quantum mechanics, (preprint), Inst, des Hautes Etudes Sci., France, (1979).

    Google Scholar 

  8. B. Mielnik, Commun. Math. Phys. 9 (1968), p. 55.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. C. Stanojevic, Trans. Am. Math. Soc. 183 (1973), p. 441; C. Stanojevic and C. Blakemore, Proc. Am. Math. Soc. 52 (1975)

    MathSciNet  MATH  Google Scholar 

  10. J.C.F. Belinfante, J. Math. Phys. 17 (1976), p. 285.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. V. Cantoni, Commun. Math. Phys. 44 (1975), p. 125; 56 (1977), p. 189.

    Article  MathSciNet  ADS  Google Scholar 

  12. G. Ludwig, Z. Naturforsch 22a (1967), p. 1303 and p. 1324; in “Foundations of Quantum Mechanics and Ordered Linear Space”, A. Hartkamper, H. Neumann eds.; Notes in Physics 29, Springer, Berlin (1973).

    Google Scholar 

  13. K.E. Hellwig, K. Kraus, Commun. Math. Phys. 11 (1969), p. 214; 16 (1970), p. 142.

    Article  MathSciNet  ADS  Google Scholar 

  14. B. Mielnik, Commun. Math. Phys. 15 (1969), p. 1.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. C.M. Edwards, Commun. Math. Phys. 16 (1970), p. 207; 20 (1971), p. 5; 260 (1972), p. 24.

    Article  ADS  MATH  Google Scholar 

  16. E.B. Davies, Commun. Math. Phys. 15 (1969), p. 277; 19 (1970), p. 83.

    Article  ADS  MATH  Google Scholar 

  17. E. Alfsen, W. Schultz, Non commutative spectral theory for affine function spaces on convex sets, Mem. Am. Math. Soc. 172 (1976), Providence R.I.; Acta Math. 140 (1978), p. 140.

    Google Scholar 

  18. S. Gudder, Commun. Math. Phys. 29 (1973), p. 249; 63 (1978), p. 265.

    Article  MathSciNet  ADS  Google Scholar 

  19. S.L. Woronowicz, Commun. Math. Phys. 51 (1976), p. 243.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. G.T. Ruttimann, J. Math. Phys. 18 (1977), p. 189; J. Austral. Math. Soc. XVIII (4) (1974), p. 433.

    Article  MathSciNet  ADS  Google Scholar 

  21. D.J. Foulis and C.H. Randall, J. Math. Phys. 13 (1972), p. 1667; 14 (1973), p. 1472; Operational approach to quantum mechanics in “Physical Theory as Logico-Operational Structure”, C.A. Hooker ed., Reidel, Dordrecht (1979).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  22. P. Mittelstaedt, Z. Naturforsch 27a (1972), p. 1358; Quantum logic in “Physical Theory as Logico-Operational Structure”, C.A. Hooker ed., Reidel, Dordrecht (1979); also E.W. Stachow, An operational approach to quantum probability in the same volume.

    MathSciNet  ADS  Google Scholar 

  23. B. Mielnik, Commun. Math. Phys. 37 (1974), p. 221.

    Article  MathSciNet  ADS  Google Scholar 

  24. R. Haag, U. Bannier, Commun. Math. Phys. 60 (1978), p. 1

    Article  MathSciNet  ADS  Google Scholar 

  25. B. Mielnik, Mobility of non-linear systems, (to appear in J. Math Phys.).

    Google Scholar 

  26. B. Mielnik, Rep. Math. Phys. 12 (1977), p. 331.

    Article  MathSciNet  ADS  Google Scholar 

  27. E. Lubkin, J. Math. Phys. 15 (1974), p. 673.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  28. J.C.T. Pool, Commun. Math. Phys. 9 (1968), p. 118 and p. 212.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  29. E.G. Beltrametti, G. Casinelli, Commun. Math. Phys. 40 (1975), p. 7; J. Philos. Logic. 6 (1977), p. 369.

    Article  ADS  MATH  Google Scholar 

  30. V. Gorini et al., J. Math. Phys. 17 (1976), p. 821; V. Gorini, A. Kossakowski, J. Math. Phys. 17 (1976), p. 1298; A. Frigerio, V. Gorini, J. Math. Phys. 17 (1976), p. 2123.

    Article  MathSciNet  ADS  Google Scholar 

  31. G. Lindblad, Commun. Math. Phys. 48 (1976), p. 119;. Phys. 48 (1976), p. 119; “A General H-theorem(…)”, preprint, Stockholm (1979).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  32. J. Schwinger, Phys. Rev. 91 (1953), p. 713.

    Article  MathSciNet  ADS  Google Scholar 

  33. J. Plebanski, private discussion at Latin-American Symposium of General Relativity, Mexico (1978).

    Google Scholar 

  34. J. Waniewski, Time inversion and mobility of many particle systems, preprint, Warsaw (1979).

    Google Scholar 

  35. W.E. Lamb Jr., An operational interpretation of non-relativistic quantum mechanics, Phys. Today 22. no. 4 (1969), p. 23.

    Article  Google Scholar 

  36. R. Haag, Subject, object and measurement, in “The Physicist’s Concept of Nature”, J. Mehra ed., Reidel, Dordrecht (1973).

    Google Scholar 

  37. Bell discussions in “Epistemological Letters” (1978–79).

    Google Scholar 

  38. B. Mielnik, Wave functions with positive and indefinite metric, preprint, Departement de Physique Theorique, Geneva (1979).

    Google Scholar 

  39. D. Finkelstein, discussion in “Hybridy” students club, Warsaw The logic of quantum physics. Trans. N.Y. Acad. Sci. D. Finkelstein et al., J. Math. Phys. 3 (1962), p. 207.

    Google Scholar 

  40. I. Bialynicki-Birula, J. Mycielski, Ann. Phys. 100 (1976), p. 62.

    Article  MathSciNet  ADS  Google Scholar 

  41. E.B. Davies, Commun. Math. Phys. 64 (1979), p. 191.

    Article  ADS  MATH  Google Scholar 

  42. N.W. Bazley, Nonlin, An. Th. Met. App. 3, no. 4 (1979), p. 539.

    MathSciNet  MATH  Google Scholar 

  43. C. Piron, B. Mielnik, Dialogue on quantum theories, (in preparation).

    Google Scholar 

  44. T.W.B. Kibble, Commun. Math. Phys. 64 (1978), p. 73; 65 (1979), p. 189.

    Article  MathSciNet  ADS  Google Scholar 

  45. R. Penrose, Gen. Rel. Grav. 7 (1976), p. 31.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  46. J.F. Plebanski, J. Math. Phys. 16 (1975), p. 2403; 18 (1977), p. 2511; J.D. Finley III and J.F. Plebanski, J. Math. Phys. 17 (1976), p. 185; 17 (1976), p. 2207; 19 (1978), p. 769. A. Garcia et al.. Gen Rel. Grav. 8 (1977), p. 841; J.F. Plebanski and I. Robinson, J. Math. Phys. 16 (1975), p. 2403; 17 (1976), p. 2203; J.F. Plebanski and I. Robinson, Complex space-times with null strings, in “Group Theoretical Methods in Physics”, R.T. Sharp and B. Kolman eds.. Academic Press, New York (1977).

    Article  MathSciNet  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1981 Plenum Press, New York

About this chapter

Cite this chapter

Mielnik, B. (1981). Motion and Form. In: Beltrametti, E.G., van Fraassen, B.C. (eds) Current Issues in Quantum Logic. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3228-2_34

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-3228-2_34

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-3230-5

  • Online ISBN: 978-1-4613-3228-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics