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Foundations of Physics

, Volume 26, Issue 9, pp 1121–1164 | Cite as

The theoretical apparatus of semantic realism: A new language for classical and quantum physics

  • Claudio Garola
  • Luigi Solombrino
Article

Abstract

The standard interpretation of quantum physics (QP) and some recent generalizations of this theory rest on the adoption of a rerificationist theory of truth and meaning, while most proposals for modifying and interpreting QP in a “realistic” way attribute an ontological status to theoretical physical entities (ontological realism). Both terms of this dichotomy are criticizable, and many quantum paradoxes can be attributed to it. We discuss a new viewpoint in this paper (semantic realism, or briefly SR), which applies both to classical physics (CP) and to QP. and is characterized by the attempt of giving up verificationism without adopting ontological realism. As a first step, we construct a formalized observative language L endowed with a correspondence truth theory. Then, we state a set of axioms by means of L which hold both in CP and in QP. and construct a further language Lv which can express bothtestable andtheoretical properties of a given physical system. The concepts ofmeaning andtestability do not collapse in L and Le hence we can distinguish between semantic and pragmatic compatibility of physical properties and define the concepts of testability and conjoint testability of statements of L and Le. In this context a new metatheoretical principle (MGP) is stated, which limits the validity of empirical physical laws. By applying SR (in particular. MGP) to QP, one can interpret quantum logic as a theory of testability in QP, show that QP is semantically incomplete, and invalidate the widespread claim that contextuality is unavoidable in QP. Furthermore. SR introduces some changes in the conventional interpretation of ideal measurements and Heisenberg’s uncertainty principle.

Keywords

Uncertainty Principle Quantum Logic Classical Physic Physical Entity Truth Theory 
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.

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References

  1. 1.
    C. Garola. “Classical foundations of quantum logic.”Int. J. Theor. Phys. 30. 1 (1991).Google Scholar
  2. 2.
    C. Garola. “Semantic incompleteness of quantum physics.”Int. J. Theor. Phys. 31. 809 (1992).Google Scholar
  3. 3.
    C. Garola. “Quantum logics seen as quantum testability theories.”Int. J. Theor. Phys. 31. 1639 (1992).Google Scholar
  4. 4.
    C. Garola. “Truth versus testability in quantum logic.”Erkenntnis 37. 197 (1992).Google Scholar
  5. 5.
    C. Garola. “Semantic incompleteness of quantum physics and EPR-like paradoxes.”Int. J. Theor. Phys. 32. 1863 (1993).Google Scholar
  6. 6.
    C. Garola. “Reconciling local realism and quantum physics: a critique to Bell.”Theor. Mat. Fiz 99. 285 (1994).Google Scholar
  7. 7.
    C. Garola. “Criticizing Bell: Local realism and quantum physics reconciled.”Int. J. Theor. Phys. 34. 269 (1995).Google Scholar
  8. 8.
    C. Garola. “Questioning nonlocality: an operational critique to Bell’s theorem.” inThe Foundations of Quantum Mechanics. Historical Analysis and Open Questions. C. Garola and A. Rossi, eds. (Kluwer Academic. Dordrecht. 1995). p. 273.Google Scholar
  9. 9.
    C. Garola. “Pragmatic versus semantic contextuality in quantum physics.”Int. J. Theor. Phys. 34. 1383 (1995).Google Scholar
  10. 10.
    A. Einstein. B. Podolsky. and N. Rosen. “Can quantum mechanical description of reality be considered complete?.”Phys. Rev. 47. 777 (1935).Google Scholar
  11. 11.
    N. Bohr.Atomic Physics and Human Knowledge (Wiley. New York. 1958).Google Scholar
  12. 12.
    N. Bohr.Essays 1958 1962 on Atomic Physics and Human Knowledge (Wiley. New York. 1963).Google Scholar
  13. 13.
    W. Heisenberg.The Physical Principles of Quantum Theory (Dover, New York. 1930).Google Scholar
  14. 14.
    B. C. Van Fraassen. “A modal interpretation of quantum mechanics.” inCurrent Issues in Quantum Logic. E. G. Beltrametti and B. C. Van Fraassen. eds. (Plenum. New York. 1981).Google Scholar
  15. 15.
    R. B. Braithwaite.Scientific Explanation (Cambridge University Press. Cambridge. 1953).Google Scholar
  16. 16.
    C. C. Hempel.Aspects of Scientific Explanation (Free Press. New York. 1965).Google Scholar
  17. 17.
    B. Russell.An Inquiry into Meaning and Truth (Allen & Unwin. London. 1940).Google Scholar
  18. 18.
    R. Carnap. “Truth and confirmation.” inReadings in Philosophical Analysis. H. Feigl and W. Sellars. eds. (Appleton-Century-Crofts. New York. 1949).Google Scholar
  19. 19.
    R. Carnap.Philosophical Foundations of Physics (Basic Books. New York 1966).Google Scholar
  20. 20.
    K. R. Popper.Conjectures and Refutations (Routledge & Kegan Paul. London. 1969).Google Scholar
  21. 21.
    P. Bush. P. J. Lathi. and P. Mittelstaedt.The Quantum Theory of Measurement (Springer. Berlin. 1991).Google Scholar
  22. 22.
    G. Birkhoff and J. von Neumann. “The logic of quantum mechanics.”Ann. Math. 37. 823 (1936).Google Scholar
  23. 23.
    A. Tarski. “The semantic conception of truth and the foundations of semantics.” inSemantics and the Philosophy of Language L. Linsky. ed. (University of Illinois Press. Urbana. 1952).Google Scholar
  24. 24.
    C. Dalla Pozza and C. Garola. “A pragmatic interpretation of intuitionistic propositional logic.”Erkenntnis 43. 81 (1995).Google Scholar
  25. 25.
    M. Jammer.The Philosophy of Quantum Mechanics (Wiley. New York. 1974).Google Scholar
  26. 26.
    H. Reichenbach.Philosophic Foundations of Quantum Mechanics (University of California Press. Los Angeles. 1965).Google Scholar
  27. 27.
    J. S. Bell. “On the problem of hidden variables in quantum mechanics.”Rev. Mod. Phys.38. 447 (1966).Google Scholar
  28. 28.
    S. Kochen and E. P. Specker. “The problem of hidden variables in quantum mechanics.”J. Math. Mech. 17. 59 (1967).Google Scholar
  29. 29.
    N. D. Mermin. “Hidden variables and the two theorems of John Bell.”Rev. Mod. Phys.65. 803 (1993).Google Scholar
  30. 30.
    J. S. Bell. “On the Einstein Podolsky Rosen paradox.”Physics 1. 195 (1964).Google Scholar
  31. 31.
    E. P. Wigner. “On hidden variables and quantum mechanical probabilities.”Am. J. Phys.38. 1005 (1970).Google Scholar
  32. 32.
    F. Selleri. “History of the Einstein Podolsky Rosen paradox.” inQuantum Mechanics Versus Local Realism. F. Selleri. ed. (Plenum. New York. 1988). p. 1.Google Scholar
  33. 33.
    D. M. Greenberger. M. A. Horne. A. Shimony. and A. Zeilinger. “Bell’s theorem without inequalities.”Am. J. Phys. 58. 1131 (1990).Google Scholar
  34. 34.
    R. K. Clifton, M. L. G. Redhead, and J. M. Butterfield, “Generalization of the Greenberger Horne Zeilinger algebraic proof of nonlocality.”Found. Phys. 21. 149 (1991).Google Scholar
  35. 35.
    J. J. Sakurai,Modern Quatum Mechanics (Benjamin. Reading. Massachusetts. 1985).Google Scholar
  36. 36.
    C. Garola and L. Solombrino. “Semantic realism versus EPR-like paradoxes: the Furry, Bohm-Aharonov. and Bell paradoxes.”Found. Phys. 26. 1329 (1996).Google Scholar
  37. 37.
    B. D’Espagnat,Conceptual Foundations of Quantum Mechanics (Benjamin, Reading. Massachusetts. 1976).Google Scholar
  38. 38.
    W. M. De Muynck. W. De Baere, and H. Martens. “Interpretation of quantum mechanics, joint measurements of incompatible observables, and counterfactual definiteness.”Found. Phys. 24. 1589 (1994).Google Scholar
  39. 39.
    H. P. Stapp. “Comments on ‘Interpretation of quantum mechanics, joint measurement of incompatible observables and counterfactual definiteness’.”Found. Phys. 24. 1665 (1995).Google Scholar
  40. 40.
    D. Aerts. “Description of many physical entities without the paradoxes encountered in quantum mechanics.”Found. Phys. 12. 1131 (1982).Google Scholar
  41. 41.
    D. Foulis, C. Piron. C. Randall. “Realism, operationalism and quantum mechanics.”Found. Phys. 13. 813 (1983).Google Scholar
  42. 42.
    G. Ludwig,Foundations of Quantum Mechanics I (Springer. New York. 1983).Google Scholar
  43. 43.
    C. Piron.Foundations of Quantum Physics (Benjamin, Reading. Massachusetts. 1976).Google Scholar
  44. 44.
    C. Garola. “Embedding of posets into lattices in quantum logic.”Int. J. Theor. Phys. 24. 423 (1985).Google Scholar
  45. 45.
    K. Bugajska and S. Bugajski. “The lattice structure of quantum logics.”Ann. Inst. Henri Poincaré XIX. 333 (1973).Google Scholar
  46. 46.
    G. M. Mackey.The Mathematical Foundations of Quantum Mechanics (Benjamin. New York. 1963).Google Scholar
  47. 47.
    J. M. Jauch.Foundations of Quantum Mechanics (Addison Wesley. Reading, Massachusetts. 1968).Google Scholar
  48. 48.
    C. Garola “Propositions and orthocomplementation in quantum logic.”Int. J. Theor. Phys. 19. 369 (1980).Google Scholar
  49. 49.
    C. Garola and L. Solombrino. “Yes-no experiments and ordered structures in quantum physics,”Nuovo Cimento 77B. 87 (1983).Google Scholar
  50. 50.
    G. Cattaneo, C. Dalla Pozza. C. Garola. and G. Nisticó, “On the logical foundations of the Jauch-Piron approach to quantum physics.”Int. J. Theor. Phys. 27. 1313 (1988).Google Scholar
  51. 51.
    G. Cattaneo, C. Garola, and C. Nisticó, “Preparation-effects versus question-preparation structures.”J. Phys. Ess. 2. 197 (1989).Google Scholar
  52. 52.
    D. Dieks. “Quantum mechanics without the projection postulate and its realistic interpretation.”Found. Phys. 19. 1397 (1989).Google Scholar
  53. 53.
    K. Gottfried. “Does quantum mechanics carry the seeds of its own destruction?.”Phys. Worlds 4 (10). 34 (1991).Google Scholar
  54. 54.
    J. Bub. “Quantum mechanics without the projection postulate,”Found. Phys. 22. 737 (1992).Google Scholar
  55. 55.
    G. Cattaneo and G. Nisticó, “Interpretative remarks in quantum mechanics.” inThe Foundations of Quantum Mechanics. Historical Analysis and Open Questions. C. Garola and A. Rossi. eds. (Kluwer Academic. Dordrecht. 1995). p. 127.Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • Claudio Garola
    • 1
  • Luigi Solombrino
    • 1
  1. 1.Dipartimento di Fisica dell’Università and INFNLeceeItaly

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