Skip to main content
SpringerLink
Log in

Towards a General Operational and Realistic Framework for Quantum Mechanics and Relativity Theory

  • Chapter
Quo Vadis Quantum Mechanics?

Part of the book series: The Frontiers Collection ((FRONTCOLL))

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover 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. von Neumann, J.V. (1932): Mathematische Grundlagen der Quantenmechanik, Springer, Berlin

    MATH  Google Scholar 

  2. Birkhoff, G., and von Neumann, J. (1936): The logic of quantum mechanics, Annals of Mathematics 37, 823–843

    Google Scholar 

  3. Wigner, E.P. (1959): Group Theory and its Applications to Quantum Mechanics of Atomic Spectra, Academic Press, New York

    Google Scholar 

  4. Mittelstaedt, P. (1963): Philosophische Probleme der Modernen Physik, Bibliographisches Institut, Manheim

    Google Scholar 

  5. Mackey, G. (1963): Mathematical Foundations of Quantum Mechanics, Benjamin, New York

    MATH  Google Scholar 

  6. Piron, C. (1964): Axiomatique quantique, Helv. Phys. Acta 37, 439–468

    MATH  MathSciNet  Google Scholar 

  7. Piron, C. (1976): Foundations of Quantum Physics, Benjamin, Massachusetts

    MATH  Google Scholar 

  8. Aerts, D. (1981): The One and the Many: Towards a Unification of the Quantum and Classical Description of One and Many Physical Entities, Doctoral dissertation, Brussels Free University

    Google Scholar 

  9. Aerts, D. (1982): Description of many physical entities without the paradoxes encountered in quantum mechanics, Found. Phys. 12, 1131–1170

    Article  MathSciNet  ADS  Google Scholar 

  10. Aerts, D. (1983): Classical theories and non-classical theories as a special case of a more general theory, J. Math. Phys. 24, 2441–2453

    Article  ADS  MathSciNet  Google Scholar 

  11. Aerts, D. (1999): Foundations of quantum physics: a general realistic and operational approach, Int. J. Theor. Phys. 38, 289–358, quant-ph/0105109

    Article  MATH  MathSciNet  Google Scholar 

  12. Aerts, D. (1999): Quantum mechanics: structures, axioms and paradoxes. In: Quantum Mechanics and the Nature of Reality, ed. by Aerts, D., and Pykacz, J., Kluwer Academic, Dordrecht, quant-ph/0106132

    Google Scholar 

  13. Aerts, D., Colebunders, E., Van der Voorde, A., Van Steirteghem, B. (1999): State property systems and closure spaces: A study of categorical equivalence, Int. J. Theor. Phys. 38, 359–385, quant-ph/0105108

    Article  MATH  Google Scholar 

  14. Aerts, D. (2002): Being and change: Foundations of a realistic operational formalism. In: Probing the Structure of Quantum Mechanics: Nonlinearity, Nonlocality, Probability and Axiomatics, ed. by Aerts, D., Czachor, M., and Durt, T., World Scientific, Singapore

    Google Scholar 

  15. Keller, H. (1980): Ein nicht-klassischer Hilbertscher Raum, Math. Z. 172, 41–49

    Article  MATH  MathSciNet  Google Scholar 

  16. Solèr, M.P. (1995): Characterization of Hilbert spaces by orthomodular spaces, Comm. Algebra 23, 219–243

    Article  MATH  MathSciNet  Google Scholar 

  17. Aerts, D., and Van Steirteghem, B. (2000): Quantum axiomatics and a theorem of M.P. Solèr, Int. J. Theor. Phys. 39, 497–502, quant-ph/0105107

    Article  MATH  Google Scholar 

  18. Aerts, D., D’Hondt, E., Gabora, L. (2000): Why the disjunction in quantum logic is not classical, Found. Phys. 30, 1473–1480, quant-ph/0007041

    Article  MathSciNet  Google Scholar 

  19. Piron, C. (1990): Mécanique Quantique: Bases et Applications, Press Polytechnique de Lausanne, Suisse

    MATH  Google Scholar 

  20. Valckenborgh, F. (2000): Operational axiomatics and compound systems. In: Current Research in Operational Quantum Logic: Algebras, Categories, Languages, ed. by Coecke, B., Moore, D.J., and Wilce, A., Kluwer Academic Publishers, Dordrecht, 219–244

    Google Scholar 

  21. Valckenborgh, F. (2001): Compound Systems in Quantum Axiomatics, Doctoral Thesis, Brussels Free University

    Google Scholar 

  22. Durt, T., and D’Hooghe, B. (2002): The classical limit of the lattice-theoretical orthocomplementation in the framework of the hidden-measurement approach. In: Probing the Structure of Quantum Mechanics: Nonlinearity, Nonlocality, Computation and Axiomatics, ed. by Aerts, D., Czachor, M., and Durt, T., World Scientific, Singapore

    Google Scholar 

  23. Artin, E. (1957): Geometric Algebra, Interscience Publishers Inc., New York

    MATH  Google Scholar 

  24. Aerts, D. (1982): Example of a macroscopical situation that violates Bell inequalities, Lett. Nuovo Cimento 34, 107–111

    Article  Google Scholar 

  25. Aerts, D. (1984): How do we have to change quantum mechanics in order to describe separated systems. In: The Wave-Particle Dualism, ed. by Diner, S., et al., Kluwer Academic, Dordrecht, 419–431

    Google Scholar 

  26. Aerts, D. (1988): The description of separated systems and quantum mechanics, and a possible explanation for the probabilities of quantum mechanics. In: Micro-physical Reality and Quantum Formalism, ed. by van der Merwe, A., et al., Kluwer Academic Publishers, 97–115

    Google Scholar 

  27. Aerts, D. (1990): An attempt to imagine parts of the reality of the micro-world. In: Proceedings of the Conference ‘Problems in Quantum Physics’ Gdansk89, World Scientific, Singapore, 3–25

    Google Scholar 

  28. Aerts, D., Aerts, S., Broekaert, J., and Gabora, L. (2000): The violation of Bell inequalities in the macroworld, Found. Phys. 30, 1387–1414

    Article  MathSciNet  Google Scholar 

  29. Aerts, D. (1985): The physical origin of the Einstein-Podolsky-Rosen-paradox. In: Open Questions in Quantum Physics: Invited Papers on the Foundations of Microphysics, ed. by Tarozzi, G., and van der Merwe, A., Kluwer Academic, Dordrecht, 33–50

    Google Scholar 

  30. Christiaens, W. (2002): Some notes on Aerts’ interpretation of the EPRparadox and the violation of Bell inequalities. In: Probing the Structure of Quantum Mechanics: Nonlinearity, Nonlocality, Computation and Axiomatics, ed. by D. Aerts, M. Czachor and T. Durt, World Scientific, Singapore

    Google Scholar 

  31. Aerts, D. (1983): A possible explanation for the probabilities of quantum mechanics and a macroscopic situation that violates Bell inequalities. In: Recent Developments in Quantum Logic, ed. by P. Mittelstaedt et al., in Grundlagen der Exacten Naturwissenschaften, Vol. 6, Wissenschaftverlag, Bibliographisches Institut, Mannheim, 235

    Google Scholar 

  32. Aerts, D. (1986): A possible explanation for the probabilities of quantum mechanics, J. Math. Phys. 27, 202

    Article  ADS  MathSciNet  Google Scholar 

  33. Aerts, D. (1987): The origin of the non-classical character of the quantum probability model. In: Information, Complexity, and Control in Quantum Physics, ed. by A. Blanquiere et al., Springer-Verlag, Berlin

    Google Scholar 

  34. Aerts, D. (1994): Quantum structures, separated physical entities and probability, Found. Phys. 24, 1227

    Article  MathSciNet  ADS  Google Scholar 

  35. Coecke, B. (1995): Hidden measurement representation for quantum entities described by finite-dimensional complex Hilbert spaces, Found. Phys. 25, 1185

    Article  MathSciNet  ADS  Google Scholar 

  36. Coecke, B. (1995): Generalization of the proof on the existence of hidden measurements to experiments with an infinite set of outcomes, Found. Phys. Lett. 8, 437

    MathSciNet  Google Scholar 

  37. Coecke, B. (1995): Hidden measurement model for pure and mixed states of quantum physics in Euclidean space, Int. J. Theor. Phys. 34, 1313

    Article  ADS  MATH  MathSciNet  Google Scholar 

  38. Aerts, D. (1995): Quantum structures: An attempt to explain the origin of their appearance in nature, Int. J. Theor. Phys. 34, 1165

    Article  MATH  MathSciNet  Google Scholar 

  39. Aerts, D., Aerts, S. (1997): The hidden measurement formalism: Quantum mechanics as a consequence of fluctuations on the measurement. In: New Developments on Fundamental Problems in Quantum Physics, ed. by M. Ferrero and A. van der Merwe, Kluwer Academic, Dordrecht

    Google Scholar 

  40. Aerts, D., Aerts, S., Coecke, B., D’Hooghe, B., Durt, T., and Valckenborgh, F. (1997): A model with varying fluctuations in the measurement context. In: New Developments on Fundamental Problems in Quantum Physics, ed. by M. Ferrero and A. van der Merwe, Kluwer Academic, Dordrecht, 7

    Google Scholar 

  41. Aerts, D. (1998): The hidden measurement formalism: What can be explained and where paradoxes remain, Int. J. Theor. Phys. 37, 291, and quantph/0105126

    Article  MATH  MathSciNet  Google Scholar 

  42. Aerts, D., and Aerts, S. (1994): Applications of quantum statistics in psychological studies of decision processes, Found. Sc. 1, 85

    MathSciNet  Google Scholar 

  43. Aerts, S. (1996): Conditional probabilities with a quantal and a Kolmogorovian limit, Int. J. Theor. Phys 35, 11, 2245

    MATH  Google Scholar 

  44. Aerts, S. (1998): Interactive probability models: Inverse problems on the sphere, Int. J. Theor. Phys. 37, 1

    Article  MATH  Google Scholar 

  45. Aerts, S. (2002): Hidden measurements from contextual axiomatics. In: Probing the Structure of Quantum Mechanics: Nonlinearity, Nonlocality, Probability and Axiomatics, ed. by Aerts, D., Czachor, M., and Durt, T., World Scientific, Singapore

    Google Scholar 

  46. Aerts, D. (2002): Reality and probability: Introducing a new type of probability calculus. In: Probing the Structure of Quantum Mechanics: Nonlinearity, Nonlocality, Computation and Axiomatics, ed. by Aerts, D., Czachor, M., and Durt, T., World Scientific, Singapore

    Google Scholar 

  47. Aerts, S. (2003): The Born rule from a consistency requirement on hidden measurements in complex Hilbert space, submitted to Int. J. Theor. Phys., http://arXiv.org/abs/quant-ph/0212151

    Google Scholar 

  48. Aerts, D., Durt, T., and Van Bogaert, B. (1993): Quantum probability, the classical limit and nonlocality. In: Proceedings of the International Symposium on the Foundations of Modern Physics 1992, Helsinki, Finland, ed. by T. Hyvonen, World Scientific, Singapore, 35–56

    Google Scholar 

  49. Aerts, D., and Durt, T. (1994): Quantum, classical and intermediate, an illustrative example, Found. Phys. 24, 1353–1369

    Article  MathSciNet  ADS  Google Scholar 

  50. Aerts, D., and Durt, T. (1994): Quantum, classical and intermediate: A measurement model. In: Symposium on the Foundations of Modern Physics, ed. by K.V. Laurikainen, C. Montonen and K. Sunnaborg, Editions Frontières,Gives-sur-Yvettes, France

    Google Scholar 

  51. Aerts, D., Coecke, B., Durt, T., and Valckenborgh, F. (1997): Quantum, classical and intermediate I: A model on the Poincarè sphere, Tatra Mt. Math. Publ. 10, 225

    MathSciNet  MATH  Google Scholar 

  52. Aerts, D., Coecke, B., Durt, T., and Valckenborgh, F. (1997): Quantum, classical and intermediate II: The vanishing vector space structure, Tatra Mt. Math. Publ. 10, 241

    MathSciNet  MATH  Google Scholar 

  53. Aerts, D., Aerts, S., Durt, T., and Lévêque, O. (1999): Classical and quantum probability in the epsilon model, Int. J. Theor. Phys. 38, 407–429

    Article  MATH  Google Scholar 

  54. Aerts, D. (1995): The game of the biomousa: A view of discovery and creation. In: Perspectives on the World, an Interdisciplinary Reflection, ed. by D. Aerts, L. Apostel, B. De Moor, S. Hellemans, E. Maex, H. Van Belle, J. Van der Veken, Brussels University Press, Brussels

    Google Scholar 

  55. Aerts, D. (1998): The entity and modern physics: The creation-discovery view of reality. In: Interpreting Bodies: Classical and Quantum Objects in Modern Physics, ed. by Castellani, E., Princeton University Press, Princeton

    Google Scholar 

  56. Aerts, D. (1999): The stuff the world is made of: Physics and reality. In: Einstein meets Magritte: An Interdisciplinary Reflection, ed. by Aerts, D., Broekaert, J., and Mathijs, E., Kluwer Academic, Dordrecht, quant-ph/0107044

    Google Scholar 

  57. Aerts, D. (1999): The game of the biomousa: A view of discovery and creation. In: Worldviews and the Problem of Synthesis, ed. by Aerts, D., Van Belle, H., and Van der Veken, J., KLuwer Academic, Dordrecht

    Google Scholar 

  58. Aerts, D., and Coecke, B. (1999): The creation-discovery view: Towards a possible explanation of quantum reality. In: Language, Quantum, Music: Selected Contributed Papers of the Tenth International Congress of Logic, Methodology and Philosophy of Science, Florence, August 1995, ed. by Dalla Chiara, M.L., Giuntini, R., and Laudisa, F., Kluwer Academic, Dordrecht

    Google Scholar 

  59. Aerts, D. (1992): The construction of reality and its influence on the understanding of quantum structures, Int. J. Theor. Phys. 31, 1815–1837

    Article  MathSciNet  Google Scholar 

  60. Aerts, D. (1996): Relativity theory: What is reality?, Found. Phys. 26, 1627–1644

    Article  MathSciNet  ADS  Google Scholar 

  61. Aerts, D. (1996): Framework for possible unification of quantum and relativity theories, Int. J. Theor. Phys. 35, 2399–2416

    Article  MATH  MathSciNet  Google Scholar 

  62. Aerts, D. (2001): The unification of personal presents: A dialogue of different world views. To be published in: Ontology of Dialogue: The International Readings on Theory, History and Philosophy of Culture, ed. by Moreva, L.M.

    Google Scholar 

  63. Sjödin, T. (1979): Synchronization in special relativity and related theories Nuovo Cim. 51B, 229–245

    Article  ADS  Google Scholar 

  64. Goy, F., and Selleri, F. (1997): Time on a rotating platform, Found. Phys. Lett. 10, 17–29

    Article  MathSciNet  Google Scholar 

Download references

Authors
  1. Diederik Aerts
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sven Aerts
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Unit of Interdisciplinary Studies, Bar-Ilan University, 52900, Ramat-Gan, Israel

    Avshalom C. Elitzur

  2. The Edelstein Center for the History and Philosophy of Science, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel

    Shahar Dolev

  3. Center for Frontier Sciences, Temple University, 19122, Philadelphia, PA, USA

    Nancy Kolenda

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Center for Frontier Sciences

About this chapter

Cite this chapter

Aerts, D., Aerts, S. (2005). Towards a General Operational and Realistic Framework for Quantum Mechanics and Relativity Theory. In: Elitzur, A.C., Dolev, S., Kolenda, N. (eds) Quo Vadis Quantum Mechanics?. The Frontiers Collection. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-26669-0_11

Download citation

Publish with us

Policies and ethics

Search

Navigation