Skip to main content

Description of Compound Physical Systems and Logical Interaction of Physical Systems

  • Chapter
Current Issues in Quantum Logic

Abstract

It seems to be difficult to give a description of the whole universe at once, so we are always obliged to consider subsystems of a bigger physical system. We all know that quantum mechanics is not compatible with this situation. A lot of problems of interpretation are due to this fact. Some physicists do not bother about this situation because for them an isolated system is an idealization of the real situation and the theory need not be able to describe such an idealization. I think the procedure of considering subsystems and describing them as isolated systems is much more fundamental. One can ask for example the following question: “Should we ever have found mathematics without considering our fingers as isolated systems?” One could protest by saying that to do quantum logic one does not need mathematics. But then it is possible to ask the following question: “Should we ever have agreed to treat two symbols a and b written on the blackboard as being two symbols and not a mass of chalk dust if we should never have seen and understood two cars as two cars, two houses as two houses, etc…”. So the situation seems to be that we use a language to describe nature and this language is built up with the notion of isolated systems. There have been several attempts to axiomatize this language (e.g. logic, set theory).

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. I. Tjing: first division, 4 Meng, The Folly of Youth (p. 15 in the Dutch translation edited by A.N.K.H. Hermes and B.V. Deventer, 1977 ).

    Google Scholar 

  2. Carlos Casteneda, Three witnesses to the nagual, in “Tales of Power”, Penguin, Harmondworth, Middlesex (1974).

    Google Scholar 

  3. C. Piron, “Foundations of Quantum Physics”, W.A. Benjamin (1976),

    Google Scholar 

  4. D. Aerts, Ph.D. Thesis (in preparation), Vrije Universiteit Brüssel.

    Google Scholar 

  5. C. Piron, Annales de la Fondation Louis de Broglie 3, no. 3 (1978), pp. 131 - 173.

    Google Scholar 

  6. R.P. Morash, Proc. Amer. Math. Soc. 27, no. 3 (1971).

    Google Scholar 

  7. J. Wilbur, Proc. Amer. Math. Soc. 233 (1977).

    Google Scholar 

  8. E. Artin, “Geometric Algebra”, Interscience Publishers, New York (1957).

    MATH  Google Scholar 

  9. B. Mitchell, “Theory of Categories”, Academic Press, New York-London (1965).

    MATH  Google Scholar 

  10. D. Aerts and I. Daubechies, Helv. Phys. Acta 51 (1978), pp. 661–675.

    MathSciNet  Google Scholar 

  11. M. Günaydin et al., Comm. Math. Phys. 61 (1978), pp. 69–85.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. D. Aerts, Sybsystem in physics described by bi-linear maps between the corresponding vector spaces, to be published in J. Math. Phys.

    Google Scholar 

  13. D. Aerts, Construction of a structure which makes it possible to describe the joint system of a classical system together with a quantum system, (submitted to Reports on Math. Phys.).

    Google Scholar 

  14. D. Aerts, Tensor products of lattices, (in preparation).

    Google Scholar 

  15. D. Finkelstein et al., CERN Report 59, no. 7 (1959).

    Google Scholar 

  16. D. Aerts and C. Piron, “Physical Justification for using the Anti-symmetric Tensor Product to Describe the Joint System of Identical Systems in Quantum Mechanics”, preprint, TENA, Free University of Brussels.

    Google Scholar 

  17. D. Aerts, “Identical Systems in Physics Described by Antisymmetric Bi-linear maps Between the Corresponding Vector Spaces”, preprint, TENA, Free University of Brussels.

    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

Aerts, D. (1981). Description of Compound Physical Systems and Logical Interaction of Physical Systems. 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_26

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-3228-2_26

  • 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