Skip to main content

Two Results in the Quantum Theory of Measurements

  • Chapter
  • First Online:
Trails in Modern Theoretical and Mathematical Physics

Abstract

Two theorems with applications to the quantum theory of measurements are stated and proven. The first one clarifies and amends von Neumann’s Measurement Postulate used in the Copenhagen interpretation of quantum mechanics. The second one clarifies the relationship between “events” and “measurements” and the meaning of measurements in the ETH-Approach to quantum mechanics.

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 99.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 129.99
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

Notes

  1. 1.

    As far as we remember, Gianni Morchio had an interest in the foundations of quantum mechanics; so he would probably have appreciated our results.

  2. 2.

    The only systems for which (in our opinion) the “measurement problem” has a satisfactory solution.

References

  1. Fröhlich, J., Schubnel, B.: Quantum probability theory and the foundations of quantum mechanics. In: Blanchard, P., Fröhlich, J. (eds.) The Message of Quantum Science. Springer, Berlin (2015). arXiv:1310.1484 (see also: Ph. Blanchard, J. Fröhlich and B. Schubnel, A “garden of forking paths” – The quantum mechanics of histories of events, Nucl. Phys. B 912, 463–484 (2016))

    Google Scholar 

  2. Fröhlich, J., Pizzo, A.: The Time-Evolution of States in Quantum Mechanics according to the ETH-Approach. Commun. Math. Phys. 389, 1673–1715 (2022)

    Article  ADS  MathSciNet  Google Scholar 

  3. Fröhlich, J., Gang, Z., Pizzo, A.: A Tentative Completion of Quantum Mechanics. arXiv:2303.11112v1 [math-ph] (2023)

    Google Scholar 

  4. von Neumann, J.: Mathematical foundations of quantum mechanics (with an introduction by Iván Abonyi). Akadémiai Kiadó (Publishing House of the Hungarian Academy of Sciences), Budapest (1980). (translated from the 1964 Russian edition by Ákos Sebestyén) (see also: G. Lüders, Über die Zustandsänderung durch den Messprozess, Annalen der Physik, 443(5–8) 322–328 (1950))

    Google Scholar 

  5. Lin, H.: Almost commuting self-adjoint matrices and applications. Fields Inst. Commun. 13, 193 (1995)

    ADS  Google Scholar 

  6. Hastings, M.B.: Making Almost Commuting Matrices Commute. Commun. Math. Phys. 291, 321–345 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  7. Kachkovskiy, I., Safarov, Y.: Distance to Normal Elements in \(C^{*}\)-Algebras of Real Rank Zero. arXiv:1403.2021v3 [math.OA] (2015)

    Google Scholar 

  8. Fröhlich, J., Schubnel, B.: Do we understand quantum mechanics – finally? In: Reiter, W.L., Yngvason, J. (eds.) Erwin Schrödinger – 50 Years After, ESI Lectures in Mathematics and Physics. pp. 37–84. European Mathematical Society Publ (2013)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jürg Fröhlich .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Del Vecchio, S., Fröhlich, J., Pizzo, A., Ranallo, A. (2023). Two Results in the Quantum Theory of Measurements. In: Cintio, A., Michelangeli, A. (eds) Trails in Modern Theoretical and Mathematical Physics. Springer, Cham. https://doi.org/10.1007/978-3-031-44988-8_9

Download citation

Publish with us

Policies and ethics