Skip to main content
SpringerLink
Log in

On the Concept of State in Quantum Mechanics: Another Way to Decoherence?

International Journal of Theoretical Physics volume 62, Article number: 46 (2023) Cite this article

Abstract

According to a formulation of the quantum theory presented by Rudolf Haag and Daniel Kastler more than half a century ago, the observables of a system, rather than the states, are the primary objects. In this paper we assume that only those observables that do really exist as measurement instruments determine the properties of the states. If this is the case, states that would be pure if all the self-adjoint operators corresponded to existing instruments may turn out to be statistical mixtures. This proposal, although not free from disconcerting implications on the very concept of state, may entail a new way of looking both at some of the most popular “paradoxes” and, more significantly, at the measuring process.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Notes

  1. The ideas expressed in this note are already present in [2].

  2. Due to the probabilistic nature of quantum mechanics, it must always be assumed the possibility of preparing many copies of the system in the same way: if all the copies are identical we say that the system is in a pure state, say |a〉; if we have ni copies of the system in the state |ai〉, we say that the system is in the statistical mixture \(\big \{|{a_{1}}\rangle ,p_{1}=\frac {n_{1}}{n};\ |{a_{2}}\rangle ,p_{2}=\frac {n_{2}}{n};\cdots \big \}\), \(n={\sum }_{i} n_{i} \).

  3. The ‘laboratory physics’ assumption differs from the algebraic approach of Haag-Kastler: there, the local algebras \(\mathfrak {A}(\text {B)}\) are the set of all observable in the bounded space-time region B, instead the ‘laboratory physics’ assumption has to do only with the observables (instruments) actually existing in a laboratory and these do not necessarily constitute an algebra.

  4. In the example considered no observable has nonvanishing matrix elements between |r〉 and |l〉 and, as a consequence, all states α|r〉 + β|l〉 are statistical mixtures. If instead both T1 and T3 (but not T2) were observables, not all such states are mixture: states with α and β real are pure, while α|r〉 + iβ|l〉 are statistical mixtures.

  5. The correct formulation of Schrödinger’s cat paradox should include not only the state of the cat, but also that of the ampoule of cyanide (|broken〉,|not broken〉) or, equivalently, the decaying radioactive atom. This was pointed out in [2]. See also [7].

  6. The concept expressed by the term decoherence finds an ante litteram application, long before the term itself was invented, see [10].

References

  1. Einstein, A., Podolsky, B., Rosen, N.: Can Quantum-Mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)

    Article  MATH  ADS  Google Scholar 

  2. Picasso, L.E.: Lectures in Quantum Mechanics – a Two Term Course, pp 338–343. Springer, Berlin (2016)

    Book  Google Scholar 

  3. Haag, R., Kastler, D.: An algebraic approach to quantum field theory. J. Math. Phys. 5, 848 (1964)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  4. Wick, G.C., Wightman, A.S., Wigner, E.P.: The intrinsic parity of elementary particles. Phys. Rev. 88, 101 (1952)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  5. Aspect, A., Grangier, P., Roger, G.: Experimental realization of Einstein-Podolsky-Rosen-Bohm gedankenexperiment: a new violation of bell’s inequalities. Phys. Rev. Lett. 49, 91–94 (1982)

    Article  ADS  Google Scholar 

  6. Yin, et al.: Satellite-based entanglement distribution over 1200 kilometers. Science 356, 1140–1144 (2017)

    Article  Google Scholar 

  7. Rinner, Stefan, Werner, Ernst: On the role of entanglement in schrödinger’s cat paradox. Cent. Eur. J. Phys. 6(1), 178–183 (2008)

    Google Scholar 

  8. Wechsler, S.D.: The Quantum Mechanics Needs the Principle of Wave-Function Collapse–But This Principle Shouldn’t Be Misunderstood. J. Quantum Inf. Sci. 11, 42–63 (2021)

    Article  Google Scholar 

  9. David Mermin, N.: Could Feynman have said this? Phys. Today 57 (5), 10 (2004)

    Article  Google Scholar 

  10. Fabri, E., Fiorio, G.: Charge superselection arising from random electromagnetic interactions. Il Nuovo Cimento 27, 1037 (1963)

    Article  ADS  Google Scholar 

  11. Zurek, W.: Decoherence and the Transition from Quantum to Classical–Revisited. Los Alamos Science Number 27. and the references therein (2002)

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Fisica, Università di Pisa, Pisa, Italy

    Luigi E. Picasso

Authors
  1. Luigi E. Picasso
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Luigi E. Picasso.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Picasso, L.E. On the Concept of State in Quantum Mechanics: Another Way to Decoherence?. Int J Theor Phys 62, 46 (2023). https://doi.org/10.1007/s10773-023-05305-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10773-023-05305-z

Keywords

search

Navigation