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The Measurement Problem: Decoherence and Convivial Solipsism

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Abstract

The problem of measurement is often considered an inconsistency inside the quantum formalism. Many attempts to solve (or to dissolve) it have been made since the inception of quantum mechanics. The form of these attempts depends on the philosophical position that their authors endorse. I will review some of them and analyze their relevance. The phenomenon of decoherence is often presented as a solution lying inside the pure quantum formalism and not demanding any particular philosophical assumption. Nevertheless, a widely debated question is to decide between two different interpretations. The first one is to consider that the decoherence process has the effect to actually project a superposed state into one of its classically interpretable component, hence doing the same job as the reduction postulate. For the second one, decoherence is only a way to show why no macroscopic superposed state can be observed, so explaining the classical appearance of the macroscopic world, while the quantum entanglement between the system, the apparatus and the environment never disappears. In this case, explaining why only one single definite outcome is observed remains to do. In this paper, I examine the arguments that have been given for and against both interpretations and defend a new position, the “Convivial Solipsism”, according to which the outcome that is observed is relative to the observer, different but in close parallel to the Everett’s interpretation and sharing also some similarities with Rovelli’s relational interpretation and Quantum Bayesianism. I also show how “Convivial Solipsism” can help getting a new standpoint about the EPR paradox providing a way out of the seemingly unavoidable non-locality of quantum mechanics.

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Notes

  1. Of course this is an oversimplified presentation of Bohr’s position which will be discussed in Sect. 3.2 with more details.

  2. Actually, the apparatus being in an entangled state with the system has no state by itself strictly speaking since through this entanglement only the system S + A has a state. So, it is only a convenient way to speak to say that it is in a superposition of \(|A_{i}\rangle \) The correct formalism in this case is the density matrix that we will describe in the following.

  3. See for example [8] for a typical exposition of this quest.

  4. See Mermin [13] for a discussion of it and for a very simple proof of the Bell, Kochen, Specker theorem.

  5. The usual presentation of contextuality is given through the observables of a spin 1 particle. The observable S\(^{2}\) which is the sum of the square of the components of the spin along any three orthogonal directions is equal to 2. Since the unsquared components have eigenvalues equal to \(-\)1, 0 or 1, that implies that one must be equal to 0. It is then possible to show that it is impossible to assign a value to one spin component without deciding which the orthogonal directions are [15].

  6. See [20] for Bohm theory and [21, 22] for GRW theory.

  7. See [23] for an open discussion between several physicists on the reasons to accept or to reject Bohm theory.

  8. Of course, this choice is not neutral for the philosophical discussion and we have to make clear that the conclusions that we will get could be mitigated in the case where either of these theories is proved to escape all the objections that today prevent from considering that it is the “best” theory according to its empirical predictions, to its fruitfulness and to its adequacy with our preexisting philosophical requirements (which is probably the most problematic aspect).

  9. See [24] for an extended description of Bohr’s position.

  10. Actually, Bohr and Heisenberg were not in total agreement. Heisenberg’s position was considered as too subjective by Bohr.

  11. See Sect. 4 for a presentation of the EPR Paradox.

  12. In particular there is the so called “many-minds” version [34, 35] that I will not analyze here.

  13. In the following, we will often omit the symbol \(\otimes \) for the tensorial product.

  14. See for example Wallace [40] who claims having proved the Born rule in this context and Kent [41] who denies that it is the case.

  15. Rovelli claims nevertheless that the assumption that an observer is merely a physical system having got information (i.e. correlation) on another system lies at the heart of the relational interpretation [23].

  16. The subjective interpretation of probability has been mainly developed by de Finetti and Savage. It amounts to say that probabilities are related to an epistemic (hence personal and subjective) uncertainty and represent the degree of belief of an agent for the happening of an event.

  17. Private communication.

  18. For a very simple proof which is useful for understanding what Bell’s inequalities mean without being involved into useless technical stuff, see Maccone [52].

  19. Of course, all that will be said here for a two-dimensional Hilbert state is applicable for any other dimensional Hilbert space.

  20. I am indebted to Chris Fuchs for this quotation from Planck inside a newspaper.

  21. Convivial Solipsism is a widely modified and extended version of a model initially proposed by d’Espagnat [7, 59]. I have first stated it in a 2000 book [67].

  22. According to some letters, Everett considered Bohr’s approach as “somewhat repugnant” [68].

  23. I will let here the concept of consciousness unanalyzed and take it as a basic given fact. Even if a proper characterization of consciousness is still an open subject in cognitive sciences, it is not the place here to dive into these problems.

  24. Actually the ontology of Convivial Solipsism and the co-construction of the mind and the world are slightly more sophisticated and will be described in more details in a forthcoming more philosophically inclined paper. A sketch of it has been given in my book [67]. The simplified version given here is however faithful enough in the context of this paper to not alter the fundamental underlying idea.

  25. See Lockwood [36] or Vaidman [72] for gedanken experiments allowing to distinguish between theories with collapse and without.

  26. Of course, I do not pretend that Bohr had Convivial Solipsism in mind when he said that. His claim was a useful assumption helping him to fight against the EPR argument. Convivial Solipsism allows to understand why Bohr was right although he probably would not have liked it!

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Acknowledgments

I am indebted to Bernard d’Espagnat whom I wish to thank first for many enlightening discussions and for comments he made on a preliminary version of this paper. Unfortunately he died this summer and I want to dedicate this paper to his memory. I equally want to thank the participants to the Colloquium “Quantum Antinomies and Reality” in June 2015 at the “Fondation des Treilles”, specially Michel Bitbol, Caslav Bruckner, Jan Faye, Chris Fuchs, Rom Harre, Richard Healey, Patricia Kauark, Franck Laloë, Jean Petitot, Thomas Ryckman, for useful discussions on this paper, during the colloquium and after. I also thank David Mermin and Rüdiger Schack for exchanges helping me to clarify my analysis of QBism and Lev Vaidman for his comments on my description of the “many worlds” interpretation.

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Authors and Affiliations

  1. LIED, UFR de Physique, Université Paris 7, CNRS, Paris, France

    Hervé Zwirn

  2. CMLA, ENS-Cachan, CNRS, Université Paris-Saclay, Cachan, France

    Hervé Zwirn

  3. IHPST, CNRS, Université Paris 1, ENS, Paris, France

    Hervé Zwirn

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Correspondence to Hervé Zwirn.

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This paper is an extended version of a conference I gave at the 14th annual international symposium “Frontiers of Fundamental Physics” (FFP14) in Marseille (France) in July 2014 [1].

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Zwirn, H. The Measurement Problem: Decoherence and Convivial Solipsism. Found Phys 46, 635–667 (2016). https://doi.org/10.1007/s10701-016-9999-5

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