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Can We Make Sense of Relational Quantum Mechanics?

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Abstract

The relational interpretation of quantum mechanics proposes to solve the measurement problem and reconcile completeness and locality of quantum mechanics by postulating relativity to the observer for events and facts, instead of an absolute “view from nowhere”. The aim of this paper is to clarify this interpretation, and in particular, one of its central claims concerning the possibility for an observer to have knowledge about other observer’s events. I consider three possible readings of this claim (deflationist, relationist and relativist), and develop the most promising one, relativism, to show how it fares when confronted with the traditional interpretative problems of quantum mechanics. Although it provides answers to some problems, I claim that there is currently no adapted locality criterion to evaluate whether the resulting interpretation is local or not.

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Notes

  1. “In RQM, physical reality is taken to be formed by the individual quantum events (facts) through which interacting systems affect one another. [...] each quantum event is only relative to the system involved in the interaction.”[17, p. 2].

  2. “any physical system provides a potential observer” [17, p. 2].

  3. “The state \({\varPsi }\) that we associate with a system S is therefore, first of all, just a coding of the outcome of these previous interactions with S.” [17, p. 3] Note, however, that the idea that the wave-function merely encodes past events is not strictly true: it also incorporates a predictive content, in particular when updated after a “collapse”. For example, when measuring one of two entangled particles, the properties of the second one are updated too, even though it is not directly measured and corresponds to no new event for the observer. Therefore it should count as a prediction encoded in the wave-function that concerns a future observer capable of having information on the distant particle (this is explicit in Smerlak and Rovelli [17]’s treatment of EPR).

  4. “What changes instantaneously at time \(t_0\) , for A, is not the objective state of \(\beta \), but only its (subjective) relative state, that codes the information that A has about \(\beta \)” [17, p. 5].

  5. Rovelli gives, as a rationale for the collapse, that acquiring new information involves interacting with the system, which breaks the linear dynamic. But this is somehow misleading: dynamics, in the sense of laws of nature governing the phenomena, need not be involved if wave-functions are mere bookkeeping devices.

  6. Although it would definitely be compatible with a panpsychist, or panexperientialist position.

  7. There might be a “preferred basis” problem here. What counts as a measuring interaction, and what doesn’t? Are there objective criteria to tell, and are they sufficient to select a unique property that is measured? However, I will leave these issues aside.

  8. According to Rovelli, bi-orthonormal decomposition is irrelevant because associated observables would generally correspond to an “uninteresting and practically non measurable quantity”, while we are interested in “certain self-adjoint operators only, representing observables that we know how to measure” [15].

  9. PMI assumes relativity to a reference, which is a system containing the described system, while RQM assumes that it is a separate system (however PMI takes the complement of the reference to be the “perspective”, and this is a separate system). This means that in PMI, an object can have a state relative to itself, that the universe has a state relative to itself, and that any object has a state relative to any perspective, which is not the case in RQM.

  10. This is clear in RQM when Rovelli analyses the observable corresponding to a measurement apparatus being correlated with a measured object: the expected probability is 1, from which he concludes that the apparatus has measured the object, without requiring that the observer actually performs the measurement. This observation is analog to the principle of reality involved in the EPR argument, that will be examined below.

  11. [9, p. 188] claims that RQM requires intuitionist logic.

  12. Perhaps they could allow inferences concerning what is possibly true for an external observer, in a way that is not already allowed by the rules given by Rovelli. This remains to be examined.

  13. There might also be interesting connections between relativist truth and the use of a tensed semantic associated with presentism. See also Dorato [7] for considerations on time and becoming in the context of RQM.

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  1. Université Catholique de Louvain, Louvain-la-Neuve, Belgium

    Quentin Ruyant

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Ruyant, Q. Can We Make Sense of Relational Quantum Mechanics?. Found Phys 48, 440–455 (2018). https://doi.org/10.1007/s10701-018-0156-1

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