This post offers a brief informal introduction to Relational Quantum Mechanics (RQM) and describes how it solves the measurement problem.
What quantum mechanics (QM) says about the phenomena it describes is strange. One central difficulty is usually summarized as the “measurement problem”. The QM model of a physical system does not assign definite values to all its observable quantities, but these values can be found when the system is experimentally measured. For example, if we are interested in the position of a moving particle, we describe it using a wave function (Ψ) and calculate its evolution in time using what is known as the Schrödinger equation. But this is not a model of a particle moving in three-dimensional space. Instead, Ψ is a function matching various positions (all the ones the particle could possibly occupy) to an array of (complex) numbers.[1] It is only when we measure the particle’s position with an appropriate apparatus that we can find it in a particular location: until then, the model can only provide us with the probability of finding it in a given volume of space (the formula for these probabilities is derived from the square of the absolute value of Ψ). Prior to measurement, the particle is said to be in a superposition of all the possible points in space.[2]
To address the problem, an interpretation of QM needs to reconcile these two things: the form of QM models (wave function—no definite values) and the outcome of measurements (realization of definite values—often called “the collapse of the wave function”). For examples of how this might be addressed, I’ll briefly mention three prominent strategies:
The Bohmian (aka deBroglie-Bohm or pilot-wave ) interpretation denies that the quantum formalism is complete and supplements it. An ontology of particles with trajectories in 3D space is posited, and the wave function’s role is to guide the trajectories. Here, there is no collapse of the wave function: at all times the particle positions are determined. The merely probabilistic predictions offered by QM is due to our ignorance of the (inaccessible) underlying dynamics.
For spontaneous collapse theories, the QM framework is not supplemented but altered. A new, stochastic, dynamics is formulated to replace the Schrödinger equation. It includes new constants of nature that make wave function collapse more likely in certain conditions (by design collapes is almost assured in realistic experimental contexts).
The Everett (aka “many-worlds”) interpretation denies that the wave function collapses. It evolves as in the Schrödinger equation. All the possible results encoded in Ψ take place but these happen in branching “worlds” that emerge when measurements take place.
RQM takes a different approach. To introduce it, it is useful to look at an extension of the measurement case called the “Wigner’s friend” scenario (after Eugene Wigner[3]). Instead of position, it is easier to picture an experiment measuring a particle’s spin. The particle can be prepared so its wave function encodes two possible outcomes (call these spin “up” or spin “down”): only one of these values will be found upon measurement (each having a probability of 50%). Next, we imagine two scientists involved in the experiment. The first, Wigner’s friend Alice, performs the measurement. This takes place in a sealed laboratory, and Wigner is positioned outside. Alice observes a definite outcome (either up or down). But Wigner would assess things differently: using QM as usual, but now to model the situation within the sealed lab, he finds that the wave function encodes two possibilities: Alice measuring up and Alice measuring down. It is only upon unsealing the lab that this (composite) wave function collapses. Until then, Alice and Wigner have two different accounts of the experiment: Alice’s definite outcome, and Wigner’s uncollapsed wave function.
This scenario highlights that QM seems to have two different and incompatible ways of treating an interaction. In the absence of any interaction, a system evolves in time as described by the Schrödinger equation. But interactions are handled in two distinct ways. On the one hand, we have a “measurement”, such as we perform in an experimental laboratory. On the other hand, QM can also describe an interaction between two systems not subject to measurement. In the first kind of interaction, a definite value of a system’s physical quantity is found (we say the wave function of the system collapses). In the second kind of interaction, we represent two (or more) systems, previously considered isolated, as now correlated in a composite system (they become entangled). In this second case the system goes on to evolve as does any isolated system. It is described only by a wave function, which, as before, encodes possible outcomes but no definite values.
The different interpretations of QM mentioned above address this extension of the measurement problem in their characteristic way: for instance, they either deny that one of the two types of interaction exists (Bohmian mechanics and Everett do without measurement-style outcomes) or attempt to unify the two by modifying the Schrödinger equation (spontaneous collapse theories).
RQM, introduced by Carlo Rovelli (Rovelli 1996), addresses the problem in a different way. It states that physical interactions are measurement-style events that reveal definite values.[4] However, this is only the case for systems directly involved in the interaction. From the perspective of an uninvolved “third-party” system, the interacting systems become entangled. The appearance of two kinds of interaction arises from a difference in perspective. The definite values of physical quantities are only manifested relative to the participants. We accept the lesson of the Wigner’s friend scenario: Alice observes a definite outcome, while while she and the measured system are entangled from the perspective of Wigner. RQM does not try to solve the measurement problem by changing or supplementing the usual formulas of QM (wave function and Schrödinger equation), but rather specifies that they always describe a system relative to a reference system.[5] This reference system, in most textbook cases, is that of the scientist or “observer”, who has interacted with the system in the past (preparing the system for measurement) but has not yet interacted again (performed the measurement). After measurement, the outcome realized is, again, only relative to the observer, not any third-party.
But RQM is not just about “observers” in the traditional sense. RQM insists that all physical systems are in the same boat. While typical examples used in discussion of QM feature scientists and their measurement devices, there is nothing special about these: all systems mutually manifest definite values for quantities when they directly interact with each other. And, like always, these same systems cannot be described as having such definite values from the perspective of other systems who are not directly involved in the interaction.
All interpretations of QM involve something counterintuitive. For RQM, the relational restriction on definite outcomes challenges our normal conception of how the world works: we normally think events or facts are part of an objective, shared world. As a reminder, it must be stressed that the relational restriction is not just a question of knowledge: it isn’t just that Wigner doesn’t know what happened in the lab: for him it did not happen, and the systems inside are in a superposition of possibilities. Of course, the Wigner’s friend scenario is a thought experiment that makes some impractical assumptions. The perfectly sealed lab is an idealization, and environmental decoherence means that Wigner cannot detect any interference effects due to entanglement, and is sure to agree with Alice on what happened in the lab.[6] But the fact that, in principle, RQM implies the co-existence of different outcomes from different perspectives is the biggest change it forces on our usual picture of nature. Much philosophical work is being done to explore the implications of what this revision really means and whether it is an acceptable price to pay for resolving the measurement problem.[7] I have another brief post (here) that discusses why I prefer RQM to the other interpretations mentioned above.
References
Adlam, E., Rovelli, C.: Information is physical: cross-perspective links in relational quantum mechanics. Philos. Phys. 1, 4 (2023). https://doi.org/10.31389/pop.8
Bacciagaluppi, G.: The role of decoherence in quantum mechanics. In: Zalta, E. N. (ed) The Stanford Encyclopedia of Philosophy (Fall 2020 Edition) (2020). https://plato.stanford.edu/archives/fall2020/entries/qm-decoherence/
Brown, M. J.: Relational quantum mechanics and the determinacy problem. Br. J. Philos. Sci. 60, 679-695 (2009). https://doi.org/10.1093/bjps/axp017
Di Biagio, A., Rovelli, C.: Relational quantum mechanics is about facts, not states: a reply to Pienaar and Brukner. Found. Phys. 52, 62 (2022). https://doi.org/10.1007/s10701-022-00579-5
Frauchiger, D., Renner, R.: Quantum theory cannot consistently describe the use of itself. Nat. Commun. 9, 3711 (2018). https://doi.org/10.1038/s41467-018-05739-8
Laudisa, F., Rovelli, C.: Relational quantum mechanics. In: Zalta, E.N. (ed) The Stanford Encyclopedia of Philosophy (Winter 2021 Edition) (2021). https://plato.stanford.edu/archives/win2021/entries/qm-relational/
Maudlin, T.: Three measurement problems. Topoi 14, 7–15 (1995)
Oldofredi, A.: The Relational Dissolution of the Quantum Measurement Problems. Found. Phys. 53, 10 (2023). https://doi.org/10.1007/s10701-022-00652-z
Rovelli, C.: Relational quantum mechanics. Int. J. Theor. Phys. 35, 1637-1677 (1996)
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
van Fraassen, B.: Rovelli’s world. Found. Phys. 40, 390-417. (2010). https://doi.org/10.1007/s10701-009-9326-5
Wigner, E.: Remarks on the mind-body problem. In Good, I.J. (ed.) The Scientist Speculates, pp. 284-302. Heinemann, London (1961); Reprinted in Wigner, E.: Symmetries and Reflections, pp. 171-184. Indiana University Press, Bloomington (1967)
[1] Another famously weird feature is that for some pairs of observable quantities, such as position and momentum, measuring one with greater accuracy reduces our ability to ascertain the other (the uncertainty principle). Also, note that for multi-particle systems, Ψ is defined in a multi-dimensional configuration space (3N dimensions where N is the number of particles in the system). Because of this, it is incorrect to picture the system (even in some “spread-out” fashion) moving in conventional three-dimensional space (or four-dimensional spacetime).
[2] The superposition does not merely reflect our ignorance of the particle’s path through space. For instance, a double-slit experiment can display interference effects due to the co-existence of the many possible trajectories represented by the QM model.
[3] See Wigner (1961/1967).
[4] For additional background, see Laudisa and Rovelli (2021). For discussion of some recent debates, see Di Biagio and Rovelli (2022).
[5] A recent article discussing how RQM handles the measurement problem in greater detail (including in the context of Tim Maudlin’s classic 1995 discussion of the problem) is Oldofredi (2023).
[6] Recently, several thought-experiments have been proposed that extend Wigner’s friend-style scenarios (involving multiple observers and experiments) in order to derive results that appear to show how genuine disagreement between observers about outcomes will occur (e.g. Frauchiger and Renner, 2018). While this literature is still subject to active debate, it seems problematic that QM under some interpretations (including RQM) would not lead to agreement among observers. In one response to this concern, Adlam and Rovelli (2023) propose an addition to RQM’s principles, postulating the existence of so-called “cross-perspective links.” Briefly, the idea is that an outcome observed by Alice should have a physical effect on her, creating a record of the information. Then, unless it is destroyed by subsequent interactions, an appropriate subsequent measurement of Alice by Wigner (or any one else) should in principle be capable of measuring the physical variable encoding the information, with the result that they will agree with Alice about the outcome.
[7] Philosophical critiques of RQM include Brown (2009), van Fraassen (2010) and Ruyant (2018).