## Thursday, January 28, 2021

### Why I Favor Relational Quantum Mechanics

I think Relational Quantum Mechanics (RQM), initially proposed by Carlo Rovelli, is the best interpretation of quantum mechanics.1 It is important to note right away, however, that I depart from Rovelli’s thinking in one important respect. He takes an anti-realist view of the wave function (or quantum state). As I will discuss below, I endorse a view that sees the wave function as representing something real (even if imperfectly and incompletely).

There are two reasons I prefer RQM. First, I think it makes better sense of QM as a successful scientific endeavor compared to other interpretations. Second, it fits neatly with an attractive ontology for our world.

Quick Introduction

Orthodox or “textbook” QM features a closely knit family of mathematical models and recipes for their use. The models describe the state of a microscopic system characterized by certain physical quantities (typically given in the form of a wave function). It gives a formula for calculating how the system evolves in time (the Schrödinger equation). Notably, because of the nature of the mathematical formalism, one typically cannot ascribe definite values to the physical quantities of interest. However, QM also offers a procedure for calculating (probabilistically) the outcomes of particular measurements of these quantities. The problem with taking orthodox QM as a universally applicable physical theory can be described in several ways (this is usually called the measurement problem). One simple way is to note an inconsistency arising from the presence of what appears to be two completely different kinds of interaction.

In the absence of any interaction, a system evolves in time as described by the Schrödinger equation. But interactions are handled in two different ways. On the one hand, we have the measurement process (utilizing the Born rule), that is, an interaction between the quantum system under investigation and a scientist’s experimental apparatus. On the other hand, we can also describe an interaction between two systems that are 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 (we say they become entangled). This system evolves in the same fashion as any isolated system. And as such the composite system may be in a superposition of states where no definite values for a given quantity can be ascribed.

In a nutshell, the RQM solution is to stipulate that a physical interaction is a measurement-style event. However, this is only true for those systems directly involved: the systems are merely entangled from the standpoint of other “third-party” systems. The appearance of two sorts of interaction arises from a difference in perspective. This is weird, of course, since particular values of the physical quantities revealed in an interaction are manifest only relative to the interaction partner(s) involved. They don’t exist in a fully objective way. All interpretations of QM ask us to accept something unintuitive or revisionary. This is the “ask” made by RQM.

Reason One: RQM Validates Quantum Theory as Successful Science

Before discussing the interpretation further, I can quickly outline a reason to prefer RQM to many competing approaches. This point is primarily a negative one. In contrast to other approaches, RQM is an interpretation that delivers a satisfying account of QM as a successful scientific theory: one that draws appropriate connections between the results of our experimental investigations and a meaningful picture of the world around us.

I obviously won’t be doing a deep dive into all the options, but will quickly sketch why I think RQM is superior. First, for a quick cut in the number of alternatives, I eliminate views that are merely pragmatic, or see QM as only describing what agents experience, believe, or know. I insist that alongside its other aims (such as prediction and practical control), a scientific theory should contribute to our understanding of nature. To do so, the theory should offer successful explanations of worldly phenomena, that is, ones that tell us (broadly speaking) what kind of things are out there and how they hang together. This means, in turn, that at least some of the elements of the mathematical models that we use should represent features of the world (allowing that the fidelity of any given representation is significantly constrained by reasons having to do with the aims of the scientist and the tools employed). I will outline in the next section of this post how I think this works in the case of RQM.

As for the remaining alternatives, I will limit the conversation to the three most prominent broadly realist approaches to thinking about QM: Everett-style interpretations, Bohmian mechanics, and objective collapse approaches, such as Ghirardi-Rimini-Weber (GRW) theory (the implied ontology of these approaches might be fleshed out in more than one way, but I will not pursue the details here.)

For these alternatives, a different issue rises to the fore. An interpretation should not just consider how the features of formal QM models might correspond to reality. It should also respect the status of quantum theory as a hugely successful experimental science. Orthodox or “textbook” QM includes not just the mathematical formalism, but also the recipes for how it is used by investigators and how it connects to our experiences in the laboratory. And here is where I think Everettians and Bohmians in particular fall short.

Note first that all three of the alternative approaches depart from orthodox QM by adding to, subtracting from, or modifying its basic elements.2 GRW changes things by replacing the Schrödinger equation with a new formula that attempts to encompass both continuous evolution and the apparent collapse onto particular outcomes observed in measurement. Bohmian mechanics adds new elements to the picture by associating the quantum state with a configuration of particles in 3D space and adding a new guidance equation for them. Everettian approaches just drop the measurement process and seek to reinterpret what is going on without it.

For the Everett framework in particular, I’m not sure the extent of its departure from orthodox QM is always appreciated. It is sometimes claimed to be the simplest version of QM. This is since it works by simply removing what is often seen as a problematic element of the theory. But in doing so it divorces QM from its basis in experimental practice. This is a drastic departure indeed.

To see this, note that to endorse Everett is to conclude that the very experiments that prompted the development of QM and have repeatedly corroborated it over nearly a century are illusory. For the Everettian, to take one example, no experimental measurement of the spin of an electron has ever or will ever have a particular outcome (all outcomes happen, even though we’ll never perceive that).

Bohmian mechanics also turns our experiments into fictions. For the Bohmian, there is actually no electron and no spin involved in the measurement of an electron’s spin. Rather, there is an orchestrated movement of spinless point particles comprising the system and the laboratory (and the rest of the universe) into the correct spatial positions.

GRW-style approaches are different, in that they are testable alternatives to QM. Unfortunately, researchers have been busy gradually ruling them out as empirically adequate alternatives (see, e.g., Vinante et.al, 2020). It is also worth noting, however, that GRW also distorts the usual interpretation of experimental results by stipulating that all collapses are in the position basis.

Unlike these approaches, RQM is truly an interpretation, rather than a modification, of orthodox QM, a successful theory that was motivated by experimental findings and is extremely well supported by decades of further testing. The measurement process, in particular, is not some problematic add-on to quantum theory – it is at the heart of it. Human beings and our experiences and interventions are part of the natural world. RQM does justice to this fact by explaining that measurements—the connections between quantum systems and ourselves—are just like any other physical interaction.

Reason Two: RQM Offers an Attractive Ontological Picture

Laudisa and Rovelli (in the SEP article) describe RQM’s ontology as a “sparse” one, comprised of the relational interaction events between systems. This event ontology has attractive features (akin to the “flash” ontology sometimes discussed in conjunction with objective collapse interpretations). There is no question of strange higher-dimensional spaces or other worlds: the events happen in spacetime. Also, one of the goals of science-inspired metaphysical work is to foster the potential unification of scientific theories. Importantly, a QM interpretation that features an event ontology offers at least the promise of establishing a rapport with relativity theory, which is typically seen as putting events in the leading role (see a recent discussion by Maccone, 2019).

But does giving this role to interaction events preclude a representational role for the wave function? Given that physical properties of systems only take definite values when these events occur, perhaps systems should not be accorded any reality apart from this context. And, in fact, Carlo Rovelli has consistently taken a hard anti-realist stance toward the wave function/quantum state. In his original presentation of RQM he gave it a role only as record of information about one system from the point of view of another, and thought it was possible to reformulate quantum theory using an information-based framework. This conflicts with my insistence above that such anti-realism was inconsistent with the aims of a good scientific theory.

Thankfully, there is no need to follow Rovelli on this point. Instead, I concur with a view outlined by Mauro Dorato recently. He suggests that rather than view non-interacting systems as simply having no real properties, they can be characterized as having dispositions:

In other words, such systems S have intrinsic dispositions to correlate with other systems/observers O, which manifest themselves as the possession of definite properties q relative to those Os. (Dorato, 2016, 239; emphasis original)

As he points out, referencing ideas due to philosopher C.B. Martin, such manifestations only occur as mutual manifestations involving dispositions characterizing two or more systems.3 Since these manifestations have a probabilistic aspect to them, the dispositions might also be referred to as propensities.

So, here the wave function has a representational role to play. It represents a systems’s propensities toward interaction with a specified partner system(s). The Schrödinger equation would show how propensities can be described across time in the absence of interaction. Now, it is true that the QM formalism does not offer a full or absolute accounting for a system’s properties, given its relational limitations. But here we should recall that models across the sciences are typically incomplete and imperfect. In addition to employing approximations and idealizations, they approach phenomena from a certain perspective dictated by the nature of the research program. But we can say the wave function represents something real (if incompletely and in an idealized way). Reality has two aspects, non-interacting systems with propensities, and the interaction events that occur in spacetime.

The idea that properties are dispositional in nature is one that has been pursued increasingly by philosophers in recent years. It fits well with physics, since both state dependent and independent properties (like mass and charge) are only known via their manifestations in interactions.4 While advocates disagree about the details, the idea that the basic ontology of the world features objects that bear dispositions/propensities has also been used more widely to address a number of difficult philosophical topics (like modality). Most importantly, perhaps, dispositions and their manifestations provide a good basis for theorizing about causation.5

Fitting Both Quantum Systems and Scientists Into the Causal Web

To conclude, I’ll briefly describe how I would flesh out this ontological picture, putting an emphasis on causation.

I mentioned above the role representational models play in explanation. To be more specific, scientific explanations are typically causal explanations: they seek to place a phenomenon in a structured causal context. When successful explanations feature models, then, these models represent features of the world’s causal structure. The suggestions above on how to view the ontology associated with RQM fit into a particularly attractive theory of this structure.

This is a modified version of Wesley Salmon’s causal process account (Salmon, 1984). Here the basic entity or object is labeled a causal process, and there are two dimensions of causation: propagation and production. Propagation refers to the evolution of a causal process in the absence of interaction, while production refers to the change that causal processes undergo when an interaction occurs. As described by Ladyman & Ross:

The metaphysic suggested by process views is effectively one in which the entire universe is a graph of real processes, where the edges are uninterrupted processes, and the vertices the interactions between them (Ladyman & Ross, 2007, 263).

According to Salmon, a propagating causal process carries or “transmits” causal influence from one spacetime point to another. The character of this causal influence is then altered by interactions. I theorize that this causal influence takes the form of a cluster of dispositions or propensities toward mutual interactions (aka a propensity profile). The interactions produce a change in this profile.6

To summarize:

1. The web of nature has two aspects: the persisting causal process and the causal interaction event (a discrete change-making interaction between processes).

2. The quantum formalism offers a partial representation of the propensity profile of a causal process. It is partial because these are only the propensities toward manifestations that take place in interactions with (one or more) designated reference systems. The Schrödinger equation represents the propagation of these propensities from one interaction to the next.

3. All manifestations are mutual, and take the form of a change in the profile of each process involved in the interaction. A quantum measurement is an interaction like any other. Humans may treat the wave function as representing the phenomena we are tracking, but we are also causal processes, as are our measuring devices. It is just that the changes manifest in us in an interaction (our altered propensity profiles) are conceptualized as epistemic.

4. Per RQM, when two physical systems interact, they are represented as an entangled composite system from the perspective of a third system. This relational representation of the composite system might in practice be thought of as a limitation on what the third system “knows.” Under certain conditions, however, this entanglement can have a distinctive indirect impact on the third system—interference effects—revealing it is not only epistemic (as always, decoherence explains why we rarely experience these effects).

There is much more to flesh out, of course. I would add to this summary an account of how composite systems form higher-level propensities of their own, based on the pattern of repeated interactions of their constituents. Also, there is an interesting question of how serious of a (relational or perspectival) scientific realist to be about the properties identified in quantum theory. My preference is to be a realist about the (singular) causal network, but view the formalism as offering only an idealized depiction of regularities in the propensity profiles of the underlying causal processes.

Notes

1 For background, see the Stanford Encyclopedia article (Laudisa & Rovelli, 2019). Rovelli’s original paper is (Rovelli, 1996 - arXiv:quant-ph/9609002). Good philosophical discussions include Brown (2009; link via academia.edu), Van Fraassen (2010; link via Van Fraassen website), Dorato (2016; preprint here, but note final version has significant changes), and Ruyant (2018; preprint here).
2 For a recent attempt to carefully describe the principles of orthodox QM, see Poinat (2020); link (researchgate).
3 What Martin calls “reciprocal disposition partners.” See Martin (2008), especially Ch. 5.
4 In addition to contemporary work by Dorato and others, there have been a handful of theorists over the decades since QM was formulated who have employed dispositions/propensities to interpret QM. See Suárez (2007) for a survey of some of these.
5 Important work here includes Chakravartty (2007) and Mumford & Anjum (2011).
6 The main changes from Salmon’s own work are as follows. The first is to be a realist about dispositions/propensities, whereas Salmon’s version of empiricism drove him to reject any suggestion of causal powers. He characterized causal processes in terms of their transmission of an observable “mark” or, in a subsequent version of the theory, the transmission of a conserved physical quantity. The second change is that causal processes cannot be said to propagate in spacetime, as Salmon envisioned, since this would be inconsistent with the non-local character of quantum systems.

References

Brown, M. J. (2009). Relational Quantum Mechanics and the Determinacy Problem. The British Journal for the Philosophy of Science, 60(4), 679-695.
Chakravartty, A. (2007). A Metaphysics for Scientific Realism. Cambridge: Cambridge University Press.
Dorato, M. (2016). Rovelli's Relational Quantum Mechanics, Anti-Monism, and Quantum Becoming. In A. Marmodoro, & D. Yates (Eds.), The Metaphysics of Relations (pp. 235-262). Oxford: Oxford University Press.
Ladyman, J., & Ross, D. (2007). Everything Must Go. Oxford: Oxford University Press.
Laudisa, F., & Rovelli, C. (2019). Relational Quantum Mechanics. Retrieved from The Stanford Encyclopedia of Philosophy, Winter 2019 Edition: https://plato.stanford.edu/entries/qm-relational/
Maccone, L. (2019). A Fundamental Problem in Quantizing General Relativity. Foundations of Physics, 49, 1394-1403.
Martin, C. (2008). The Mind in Nature. Oxford: Oxford University Press.
Mumford, S., & Anjum, R. L. (2011). Getting Causes from Powers. Oxford: Oxford University Press.
Poinat, S. (2020). Quantum Mechanics and Its Interpretations: A Defense of the Quantum Principles. Foundations of Physics, 1-18.
Rovelli, C. (1996). Relational Quantum Mechanics. International Journal of Theoretical Physics, 35, 1637-1678.
Ruyant, Q. (2018). Can We Make Sense of Relational Quantum Mechanics. Foundations of Physics, 48, 440-455.
Salmon, W. (1984). Scientific Explanation and the Causal Structure of the World. Princeton: Princeton University Press.
Suárez, M. (2007). Quantum Propensities. Studies in History and Philosophy of Modern Physics, 38, 418-438.
Van Fraassen, B. (2010). Rovelli's World. Foundations of Physics, 40, 390-417.
Vinante, A., et.al. (2020) Narrowing the Parameter Space of Collapse Models with Ultracold Layered Force Sensors. Physical Review Letters, 125, 100401-100401.