What Ontology for Relational Quantum Mechanics?

Abstract

In this paper, we evaluate some proposals that have been put forward to clarify the ontological consequences of relational quantum mechanics. We first focus on priority monism and ontic structural realism and argue that these views are not suitable for providing an ontological interpretation of the theory. Then, we discuss an alternative interpretation that we regard as more promising, based on so-called ‘metaphysical coherentism’, which we also connect to the idea of an event-based, or ‘flash’, ontology.

1 Introduction

In the last 25 years or so [30], relational quantum mechanics (RQM henceforth) has attracted the attention of many philosophers working in the field of quantum mechanics [3, 4, 7,8,9, 11, 13, 20, 21, 24, 29, 32, 34, 35].

On the assumption that RQM is a plausible interpretation of quantum theory,¹ this paper aims to evaluate the main proposals that have been formulated to clarify the ontological consequences of RQM. In more detail, we shall first focus on priority monism [18] and ontic structural realism (OSR; [7]) and argue that these views are not suitable for providing an ontological interpretation of RQM. In the second half of the paper, we discuss an alternative that we regard as more promising.

The structure of the paper is as follows. In the first section we briefly present the essential tenets of RQM. In the second section we evaluate the monistic reading of the theory, while in the third we evaluate Candiotto’s relation-centered analysis. After critically assessing these two interpretations, we bring to bear a recent proposal by Morganti [26] and Calosi and Morganti [5] and argue that quantum systems as described by RQM are best understood in terms of mutual dependence as per ‘metaphysical coherentism’. Before closing, we briefly consider the role that Rovelli himself attributes to events in the context of RQM. We suggest that both an ontology of events (or ‘flashes’) and coherentism represent viable answers to the question: what is RQM about? In fact, we will argue, the two views are perfectly compatible with each other.²

2 A Brief Presentation of RQM

In this section we briefly present RQM. The content of the theory can be summarized via the following principle:

(P) Quantum systems only acquire definite values for their state-dependent properties through interactions with other information-gathering physical systems.

(P) claims that state-dependent quantum properties do not have absolute values that could be regarded as intrinsic features of the physical systems that possess them. They are instead essentially relational since they depend on interactions between their bearers and other physical systems. The outcomes of these interactions can be described as events of the form ‘system S₂ acquires property C with respect to, and due to an interaction with, system S₁ at time t₁’. Notice that (P) does not imply that the qualitative content of quantum systems is entirely extrinsic, nor that properties only exist insofar as interactions lead to the acquisition of determinate values. In this connection, two remarks are in order. As to the first, it is important to stress that RQM involves only a proper subset of the properties of quantum systems, namely the state-dependent ones. In fact, at least prima facie, state-independent properties cannot possibly be regarded as relational as required by (P), since to be relational is defined here as ‘depending on the state of a certain (distinct) physical system’. Concerning the second remark, it seems entirely possible for actual properties of physical systems not to correspond to fully manifest, determinate values. For instance, one might interpret the pre-interaction properties of quantum systems as dispositions [11], or as ontically indeterminate—e.g., as determinables without a corresponding determinate [4, 6, 36, 37]. In both cases, such properties would be physically real in spite of their not having determinate and detectable values. For now, however, let us focus on the key feature of RQM, namely the principle of relationality (P).

As an illustration, consider a quantum system S and two observers,³F and W, in a Wigner’s friend scenario. In Rovelli’s approach, two different observers “can give different accounts of the same physical sequences of events” [30], p. 4). Suppose that the quantum system S is in a superposition of spin states⁴

$$ {\left| \psi \right.}{>_{{\text{S}}}} = {\text{a }}\left| { \uparrow >_{{\text{S}}} + {\text{b }}} \right| \downarrow >_{{\text{S}}} , $$

(1)

where, as usual,

$$ \left| {\text{a}} \right|^{2} + \left| {\text{b}} \right|^{2} = 1 $$

(2)

Let us now suppose that Wigner’s friend F correlates with S. Due to the linearity of the evolution, at t₁ we have

$$ {\text{ready}} >_{{\text{F}}} \left( {{\text{a}}\left| { \uparrow >_{{\text{S}}} + {\text{b}}} \right| \downarrow >_{{\text{S}}} } \right) \to a\left| {{\text{up}}_{{\text{F}}} } \right| \uparrow >_{{\text{S}}} + {\text{b}}\left| {{\text{down}}_{{\text{F}}} } \right| \downarrow >_{{\text{S}}} $$

(3)

Let us further suppose that, upon measurement, at t₂ F measures spin up:

$$ {\left| {\psi} \right.} {>_{{\text{S}}}} = {\text{a}}\left| {{\text{up}}_{{\text{F}}} } \right| \uparrow >_{{\text{S}}} + {\text{b}}|{\text{down}}_{{\text{F}}} | \left.\downarrow >_{{\text{S}}} \to \right|{\text{up}}_{{\text{F}}} | \uparrow >_{{\text{S}}} $$

(4)

Relative to Wigner (W), who at t₂ has not interacted with the joint system S + F yet, the state is instead still a superposition of the form

$$ {\text{a}}\left| {{\text{up}}_{{\text{W}}} } \right|{\text{up}}_{{\text{F}}} \left| { \uparrow >_{{\text{S}}} + {\text{b}}} \right|{\text{down}}_{{\text{W}}} \left| {{\text{down}}_{{\text{F}}} } \right| \downarrow >_{{\text{S}}} $$

(5)

In other words, according to the information available to him, Wigner can find with probability |b|² that his friend has observed, say, spin down (5). But, given (4), this seems to contradict F’s observation that at t₂ S has already a determinate spin-up value (for a similar reconstruction, see [3], p. 693). Consistently with quantum mechanics, objectivity can be re-established only when F and W relativize their descriptions to their different perspectives, which for clarity we refer to as (A) and (B).

• (A) According to W, F has measured either spin up or spin down and, accordingly, there is a non-zero probability that, upon further observation on the joint system at t₃, W finds |down_F |↓|> _S;

• (B) According to F, instead, at t₂ his own measurement resulted in spin up, hence the probability for spin down already went down to 0.

Thus, not only does RQM make (certain) physical properties relational: it also makes their values relative. However, when Wigner and his friend correlate, they agree on both (A) and (B). More generally, they are always able to find a coherent overall story of the relevant physical processes, which crucially includes a relativization of measurement outcomes to observers: intersubjective agreement is regained.

The foregoing leads to a question concerning the identity of the events that correspond to the acquisition of determinate values by physical properties: given the relative/relational nature of qualitative profiles in RQM, how is one to make sense of the abovementioned expression “different descriptions of the same sequences of events”? We can assume that the identity of a sequence of events is either intrinsic or relational (dependent on relations with other events). How should we choose between these two alternatives in this particular case? What does it mean, in RQM, to talk of sameness of events having different descriptions relative to different systems, as stated by Rovelli in the above quotation?

If it made sense to talk about “the same sequence” described in two different ways by, say, F and W, there should be an absolute state of the matter about the state-dependent properties of physical systems. For, if the qualitative profile of a physical systems were entirely analysable in terms of interaction events, and the latter had an objective, perspective-independent content which makes them the same across different descriptions, then it would follow that the qualitative profile of physical systems is also an objective, perspective-independent matter. This would hold, in particular, for the state-dependent properties that RQM focuses on.⁵ But this conflicts with (P). Since tertium non datur, it follows that in RQM the identity of outcomes/events (supposedly, the building blocks of the physical content of space–time) must be extrinsic, that is, relational/structural. This conclusion is reinforced by the following passage: “There is no physical meaning to the state of an isolated system. A physical system (or, more precisely, its contingent state) is reduced to the net of relations it entertains with the surrounding systems, and the physical structure of the world is identified as this net of relationships” ([21], p. 1).⁶

Thus, the relational nature of quantum properties in RQM entails that, strictly speaking, it makes no sense to talk about different descriptions of the same event or chain of events. If, to be more dramatic by going against the letter of RQM, we replace ‘physical system’ with ‘observer’,⁷ every “physical observer” “experiences” certain events from a particular perspective (say, Wigner’s), which always includes an essential reference to the perspective of some other observer (his friend F). There is nothing more to reality than this. However, notice, this does not entail solipsism. Indeed, solipsism is avoided exactly to the extent that there is no isolated system: any “perspective” can only actualize (though in different ways) in relation to other “perspectives” and, far from being a subjective image that replaces reality, this ‘network’ of perspectives is exactly what constitutes the objective physical reality.

Coming now to the question concerning the ontology of RQM, in view of the foregoing two options emerge:

• (1) A strongly monistic ontology, according to which the truly fundamental physical entity is the universe as a whole, which is constituted by a plurality of systems that acquire a physical characterization only in relation to one another, hence ‘holistically’;

• (2) A structuralist ontology, according to which relations between physical systems are more fundamental than the systems themselves and their monadic properties.

Option (1) may appear quite natural given the characteristic features of RQM: positing relationality at the fundamental level seems to immediately lead to a strong form of metaphysical holism. Option (2) is also prima facie plausible, and in recent work it has been explicitly presented as the correct ontology of RQM if the initial state contained [7]. Nonetheless, in the next two sections we will argue that, in fact, neither of these views is suitable for providing a metaphysical interpretation of RQM.

3 Why RQM is Incompatible with Priority Monism

In the literature on metaphysical fundamentality, one usually distinguishes between two kinds of metaphysical monism: ‘Existence monism’ and ‘Priority monism’. While the existence monist claims that there are no parts and only the whole exists [16, 17], the priority monist grants the pluralist the existence of parts but at the same time “holds that the whole is prior to its parts, and thus views the cosmos as fundamental, with metaphysical explanation dangling downward from the One” ([33], p. 31).

In the present context, the notions of fundamentality and priority are usefully linked to explanation: what is metaphysically (more) fundamental corresponds to what plays the role of (more) basic explanans in our best scientifically-grounded account of reality. Translated in physical language, we could say that the fundamental whole, or the One, is the universe U, including its non-observable parts. Its “explanatorily dependent” parts involve, say, the seeds of galaxies resulting from cosmic inflation, or the planets in the Solar system. Consider, for instance, the cosmic background radiation revealed by the WMAP.⁸ To the extent that it, together with other pieces of evidence, confirms the Big Bang theory of the universe, we can say that the initial state of the Universe is the whole that, together with the laws of cosmic evolution, acts as the fundamental explanans for every later physical event and fact, including today’s uniform presence of the background radiation.⁹

Fig. 1

Representation of the anisotropies measured by WMAP

The existence of an initial state of the Universe dating 13.77 billion year ago, however, might be taken as an objection to RQM: if that state were “point-like” it could not be interpreted in relational terms. One could object that, if the initial state of the universe consisted of hypersurfaces of some kind, RQM would still be applicable because U would have parts. More generally, it is fair to point out that we have no evidence about the nature of the initial state: arguably, at the initial singularity quantum effects were present that may imply some degree of mereological complexity. However, so far no quantum theory of gravity has been empirically confirmed and, consequently, at present this is not a promising line of defence for the supporter of RQM. A least for the sake of the argument, let us then suppose that at the Big Bang there was indeed no system in terms of whose state we might relationally ascribe a property: U had no parts, and there was nothing external to it. In this case, it does seem to immediately follow that RQM cannot explain in its framework the status of at least one physical state, and a rather important one indeed: namely, the initial state of the Universe. For this reason, one may conclude, that the relational interpretation should be discarded.¹⁰

What we have here is, in our opinion, another illustration of the fact that one’s modus ponens is another’s modus tollens. True, one may see a fatal conflict between the idea of an initial state of the universe and the assumption that physical reality is fundamentally relational. Incidentally, this would not be a problem for our present purposes: since priority monism appears instead to be perfectly applicable to the initial state of the universe, it would in any case follow that RQM and priority monism are incompatible. However, if only because of the working assumptions of the present paper (see footnote 1), which presupposes the validity of RQM, we will argue here in favour of the opposite viewpoint. Namely, that RQM is in fact perfectly compatible with the claim that the initial state of the universe has no determinate (state-dependent) properties, while priority monism is not since to be prior to be the parts it should have determinate properties.

Let us start with a quotation from Rovelli: “Do different observers O and [P] get the same answers out of a system S is a meaningless question. It is a question about the absolute state of O and P” ([30], p. 204). What RQM rules out is, that is, the possibility that a physical system can be in a determinate state independently of some other physical system—that is, in an absolute, non-relational, manner. However, it would be an additional, and to our mind unwarranted, move to infer from this that RQM requires that at least two physical systems exist. Indeed, the supporter of RQM can, and should, contend that the initial state of the universe is ‘special’ in the same way in which the total state of the universe is: in both cases, since there is no external ‘observer’, the physical system being considered simply does not have definite values for its state-dependent properties.

On the other hand, the same sort of considerations arguably renders priority monism unworkable in the present context. For, the universe has undeniably evolved from its initial state, coming to possess (parts and) determinate state-dependent properties. But if there is something with respect to which U acquires determinate properties, it cannot be external to U, since U is all there is. Hence, it must be identified with one or more of its proper parts P_i. This, however, contrary to the requirements of priority monism, entails that the universe U cannot be explanatorily prior to P_i since the former depends on the latter for the determinateness of its properties.¹¹

What we are claiming, notice, is not that what is (meta)physically fundamental must have absolute values for all its properties: it is well-known that in quantum mechanics not all properties of a physical system can possess definite values.¹² The idea is, rather, that if U is more fundamental than its parts (as priority monism requires), then it cannot depend on them in any way, and it must instead be the case that the parts depend on U for their properties. However, according to RQM, neither is the case. On the one hand, U doesn’t have definite properties independently of its parts. On the other hand, the properties of any proper part of U (even the smallest) must always be defined with respect to some other proper part of U, and never essentially depend on U as a whole.¹³

In anachronistic but evocative language, any of these parts of U can be compared to a Leibnizian monad, representing or “reflecting” U from its particular perspective. The separation between U and the monad reflecting it is ontologically basic. The main difference with Leibniz’s monadology is, that in relational quantum cosmology there is ‘no monad of the monads’ since, as we have seen, each system can only have (as a matter of ontological, not merely epistemic, fact) partial information about U.

How could one attempt to re-establish the consistency between priority monism—which appears in any case plausible in view of quantum mechanical non-separability¹⁴—and RQM? First, it could be contended that in order to ground the determinate properties of the parts, the fundamental entity need not have determinate properties. Here, we cannot enter a detailed discussion of fundamentality and indeterminacy (for a recent discussion, see [23]). We just note that the burden of proof would in this case be on the monist, who should explain how determinateness can emerge (albeit in a local and perspectival manner) from what is fundamentally indeterminate. Especially so in view of the fact that, as pointed out earlier, Rovelli seems to explicitly think that it is physically meaningless to attribute to physical systems states that allegedly describe state-dependent properties independently of interaction.

Secondly, one could hold that priority monism only applies to classical, non-quantum universes, while RQM addresses quantum mechanics. On this hypothesis, it would not be possible to discuss the consistency of the two theories since they would apply to two different domains (classical and quantum respectively). However, this strategy would obviously not be successful. Apart from the fact that priority monism is quite often discussed in a quantum regime—entanglement being regarded as an important evidential support [33]—here we are discussing whether priority monism is a good interpretative stance with respect to relational quantum mechanics.

A third strategy to reconcile priority monism with RQM consists in claiming that, as a matter of fact, RQM is compatible with the idea that there is an absolute state of the universe. In particular, one could contend that there in fact is a definite quantum state of the universe before any correlation between it and any of its parts and that, crucially, the information exchange caused by interaction has just the epistemic function of revealing it. To the extent that priority monism seems to call for definite relations between the whole and its part, the consistency with RQM would be vindicated: the whole would be prior to the parts, and the latter would be prior to it only in the “innocent” epistemic sense that reference to available information provided by them is necessary for us to uncover the objective, fundamental properties of the whole. The fact that the word “information”, which is used a lot in the context of RQM, has an epistemic overtone may certainly add to the apparent plausibility of this argument.

This proposal, however, would be tantamount to abandoning RQM. First, the notion of “exchange of information” in RQM has, controversially but purportedly, a mind-independent meaning.¹⁵ At most, one could argue that the interaction or exchange of information between a part P of the universe U and the remaining part U–P disturbs the prior definite state of U. However, it is a fundamental tenet of RQM (recall principle (P) above) that definite values for physical (state-dependent) properties do not pre-exist and are literally generated by physical interactions or correlations. This point can be reinforced by considering the historical development of quantum theory. One could identify the early phase of the ‘Copenhagen interpretation’ championed by Bohr with the idea that measurements affect pre-existing, definite facts. But, as Jan Faye, for instance, has plausibly argued, in his response to EPR Bohr himself abandoned this view [15]. After 1935, Bohr explicitly defended instead the view that state-dependent quantum magnitudes are fully indeterminate before measurement since they are entangled with the measurement apparatus. In a nutshell, an ‘ignorance’ or ‘disturbance’ interpretation of standard quantum mechanics is arguably empirically inadequate. This was acknowledged even by Bohr’s archenemy, John Bell: “the word [‘measurement’] very strongly suggests the ascertaining of some pre-existing property […] Quantum experiments are not just like that, as we learnt especially from Bohr. The results have to be regarded as the joint product of ‘system’ and ‘apparatus’, the complete experimental set-up” (quoted in Whitaker [38], p. 180). Given the close resemblance between Bohr’s philosophy of quantum mechanics and its development in RQM [13], it is plausible to conclude that this is also the case for RQM, which definitely seems to be intended by Rovelli as more than a merely epistemic interpretation of quantum theory.

Before closing this section, we should point out two additional reasons for believing that there is conflict between RQM and priority monism, namely (1) the former’s locality vs. the latter’s holism and (2) the former’s symmetric nature vs the latter’s asymmetric arrow of explanation.

Starting from (1), contentious as this may be, Rovelli argues that RQM is an entirely local theory. To see the grounds for this claim, let us go back to the familiar Wigner-type scenario already considered above. In RQM, the interaction between the system S and Wigner’s friend F is always local, exactly as the interaction between S + F and W. More generally, according to RQM, in any EPR-type setup involving two space-like entangled systems A and B the measurement outcome obtained locally in, say, wing A of the experiment does not interact with the outcome obtained in wing B (and conversely). Unlike what happens, for instance, in Bohmian mechanics, in RQM there is no action at a distance. Therefore, from the viewpoint of Wigner, who is located in A, the outcome in B revealed by her far away friend F is indeterminate, even though, given the property of the singlet state, it is possible for him to predict with probability 1 that F will measure, measures, or has already measured¹⁶ a perfectly correlated or anticorrelated outcome. Clearly, while compatible with monism, this stress on the locality of property-attributions and interactions pushes towards a pluralistic ontology.

As for (2), according to priority monism metaphysical hypotheses invoking the whole as a common ground for all the ‘local’ matters of physical fact [18] presuppose the asymmetric character of the relation of explanation (hence, dependence/grounding). If a whole with its set of properties A (the universe) is explanatorily prior to the properties of its parts B, then the set of properties A grounds the set of properties B and it cannot be the case that B explains or grounds A.

However, in the context of RQM explanation is essentially symmetric (something that will become particularly relevant when we will discuss the coherentist notion of dependence in Sect. 5). In fact, in RQM, when A interacts locally with B, thereby acquiring some determinate (B-relative) properties, the same occurs to B in relation to A. It might be objected that when a macroscopic instrument B measures some property of the quantum system A, the atomic system A acquires very little information from B, since it interacts only with a few of its atomic constituents. This, however, is a merely epistemic fact connected to the circumstance that the magnification of the properties of A is needed for pragmatic reasons related to prediction and testing. In any measurement scenario, the flow of information between A and B is still symmetric and two-way.¹⁷ Pending further arguments to the effect that the symmetric dependence between physical systems is derivative on an asymmetric dependence of all physical systems on the cosmos, this again pushes towards a metaphysical scenario in which priority monism is false.

4 RQM and Ontic Structural Realism

Another option that has been explored recently is to interpret RQM in terms of an ontology of relations. In particular, Candiotto [7] has argued that RQM is naturally understood as supporting a structural ontology as advocated by defenders of OSR (see also [35]). OSR is the conjunction of an epistemological thesis and an ontological thesis. The epistemological thesis concerns what we can reasonably believe about the truth content of scientific theories. It consists of the claim that:

The discontinuity across theory-change in the history of science emphasised by scientific anti-realists is compatible with a degree of structural (formal) continuity, and the empirical success of science is best explained in terms of the (approximate) truth of the preserved structural claims (Structural scientific realism—SSR, for short).

The ontological thesis has it that:

Reality is at root relational, in the sense that physical relations are more fundamental than (or at least as fundamental as) objects (Ontic Structuralism—OS).¹⁸

OSR corresponds to SSR plus OS. It was originally endorsed based on the idea that turning structuralism from an epistemological to an ontological thesis ‘fills the gap’, so to put it, between epistemology and metaphysics. For present purposes, we can set the realist component aside and focus in particular on OS, i.e., the claim that reality as described by our best current science—especially physics—is analysable in terms of relational structure.

This structuralist ontological component is, quite importantly, often endorsed on the basis of contemporary physics and its allegedly relational nature. Arguments that have been invoked in favour of OS include (but are not limited to) reference to the following: the underdetermination between individuals and non-individuals in quantum mechanics, the role of group-theory in quantum theory and the analysability of properties in terms of invariance, permutation symmetry in quantum statistics, weak identity conditions for space–time points as a solution to the problem represented by the ‘hole argument’ in the context of general relativity, the failure of haecceitism and the suspicious nature of alleged non-qualitative metaphysical factors.¹⁹ Crucially, RQM seems to add to the list: since it makes no sense to talk about individual physical systems and their monadic intrinsic properties and properties are essentially relative to other physical systems, the argument goes, in the context of RQM physical relations must be prior to objects and their monadic, intrinsic properties.

This is indeed Candiotto’s key claim: since interactions (“between systems and instruments” [7, Sect. 2] and more generally between physical systems) play a crucial role in RQM, it is natural to interpret it in terms of relations, objects turning out to be mere ‘nodes’ in relational structures, as by now traditionally contended by ontic structural realists. This is certainly an appealing claim, and one that echoes similar ones that can be found in several places in the literature (see, e.g., [14, 27]). However, we believe that, upon scrutiny, the structuralist interpretation of RQM fails. There are three basic reasons for thinking that this is the case, which we will now list in increasing order of importance.

First of all, the notion of structure is notoriously ambiguous and, lacking a precise characterization of it, not only is it difficult to understand precisely what OS amounts to. In addition, and more specifically, it is also quite complicated to establish whether the role played by relationality in the context of RQM is the same as that postulated in the context of OS. Consider, for instance, the ontic characterization of information offered by Ladyman et al. [19] on the basis of the work of Dennett. Is this characterization sufficiently similar to what Rovelli had in mind when introducing the very idea of property-acquisition as based on the exchange of information between quantum systems? It is unclear that the answer to this question should be in the affirmative. Here, at any rate, we will just mention this general worry without attempting to say anything more about the notion of (ontically loaded) relational structure.

Moving on, a second worry has to do with the extent to which RQM actually invites, so to put it, to ‘structuralise’ properties. In particular, it is a central assumption of OS that all physical properties are entirely relational, and objects (may) have to be entirely ‘dissolved’ in a network of relations. That is, OSists insist that state-independent properties, i.e., the essential properties of physical systems, determining the kind of things they are, are also structurally analysable (see [27]). However, RQM is, as we pointed out earlier, a theory concerned with state-dependent properties only: property-attributions can be (and must be) made relational only insofar as properties that depend on the state of the system are concerned. It is of course an open question whether a structuralist reduction of state-independent properties is in fact possible, and we will not try to settle the matter here (for some considerations in support of a negative answer, however, see [25]). For present purposes, it will suffice to notice that, to the extent that RQM explicitly leaves certain properties out of its relational analysis, it does NOT naturally lend itself to an interpretation in terms of OS.²⁰

OSists may insist that at least some of the properties described by RQM are amenable to, if not require, a structuralist interpretation. A third counterargument to the structuralist position, and probably the most important one, then becomes relevant. It is that Rovelli’s emphasis on interaction is by no means to be interpreted in terms of relations being metaphysically fundamental. For, it is one thing to claim a) relations play a fundamental role in the theory in the sense that interactions between physical systems are presented as the cause of those events that correspond to properties acquiring definite values (relative to systems other than the property-bearer, with which the latter interacts); and a different thing to claim that (b) properties (and objects) are literally to be regarded as derivative on relations, the latter being the fundamental constituents of reality. Crucially, (b), but not (a), requires that physical relations be regarded as basic, our metaphysical description of physical reality consequently demanding radical revision.²¹ On the other hand, RQM is committed to (a), but not necessarily (b). The emphasis, that is, is on relationality, not relations. In connection to this, remember our earlier remarks concerning putatively different descriptions of the same event: if we were right there, it follows that on RQM there simply are no objective, system-independent, elements of reality—not even physical relations!—that can be the ground for the qualitative profile of everything. Rather, all (state-dependent) elements of reality are relational. To put it schematically, a typical relation such as, for instance, ‘…has opposite spin in the x-direction relative to…’ is something different from a typical monadic and extrinsic property such as, for instance ‘…is spin up in the x-direction with respect to…’. And what RQM invites us to do is not to reduce the latter to the former, but rather to understand that all (state-dependent) properties are to be analysed in terms of the latter.

In view of the foregoing, pending further independent arguments in favour of OS, it is perfectly possible, and we think preferable, to contend that RQM, far from urging an ontology of relational structure, suggests instead an ontology of more or less ‘traditional’ objects and properties, which however are always dependent on one another as far as the possession of state-dependent properties is concerned.²²

This means that it is advisable to understand quantum systems described by RQM as based on traditional metaphysical categories—e.g., the bundle theory of properties [28]. However, there still seems to be something left to explain: what does the ‘relational’ in RQM refer to at the ontological level? In the next, concluding section, we put forward our own philosophical understanding of RQM and the sort of dependence it posits among quantum systems.

5 RQM, Metaphysical Coherentism and Events

The core of our positive proposal is that RQM can (and perhaps should) be interpreted in terms of Metaphysical Coherentism in the sense proposed by Morganti [26] and by Calosi and Morganti [5]. That is, in terms of the mutual ontological dependence between different entities and their properties. In a bit more detail, metaphysical coherentism is essentially a rejection of

• (i) The traditional foundationalist conceptions of reality in terms of levels, ‘hierarchical’ dependence-chains and fundamentality;

• (ii) The Hume–Lewis idea that fundamental entities must be absolutely independent.

Contrary to (i), we suggest that RQM should be interpreted, as coherentism requires, in terms of physical systems being (at least in certain cases) mutually dependent on each other, hence not giving rise to a pyramidal hierarchy, but rather to the ontological counterpart of a Quinean web of belief, each belief/entity being interdependent with some other.²³

As for (ii), we take it that ‘Hume’s Dictum’, according to which there are no necessary connections between distinct fundamental entities, is also straightforwardly falsified by RQM. On the one hand, at least some of the physical systems described by quantum theory are arguably fundamental. On the other, RQM clearly describes physical systems as necessarily connected to other physical systems. In particular, as far as state-dependent properties are concerned, the laws of the theory are straightforwardly interpreted as descriptions of the ways in which one system affects, and at the same time is affected by, other systems at the level of its qualitative content. In metaphysical jargon, we suggest that RQM is best interpreted as presenting physical systems as ontologically dependent on each other (i.e., as symmetrically dependent) for their qualitative profiles, their mutual dependence setting constraints on possible properties that have the force of nomological necessity. Thus, it seems that metaphysical coherentism provides a natural setting for interpreting RQM.

For a very simple illustration, consider two fermions in the singlet state. Entanglement, according to the metaphysical coherentist, should be understood in terms of contingent mutual relations of ontological dependence among physical systems with respect to their properties. Given the singlet state:

$$ {|\psi}{>} = 1/\surd 2(| \uparrow >_{1} | \downarrow >_{2} - | \downarrow >_{1} | \uparrow >_{2} ) $$

we can interpret it as the mereological composite of two systems 1 and 2, each one of them identified as a particular instance of a kind of thing by its distinctive state-independent properties. According to the coherentist, upon interaction systems 1 and 2 become symmetrically connected in such a way that they can only have some of the spin values that were possible before interaction. In particular, they give rise to an entangled system with total spin 0, and because of this, given Pauli’s Exclusion Principle, only opposite spin values are admissible after interaction. The relevant properties, i.e., the actual spin values of the two fermions are monadic (they ‘belong’ to 1 or 2) yet extrinsic/relational.

Of course, the idea is that this applies generally to all physical scenarios. Consider for instance our Wigner’s friend scenario. There, starting from physical system S in state

$$ {\left| \psi \right.}{>_{{\text{S}}}} = {\text{a}}\left| { \uparrow >_{{\text{S}}} + {\text{b}}} \right| \downarrow >_{{\text{S}}} $$

(see Formula 1 above) a measurement performed by Wigner’s friend F led to a determinate outcome, say, |up_F |↑>. Yet, from Wigner’s perspective the S + F system was in state

$$ {\text{a}}\left| {{\text{up}}_{{\text{W}}} } \right|{\text{up}}_{{\text{F}}} \left| { \uparrow >_{{\text{S}}} + {\text{b}}} \right|{\text{down}}\;{\text{W}}\left| {{\text{down}}\;{\text{F}}} \right|{\downarrow} >_{{\text{S}}} $$

(see Formula 5) which entails that, according to W, S does not have a definite spin value in the relevant direction. As mentioned, RQM solves the problem by making the attribution of the properties in question relative (and necessarily so). This, we are claiming, means to attribute to physical systems exactly the features postulated by metaphysical coherentism. In particular:

• (1) The system S does not have a determinate spin on its own, yet it does have a determinate spin value with respect to F and/or W, which means that S is dependent on F and/or W with respect to its qualitative profile;

• (2) The dependence in question is symmetric: insofar as their report of S’s properties is regarded as one of their qualitative features, F and W are dependent on S for their qualitative content; generalizing, every interaction modifies the state of the interacting entities.

Two remarks are in order at this point. First, one may object that, since it is a metaphysically thick, realist view, coherentism does not mesh well with the claim that (state-dependent) properties have no objective, absolute values. However, the perspective-relativity of dependence is not an issue for the coherentist insofar the dependence relations in question are symmetric, which we argued is the case. More generally, it is simply incorrect to take metaphysical realism to imply, or coincide with, objectivism about things, properties, facts, etc.²⁴ Secondly, one could complain that coherentism does not explain the perspective-relativity of dependence. This is certainly the case, yet, once again, we do not think this is an issue for our proposal. Indeed, the key interpretative issue raised by RQM, or at any rate the one we aimed to tackle in the present paper following the extant literature, does not have to do with the origin of the characteristic perspectival nature of the quantum domain as described by the theory. Rather, it has to do with the ontological status that should be attributed to physical systems and their properties once one assumes RQM to be the (approximately) correct description of the world, and consequently accepts relationality as a fact.

Before closing, there are a couple of other questions that need to be addressed. First of all, how is coherentism better than, or even just different from, the ontological interpretations that we have already considered—i.e., monism and structuralism?

The answer to this question is straightforward. The proposed coherentist construal is more plausible than priority monism because the postulation of symmetric dependence between proper parts of the universe by no means entails that the whole is (asymmetrically!) prior to the parts—which, as we have seen, is an unnecessarily strong claim. Also, the proposed coherentist construal is more plausible than structuralism because hypothesizing ontological dependence relations between physical systems by no means entails that those physical relations are more fundamental than objects with their monadic properties.²⁵ Consequently, the coherentist can provide an explanation of the essential relationality of RQM without incurring the costs of an ontology of physical relations—which, as we have seen, requires that the structuralist analysis be carried over in contexts where physics may not justify it. Even if OS and coherentism were equally physically grounded, which in fact we provided reasons for doubting, the following should, in particular, be noted. While OS reifies the explanans, claiming that interactions are literally fundamental constituents of reality, coherentism takes the empirical evidence to ‘merely’ urge a change in the form of explanation: accounting for interactions is no doubt essential for a complete description of physical reality, yet this can perfectly be done in terms of an ontology of (ontologically interdependent) objects. Other things being equal, this seems to be a clear advantage in terms of the minimisation of revision of established beliefs.

One last open question concerns the connection (if any) between the coherentist view of RQM and the idea of an ontology of events, or ‘flashes’. As illustrated, for instance, by Allori [2], so-called primitive ontologies are increasingly popular in the philosophy of quantum mechanics. In a nutshell, these aim to extract from the theory a description of some fundamental structure of matter in three dimensions. According to flash ontology, for instance, this fundamental structure is one of local events in space–time. While usually developed in the context of collapse interpretations (flashes corresponding to the spontaneous collapses that replace superpositions with determinate states), the flash ontology might also be plausibly regarded as the natural framework for RQM: the basic events, in this case, would be those corresponding to local interactions between physical systems, determining the (perspectival, relative) state-dependent properties of those systems.

Now, there may seem to be a tension at this point between the coherentist claim that on RQM physical systems and their properties fundamentally depend on each other, and the claim, sometimes explicitly endorsed by Rovelli himself (see, e.g., [22], introduction), that the basic ontological entities are events of the form ‘system S acquires property P with respect to system Q (and conversely) at a certain time t’. The tension consists in the fact that, on the former construal, physical systems and their properties are fundamental, and events involving them are derivative. On this understanding, events are a by-product of interactions between physical systems that in the theory are presented as the cause of the determinateness of the system’s monadic properties (relative to systems other than the property-bearers). On the latter construal, instead, the opposite would be the case: events as the basic inhabitants of the space–time four-dimensional continuum would be basic, and objects/physical systems/substances and their properties would be derivative.

While we acknowledge the significance of this issue, however, we think it is not essential to settle the matter here. In fact, we take it to be nearly impossible, as a number of additional open problems would have to be dealt with, having to do with the relationship between relativity and quantum mechanics, the prospects of various hypotheses concerning quantum gravity, the metaphysics of space, time, objects and persistence and more. As things stand now, at least for present purposes, we think it is sufficient to point out that a systematic ‘translation’ between the two views seems possible. That is, talk of physical systems exhibiting properties and being ontologically dependent on other physical systems for their ontological profile (at any particular time t) can always be turned into talk of events of the form ‘S acquires property P in relation to Q—and Q acquires property R in relation to S—at time t in virtue of the mutual ontological dependence between S and Q’. The converse translation, is of course, also entirely feasible. The former option is likely to be more useful when one wants to emphasise the role of interaction and its outcomes from a spatio-temporal, hence relativistic, point of view. The latter may instead be more appropriate when one aims to move from a description of the physical content of specific points/regions of space–time to a more traditional ontology of persistent things and their properties. On this, however, RQM need not (and indeed should not be expected to) establish any order of metaphysical priority.

6 Conclusions

In this paper, we have identified and critically compared some proposals that can be advanced to clarify the ontological consequences of RQM. Focusing first on the more popular ones, we started by discussing priority monism and ontic structuralism and argued that these views are not suitable for defining an ontological interpretation of the theory. Monism is unable to account for the sort of mutual dependence exhibited by the proper parts of the universe, and for the seeming non-epistemic dependence of the cosmos on its proper parts. As for ontic structuralism, besides being notoriously vague on the key notion of relational structure, it seems to unwarrantedly move from Rovelli’s emphasis on interactions between physical systems to the claim that reality is at root wholly analysable in terms of physical relations. Starting from these negative results, we endorsed an alternative that we regard as more promising, based on so-called ‘metaphysical coherentism’. We suggested that metaphysical coherentism, with its emphasis on symmetric ontological dependence between more or less traditional objects and properties, makes it possible to achieve the best of both worlds: that is, to make relationality metaphysically fundamental while at the same time not requiring a seemingly impossible, or at least implausible, kind of metaphysical revision. At the same time, however, we left it open whether the truly fundamental ontology of RQM is one of events, or ‘flashes’, in space–time. On this alternative construal, we suggested, the fundamentalia would change (spatio-temporally localized events rather than three or four-dimensional continuants with their properties) but the essential relationality, i.e., ontological interdependence, of the physical contents of reality would not be affected. Given this and the inter-translatability of event talk and object talk, we suggested, the coherentist emphasis on symmetric dependence remains in any case unaffected, and arguably represents the most plausible way to pick out the essential, revolutionary message of RQM.