Relational Quantum Mechanics at the Crossroads

Ever since Carlo Rovelli introduced Relational Quantum Mechanics (RQM) to the public [1], it has attracted the interest and stimulated the imagination not only of physicists, but also, and in particular, of philosophers. There are several reasons why that is so. One of them is, quite simply, that a renowned and highly esteemed researcher had offered a new programmatic attempt to make sense of the long-standing puzzles at the foundations of quantum theory, which only happens every so often. What is more, the key to these puzzles was supposed to lie in an essentially conceptual move, in the exposure of an “incorrect notion” [1, p. 1637]. But the modern-day philosopher regards concepts as something like their natural hunting ground. If mention is made of the word, it makes them sit up as if somebody had yelled their name.

The suspect Rovelli had identified was the notion of the absolute state of a physical system. Similar to how relativity taught us to live without absolute lengths, times, and energies, he said, quantum theory requires us to do away with absolute (state-dependent) properties tout court. With the wisdom of hindsight, we know now that this made him a forerunner of a broader contemporary renaissance of relativism in the quantum domain, a renaissance that unfolded in perspectival modal interpretations [2,3,4], relative-facts readings of Everett [5, 6], QBism [7], pragmatism [8], and certain neo-Copenhagen approaches [9,10,11]. Within this broader trend, Rovelli pioneered what has since become perhaps the most important current, bound together by a number of family resemblances. The contributors to this current conceive of the world as a genuinely chancy place; they primarily regard quantum states as predictive tools; they often have an affinity for information-theoretic talk and thinking; they believe that physical states and properties are relative to other systems, rather than contexts (as on Bohrian views) or the states of other systems (as on Everett-style relative-fact interpretations). And finally, they typically motivate this relativity by consideration of certain thought experiments.^{Footnote 1} Traditionally, this role was played by ordinary Wigner’s friend cases. More recently, the relativist movement has been given a boost by sophisticated “Bell-Wigner mashups” [12], developed into no-go theorems that purportedly rule out observer-independent measurement outcomes for single-world interpretations (cf. inter alia [9, 13, 14]).

Philosophers have a pedigree of several millennia in wrestling with relativism, which may well be another reason why they are attracted to its quantum renaissance and believe they might be able to contribute fruitful insights.^{Footnote 2} Indeed it is an interesting coincidence, if a coincidence it is, that this renaissance took place around the time when analytic philosophers seriously began putting the notion of ‘relative truth’ on rigorous theoretical footing [16,17,18], mapping out the conceptual space for a coherent notion of ‘perspectival facts’ not wedded to idealist premises [19,20,21,22,23,24], and outlining the contours of ‘perspectival objectivity’ [25] as well as ‘perspectival realism’ [26,27,28] in the philosophy of science. Common to these endeavours and Rovelli’s project is the striving for a version of relativism, in the respective domains, that is decidedly not a mystifying murmur but a clearly articulated theoretical possibility even for the hard-headed. Rovelli is at pains to stress that his outlook on quantum theory is a naturalist and realist one. Neither does it ascribe any special powers to consciousness, nor does it reduce the goings-on in the universe to the mental lives of advanced apes, nor does it render them dependent on anybody’s whims, knowledge, or conceptual scheme. It is the physics, and only the physics, that determines the states of systems relative to each other, and in so doing it does not care much what we think or know of it.

RQM has always been an interpretive programme rather than an interpretation carved in stone, revolving around a bundle of ideas subject to (at times continuous, at times rather discrete) changes and reconstruction works. This state of flux has sometimes made it difficult to keep track of its commitments. Still, by now, it looks as if a fairly definite set of core tenets ripe to be canonised has slowly emerged from many years of refinement. Most of the papers assembled in this special issue deal with ‘classical’ RQM in this well-known shape. As it turns out, however, Rovelli qua restless thinker was to entertain significant modifications once again, this time in joint work with Emily Adlam [29]. Therein, the authors introduce a new axiom designed to enable communication across perspectives, and effectively bid farewell to “unbridled” relativism [29, p.8]. Whether this new version will catch on and supersede earlier ones remains to be seen. If so, RQM will part ways with relativists in the quantum domain, and outgrow a trend it has had a determining influence on. Relational Quantum Mechanics has reached a crossroads.

In this situation, it would be pointless for us to attempt a canonical presentation of the interpretation. As far as ‘classical’ RQM is concerned, such a presentation has already been provided by a much more authoritative source [30]. What is missing, though, is a systematic retelling of the story that has led to the current state of play. And sometimes, indeed many times, retracing our steps gives us a better sense of where we are and provides us with a clearer idea of which new paths diverge from there. We will spend some time and words detailing how we got to the crossroads we take RQM to have reached, what it consists in, and where we could go now. This is the overarching narrative that is developed throughout this paper-length introduction. In light of this, it is structured as follows: in §2-5 we present a somewhat opinionated history of RQM. Naturally, we had to be selective, and we make no claim that this is the only way to tell this story.^{Footnote 3} But we hope that our way is perspicuous for our broad argument, and also places RQM firmly in the debate over quantum foundations. In §6 we offer, briefly, a bird’s eye view of where we stand now. We do that by engaging directly with the papers in the special issue, which offer an outlook on the state of the art. We do it briefly, because we think that the papers should speak for themselves. Finally, in §7 we indicate new paths waiting to be explored and argue why we think they are relevant. Thus, we draw attention to open questions in classical RQM, we shed light on recent developments, and we identify important directions for further research: past, present and future of RQM.

Ask one philosopher what the ‘measurement problem’ is and you get three [31] to five [32] to six answers [33] on average. But one traditional way of setting up the issue^{Footnote 4} is this: As presented in the textbooks, quantum mechanics provides not one but two rules for the dynamical evolution of the mathematical objects (vectors or functions) that represent the states of physical systems. On the one hand, we are told that these objects usually evolve in accordance with a certain differential equation (Schrödinger’s equation, in the non-relativistic case). Call this rule 1. On the other hand, the vectors or functions are supposed to sometimes make discontinuous, stochastic jumps, namely when a measurement is performed on the system. Call this rule 2.

Now, this set of rules is either weird or weird and inconsistent; either way, it is (hopelessly) ambiguous. It is weird\(_{1}\) if we take it to say that the ordinary dynamical laws somehow cease to apply to physical systems when they undergo ‘measurement’. One may on principle find it hard to believe that any such high-level notion should enter non-trivially into the laws of microphysics. It is, after all, tempting to think that measurements are at bottom ordinary physical interactions, interactions that can just as well be modelled by means of the ordinary dynamics as any other. But if we make this assumption, the rulebook threatens to become weird\(_2\) and inconsistent. Weird\(_2\), because rule 2 should in this case be entirely superfluous. Inconsistent, because the results we get with and without application of rule 2 do not in fact match up. In any case, the rules are ambiguous, because it is utterly unclear what counts as a ‘measurement’. If one were mischievous, one could say that rule 1 always applies except when it doesn’t, in which case rule 2 applies instead.^{Footnote 5}

The founding idea of Relational Quantum Mechanics is to remedy weirdness\(_1\) and ambiguity by replacing ‘measurement’ with any old interaction, and to remedy weirdness\(_2\) and inconsistency by means of relativisation. As regards the first conjunct, the thought is that ‘interaction’ is a notion that can more plausibly be employed, and hopefully more rigorously defined, at the microlevel.

Elaboration of the second conjunct requires a little stage-setting. Following Rovelli [1], the matter can be brought into sharp relief by means of Wigner’s well-known thought experiment. Suppose, then, that Wigner’s friend Alice is (for unknown reasons) locked in an isolated laboratory, where she performs (likewise for unknown reasons) a repeatable measurement of a two-valued variable q on a system S at time t. Suppose further that the system initially was in a superposition of eigenstates of q. Alice observes one of the possible outcomes and collapses the state vector she assigns to S onto the appropriate eigenstate, in accordance with rule 2. Now, cut to Wigner, who is mucking about outside the lab. Bored by the wait, he wonders what quantum physics can teach him about the happenings in there. Well, surely, he thinks, Alice and S (plus the rest of the lab, which we ignore for convenience) make up a physical system he can ascribe a state vector to. And surely, he should be able to model their interaction unitarily (viz., applying rule 1) at least until he makes a measurement on them. On Wigner’s account, then, this composite system evolves from the initial state:

to the state

at time t.^{Footnote 6}

Now, note the striking discrepancies between Alice’s and Wigner’s descriptions. For one thing, the Born probabilities they ascribe to possible future measurements on S do not line up: Whereas Wigner would say that the probability for a subsequent measurement of q to yield outcome \(q_1\) is \(|c_1|^2\), according to Alice it would be either 0 or 1 (depending on the first measurement result). For another, they would presumably also disagree about the properties of S at t: whereas Alice would either claim that S possesses \(q_1\) or that it possesses \(q_2\), Wigner’s description does not single out any determinate q-property at all.^{Footnote 7} If we accept both accounts, as we have just interpreted them, we seem to run into contradiction.^{Footnote 8}

However, the contradiction dissolves if probabilities and properties are relative. In that case, Alice can be right about the properties and probabilities as they are relative to her, and Wigner can be right about the properties and probabilities as they are relative to him. On this picture, rule 2 neither generates inconsistencies, nor is it obsolete: it is essential for Alice to get matters right as they are relative to her. What we need to abandon is the notion of an absolute state of a system, in both senses of the word ‘state’, as referring to quantum or physical states. Voilà, the crucial conceptual move alluded to at the very beginning: the initial spark for Relational Quantum Mechanics.

The new rulebook we end up with, then, looks something like this: the states of physical systems are still represented by the same type of mathematical object as before, but now regarded as relative to a second reference system. In general, the mathematical object evolves according to the relevant differential equation. However, the state vector of one system relative to another does make stochastic jumps whenever it comes to a physical interaction between the two. In such an interaction, the systems acquire determinate properties relative to each other. In fact, over time, the idea emerged that systems only ever have determinate properties at, but not in between, interactions, resulting in a view where any physical process is really “a very fine-grained but discrete swarming” [37, 9] of flash-like relative property realizations, or ‘events’. When relative properties have been established between two systems, this manifests itself in a correlation between their variables, as encoded in the quantum state assigned to their composite by an external observer.

Admittedly, this leaves many questions unanswered. How exactly are we to think of relative quantum probabilities? Can the notion of an ‘interaction’ really be rendered sufficiently precise? And how does the story generalise to non-ideal or continuous measurements? Is there any restriction on admissible targets of relativization? But it’s the first step that is the hardest, they say, and it needs to be taken before the others.

In the seminal paper that first introduced a wider audience to these ideas [1], the word ‘information’ appears a respectable 183 times. The role it plays is twofold. Firstly, Rovelli used the locution that an observer ‘has information’ about some quantity as a notational variant to express that the quantity has a determinate value relative to her. Here, mutual ‘information’ is used in the minimal sense of a correlation between the configurations of two systems. As we saw earlier, from a third-person perspective, that is exactly what is established in an interaction. And secondly, Rovelli built on this association to complement his interpretive approach with a loose derivation of the basic quantum-mechanical formalism from two information-theoretic axioms. Again, this was pioneering work, preparing the ground for a clutch of epistemic interpretations [38,39,40,41] and a new wave of attempts, ongoing to this day, of reconstructing quantum theory from transparent physical principles (cf. inter alia [41,42,43,44]). However, the connection between the relativity of dynamical states and Rovelli’s informational axioms was not altogether clear, which explains why the literatures that sprang from these two contributions immediately decoupled. In fact, as underlined by Stacey [45, p. 2], we know by now that Rovelli’s postulates are satisfied by entirely non-relativist and indeed non-quantum toy models (cf. [41]). To this day, an in-depth exploration of the relationship between RQM and the reconstruction programme remains a desideratum. In this connection, it merits attention that Yang recently set out to recover quantum theory from explicitly relativist premises [46][47].

The information-theoretic gloss notwithstanding, RQM did initially grant a substantive representational rather than purely epistemic role to the quantum state. In particular, it was said that “[f]or a fixed observer, the eigenstate-eigenvalue link is maintained”[1, 1673]. Soon, however, this ontological import was to be denied. There were several reasons for this. To some extent, the information rhetoric had developed a life on its own, acting as a greenhouse for the mushrooming of new epistemic interpretations which promised pellucid explanations of quantum oddities like the state collapse. But another driving force was the question of non-locality.

Laudisa [48] had been first to suggest in print that RQM may offer a new twist on this long-standing problem child. Non-locality, so the thought goes, has to do with physical systems affecting each others’ properties at a distance. According to RQM, though, which properties are elements of reality at a given coordinate time is a reference-dependent affair, and this may provide precious additional manoeuvring space. What we see here is an instance of a general idea that was to shape the debate about locality in RQM. At least since Bell’s groundbreaking work, non-locality has been framed as a matter of influences between beables over space-like separation. This conception invites the idea that non-locality can, in principle, be avoided through ontological austerity - through the acceptance of fewer beables. We will soon have opportunity to question this idea in some ways. But first, we shall trace the influence it has exercised.

While Laudisa himself essentially argued that the violation (or not) of locality becomes doubly relative to both reference systems and inertial frames in RQM, Smerlak and Rovelli [49] aimed to defend the stronger claim that such violations can be altogether avoided. The price to pay was a deflated reading of quantum states—an epistemic turn. Consider a typical EPR set-up, where two observers Alice and Bob have access to one of two entangled electrons each. If Alice measures the z-spin of her particle, thereby also projecting the state vector of the far-away particle onto a spin eigenstate, this is merely an update of information according to Smerlak and Rovelli. But note what is happening here: the (relativised) eigenstate-eigenvalue link is broken. Although Alice’s measurement collapses the quantum state of the distant particle, we are not allowed to deduce that the latter has genuinely acquired a determinate (relative) z-spin at that very moment. For the same reason, Alice’s ‘having information’ about the electron is no longer synonymous with it possessing determinate properties relative to her. On this basis, Smerlak and Rovelli claimed that there was no ‘spooky action at a distance’ involved in the relational EPR scenario. The second particle would only acquire a property relative to Alice when she would later interact with it or with Bob, and this would of course have to take place within the future light-cone of her first measurement.

Since then, Rovelli espoused the view that quantum states are merely epistemic creatures. He later supported this with the observation that they are not time-reversal invariant, given the Projection Postulate [50]. Still, one may hesitate. For a start, one wonders how this stance goes together with the idea that any system has a well-defined quantum state relative to any other [51, section 2.3]. In what sense can the quantum state of one electron relative to another be considered ‘epistemic’ (cf. [52])? More generally, the problem is that we are not told how to think of the probabilities for mutual interactions that are encoded in state vectors. Are they arbitrary credences, completely and utterly at the mercy of the spectator’s whims? The literature review seems inconclusive. While Smerlak and Rovelli assert that quantum probabilities are “clearly to be interpreted subjectively” [49, 431], at other times Rovelli takes them to provide “something objective” [53, p. 221]. Both Stacey [45, p. 4f.] and Pienaar [54, 6] maintain that the pronouncedly non-mentalistic conception of ‘information’ operative in RQM requires objective probabilities that even have (some) “ontic hold upon the world” (ibid.)^{Footnote 9} Weststeijn [55] argues that RQM could and should bid farewell to the epistemic view of quantum states; and then there is also Dorato’s proposal that they describe real probabilistic dispositions of physical systems [56][51, sect. 3.2].

Allow us a little detour to conclude this section. This serves to draw particular attention to one more ramification of the epistemic turn: namely, that it threatens to render the task of defining a precise dynamics for RQM even more difficult than it already was. As anticipated above, one would ultimately hope the interpretation to specify rigorously when an interaction with which possible outcomes occurs between two systems. In Rovelli’s original presentation, we seemed to get the seeds of a (liberal) story: According to that story, one system had a determinate property relative to another whenever there was a correlation between said property and some pointer of the second system, as witnessed by their joint quantum state relative to a third observer. Admittedly, this account faces difficulties. As argued by Pienaar in his contribution to the present issue [57, pp. 21-25], it would imply that systems can simultaneously have determinate relative properties that correspond to non-commuting observables. Also, it fails to provide agents with a means of predicting the timing of their own interactions (cf. [58]).^{Footnote 10} More importantly for present purposes, however, the idea that correlations encoded in state vectors are the measure of relative properties is also flatly at odds with the notion that said vectors are not descriptive of ontic states.

Consequently, Di Biagio and Rovelli now declare that ”[e]vents cannot be read out of the state" [59, 5] in their reply to Pienaar. An observer, they say, needs additional information to learn which relative properties are actual—“for example the dynamics that coupled the two systems and, in particular, what variables are involved in the interaction" (ibid.). This response is likely to raise further questions. On the one hand, it seems hard to square with the rejection of hidden variables. On the other, it proves difficult to see how the external observer should collect any such additional information, given that the probabilities for any measurement she could perform on the two systems of interest are fully determined by their joint quantum state. So, what exactly is that extra information supposed to be, how can it be gathered, and how does it allow one to infer relative properties?^{Footnote 11} Pending answers to these questions, we do not have a dynamics. Consequently, it is unclear how we could use RQM to make probabilistic predictions for the actualisation of properties (even only relative to us) without bringing in experiential heuristics or ad hoc premises about when interactions in which bases ordinarily occur. It seems like the epistemic turn has thrown us back into the old problems of identifying a preferred basis and determining the timing of an interaction in largely unmitigated form (cf. [58, 5-14] for related criticisms and [29, pp. 15–17] for discussion).

But enough with detours. Back to non-locality, you say. Have we not agreed that that is a matter of influences between beables at space-like separation? Whether these beables are, moreover, aptly said to be represented by some mathematical object or other is of no further consequence. The interpretation of the quantum state thus bears on the issue only indirectly. And really, the key metaphysical question negotiated in the literature on locality in RQM lies elsewhere: namely, it concerns the ontological status we should ascribe to interactions we are not ourselves partaking in.

Coming back to our EPR situation, observe that Alice can reconvene with Bob at a later \(t_2\), ask him about his measurement outcome at \(t_1\), and register the reply. At least in this loose sense, then, it can be said that Bob ‘informs her about the outcome of his earlier interaction with the electron’. But how is Alice herself to think about this interaction? It seems to us that there are at least four possibilities, usefully organised in two categories:

• Relativism: Whether an interaction has taken place between Bob and his electron at \(t_1\), and whether the electron has therein assumed a particular property relative to Bob^{Footnote 12}, is itself relative to a system. This is one more relative fact. This can be further spelled out as follows:

  • Deflationism: Relative to Alice, there is no event between Bob and his electron at \(t_1\). For Alice, her own interaction with Bob only establishes that Bob has certain (relative) properties at \(t_2\).

  • Ignorance: Relative to Alice, there was an event between Bob and his electron at \(t_1\), which she may or may not learn about at a later time.

  • Retro-Determination: Relative to Alice, at \(t_1\), there is no event between Bob and his electron (at that time). However, at a later time, it becomes the case, relative to her, that there was such an event at \(t_1\). This could be either a) as soon as this event lies within her past light cone or b) as soon as she interacts with Bob to find out about it.

• Absolutism: It is an absolute fact that there was an interaction between Bob and his electron at \(t_1\), and that the electron assumed a particular determinate property relative to Bob.^{Footnote 13}

The choice between these options, which all have their share of advantages and disadvantages, is of interest in and of itself. But insofar as there can be talk of correlations or influences only between events that are real, one may also expect them to have different implications for locality.

Indeed, the decisive move in Smerlak and Rovelli’s exorcism of action at a distance was a rejection of Absolutism and Ignorance. Relative to Alice, they claimed, there simply was no interaction between Bob and his electron at \(t_1\); and consequently, Bob’s pointer variable had no definite state at all (relative to her) at that time [49, p. 436f.]. What was missing was an explicit discussion of how Alice was supposed to interpret Bob’s outcome report when she would meet him again. Should she really not be able to take it seriously as a reliable account of real happenings, as the Deflationist would have it? And relatedly, how should she make sense of the striking correlations between her own spin observations and Bob’s reports?

The importance of the point was later recognised by Martin-Dussaud, Rovelli, and Zalamea [62]. In what sounds like an endorsement of variant a) of Retro-Determination, they declare that the existence of events outside of one’s past light cone is only “a matter of metaphysical faith”, while the existence of those inside of it is “a matter of experimental fact” [62, p. 102]. But if this is so, then later Alice is, after all, faced with what she has to interpret as correlations between two space-like separated measurements,^{Footnote 14} - correlations, moreover, that violate Bell’s inequality. This much is granted by Martin-Dussaud, Rovelli, and Zalamea. They argue, however, that Alice could trace these correlations back to a common cause, because (they say) Reichenbach’s principle of decorrelating explanations is unsuitable for indeterministic contexts. In other words, they deny that the mathematical constraint Bell called ‘local causality’ accurately captures the physical notion at stake.^{Footnote 15}

Of course, this escape plan, if viable at all, is equally open to any indeterministic interpretation. In contrast, Pienaar [63] sets out to search for an approach more specifically tuned to the traits of RQM. Taking the operationalist overtones in Rovelli and collaborators one step further, he argues that RQM lends itself to a Deflationist reading. On this reading, the question of non-local influences between Alice’s and Bob’s measurements does not even arise: all events that would be real for Alice would lie on her own (timelike) world-line. And so, violations of ‘local causality’ would be out of the question.

From a bird’s eye view, Martin-Dussaud, Rovelli, and Zalamea’s work signifies a departure from the attempts of saving locality by expunging beables, while Pienaar’s proposal is the iron-willed implementation of this very strategy to the very end. But although Rovelli and others were happy to epistemicize quantum states, Pienaar’s proposal has not caught on. Presumably, the Deflationist diet has seemed all too scanty and egocentric to many. For instance, Ruyant (2018) argues that it would bring RQM dangerously close to QBism or even instrumentalism. “I have no reason to believe”, Di Biagio and Rovelli write, “that reality comes into being only when it interacts with me, and not also when anything interacts with anything else” [59, p. 14].

One critical issue, then, is how much ontological sacrifice locality would even be worth. But by now, it should also dawn on us (it certainly dawned on Ruyant and Pienaar) that there is something suspicious about the core presupposition of the debate: the presupposition that the right thing to worry about is whether there are influences between beables at a distance. Focusing in on this question, one is led to the idea that denying (or relativising) the existence of beables is a way to stay local, an approach that culminates in the defence of Deflationism. But if what we are ultimately after is the coherence of quantum mechanics with the physical lessons of relativity theory - viz., if our preference for locality is not merely dogmatic in nature - this does not look like the right starting point. As Ruyant [60, p. 444] observes, any theory, however wildly non-local on its standard reading, would come out ‘local’ in the sense just defined if only interpreted in accordance with Deflationism. The solution looks almost trivial, so as to raise the suspicion that we are not asking the right question. And it is telling that precisely the same dialectic has unrolled in the literature on QBism, with Mermin, Fuchs, and Schack [7] recommending the Deflationist resolution of Bell non-locality and Cavalcanti objecting that “nothing could possibly count as evidence of nonlocality" if this strategy were accepted [64, p. 11]. Cavalcanti even goes on to argue that QBists should instead reject Reichenbach’s principle.

Here is another way to make the same point. It would surely be possible to interpret Special Relativity (SR) itself along deflationist lines, granting reality only to those events one is directly involved in and treating all others as a useful fiction. If one would do that, however, the import of the finite speed of information propagation in SR itself would be transformed, too: It would then turn into a constraint on the influences that would be present between ‘events’ if one were to grant existence to all of them (ultimately, a constraint on the types of records we can possibly encounter). Put differently, the physical meaning of locality in SR is itself not independent of the most basic ontological assumptions, and cannot be fixed prior to these. Hence, one worries that the relegation of events to the realm of non-existent shadows is besides the point insofar as it does not cut ice for the reconciliation of quantum and relativistic world views; that it is a metaphysical sleight of hand that works only by subjecting the two theories to wildly different ontological presuppositions, measuring the meaning of locality in SR against the backdrop of one and its fate in quantum theory against the backdrop of another,^{Footnote 16} It is a bit like interpreting quantum mechanics with an idealist hat on and thereby declaring it consistent with relativistic locality read as a constraint on ‘external’, physical goings-on. If this is right, the notion that there could be something about the ontology of RQM - the relativisation of the existence of beables - that helps preserve locality is beginning to look suspicious.

It does not follow that the ontology of third-party interactions is of academic interest only, though. For as we have seen, it is intimately connected to the correct understanding of reports, that is, the communication and comparison of information between observers. This brings us to one of the most challenging and most controversial, but also most interesting aspects of Rovelli’s views, and it will ultimately also bring us to the crossroads promised in the title of the present piece.

The worry that RQM is in some way inhospitable to the notion of a common reality shared by everybody has been around since its inception. It is a worry which can spring from different sources. Of these, a naïve identification of relativity with subjectivity would be the least compelling: As Laudisa and Rovelli [51, section 1.2] remind us, the fact that velocity is an observer-relative magnitude by no means implies that there is anything subjective about it. But have a look at these two puzzles instead, puzzles that readily suggest themselves in light of the relativity of properties:

• If systems randomly acquire properties that are always only relative, how come that we by and large all seem to agree about their features? Is this some sort of miraculous coincidence? Wouldn’t it perhaps be a reason to think that properties are absolute, after all?

• If RQM is on the right track, are we not all hopelessly locked in our personal vantage points? Think about it this way: All I can ever learn about other systems by interacting with them is the properties they have relative to me. This even extends to other observers, since they are physical systems, too. But then it seems impossible in principle to find out what is the case relative to them.^{Footnote 17}

The two issues are intertwined: If it were true that we are trapped in our very own points of view (even our own view on the behaviour and assertions of others), this may help explain an appearance of intersubjective agreement where no genuine conformity across perspectives is to be expected. Or, turning things around: if one and the same system can actually possess wildly different properties relative to different observers, the fact that we do not encounter such blatant discrepancies could be taken to establish that perspectives must be informationally isolated (if RQM is to be empirically adequate).

Keeping the two questions in mind—can observers access each others’ perspectives?, and can we explain why these should be mutually coherent?,—let us have another look at the ontological menu. For concreteness, return to Alice’s and Bob’s get-together at \(t_2\), during which Bob tells Alice about his spin measurement. On a Deflationist view, Bob’s report is, for Alice, a probabilistic manifestation of properties he acquires relative to her and nothing more. Alice cannot really take it to be ‘about’ anything, as Bob’s measurement is not even real for her.^{Footnote 18} If communication across viewpoints is what we are after, this does not look like the most auspicious of starts. This problem does not arise with Absolutism, according to which (the clue is in the name!) there is an absolute fact about the spin property Bob’s electron manifested relative to him. Here is a fact regarding Bob’s experiences, then, that Alice can regard as a target of potential inquiry. If we want to strictly adhere to the notion that physical interactions can only ever inform us about states of affairs that are entirely relative, however, it is a target she cannot hope to reach. Moreover, let’s not forget that we would not have a reason to expect the absolute facts about what is the case relative to Bob to show any systematic connection to the facts about what is the case relative to Alice.

Looked at in this light, it is natural to try and pursue one of the remaining Relativist possibilities. And as it turns out, they offer a package of solutions to our difficulties that (whether ultimately tenable or not) is of remarkable elegance. For a start, Ignorance and Retro-Determination.^{Footnote 19} do provide a fact about Bob’s perspective that Alice can take his report to be about; for, we are now assuming that relative to her, Bob’s spin measurement is real, and did result in a determinate spin property relative to him. But as all of this is itself relative to Alice, we can also unproblematically assume that it is revealed to her in the relative values Bob’s pointer variables take on in their interaction. And as a bonus, if we do, the quantum formalism by itself conveniently ensures the desired coherence.

Here is how this works. Supposing that Bob’s measurement on electron \(e_1\) occurs first, the quantum state Alice ascribes to the composite of the two electrons \(e_1, e_2\) and Bob prior to her own experiment looks something like this (neglecting constants):

(For simplicity, we have assumed that Bob’s is known to be an ideal measurement along the z-axis, and altogether ignored interactions with the environment.) Now, Rovelli maintains, Alice could find out whether \(e_1\) assumed z-spin up or down relative to Bob by checking whether \(Bob \oplus e_1\) are in state \(|\uparrow _z\rangle _{e_1} |\uparrow \rangle _B\) or in state \(|\downarrow _z\rangle _{e_1} |\downarrow \rangle _B \). If she does, the above quantum state is projected onto one of its ‘branches’, depending on the outcome she receives. That is, the state of \(e_1 \oplus Bob \oplus e_2\) relative to Alice evolves to either

Observe here that in both cases, Alice can be certain that if she were to check, she would find that \(e_1\) and \(e_2\) possess opposite z-spins, and that Bob’s report about the spin of \(e_1\) would match her own observations. So, at least in typical situations, in which no decisive intermediate disturbance of Bob’s pointer variables has taken place, Alice can straightforwardly trust his utterances as a reliable information source about what is going on relative to him - relative to herself.

We thus seem to have achieved what initially looked like the squaring of the circle: We reconciled the assumptions that interactions i) only ever inform us of states of affairs as are relative to us, and ii) nonetheless are an adequate means to find out what is the case relative to others. The price to pay is another relativisation of what is the case relative to whom. This allows us to associate the properties systems have relative to each other with variables of the composites they constitute. Here is Rovelli in original sound:

“If the statement ‘q has a value relative to O’ [...] has any comprehensible physical meaning at all, this meaning should be related to the contingent state of the S-O system. According to the main hypothesis here, asking about the observer-independent contingent state of the S-O system has no meaning [\(\ldots \)] [But] we can make statements about the state of the S-O system, provided that we interpret these statements as relative to a third physical system” [1, p. 1653].

We have explicitly introduced second-order relativity. But as one of us has argued elsewhere [66], the moral really cuts deeper than that. By much the same logic as before, the dynamical properties one system \(S_1\) has relative to another \(S_2\) relative to another \(S_3\) can be associated with observables on \(S_1 + S_2+ S_3\), and so should be relative, too, and so on for higher levels. What we end up with, then, is a thoroughly relativist theory on which no specification of ever more references makes it possible to recover absolute statements (as anticipated by [58, 13]), and which hence really does not allow for a God’s eye ‘view from nowhere’ (cf. [59, p. 11]). This is noteworthy insofar as the infinite regress of relativisations has been regarded by some as a problematic or even incomprehensible consequence of stronger forms of relativism (cf. [67]; [68, p. 121]; [69, 52-56]). It is also of metaphysical interest insofar as it renders RQM outright incompatible with the traditional paradigm of relativity as relationality. According to this paradigm, relativism is the (alleged) discovery that the facts in a certain domain really turn out to be about relations; they are ‘relative’ only in the mundane sense that all relata need to be made explicit in order to completely specify a possible state of affairs, whose obtaining or not, however, is still an absolute question. This is certainly the way in which we ordinarily conceive of relativity in physics. But if it is true that relativity iterates endlessly in RQM, this conception collapses: we cannot simply re-conceive of properties as relations, because no adicity would be sufficient to make the holding of those relations itself an absolute question. If we want to have any facts at all, we are forced to accept that it is the the facts themselves that obtain merely relatively—that is, we need to adopt the more adventurous notion of perspectival facts.^{Footnote 20} As it turns out, RQM seems to imply that facts about what the facts are from some particular perspective are themselves perspectival, and so on, perhaps ad infinitum and beyond.^{Footnote 21}

This is a radical metaphysical outlook which is as vertiginous as fascinating. It immediately raises a host of tricky questions about the connection between the multiply perspectival facts that supposedly make up reality and our lives as situated agents—our experiences, beliefs, and assertions—most of which still await discussion. One point that has already created persistent controversy, however, is whether the squaring of the circle succeeds in the first place: Does the interpretation, as we have outlined it, really allow us to transcend the fetters of our own points of view? And in particular, does it enable intersubjective communication in a sense robust enough to support the scientific confirmation of quantum theory itself? It is here that the parting of the ways occurs.

Quite often, it seems to us, the objections raised by critics of classical RQM suffer from a refusal or failure to take higher-order relativity into serious consideration. It would, for instance, seem to be a misunderstanding to take the relativity of variables to imply that ‘one and the same interaction can have different outcomes relative to different observers’ (cf. [56, p. 252f.]; [58, p. 17];[71, p. 2]). If our account of ‘classical’ RQM is right, there is no reference-independent fact about what happens relative to any particular system; and relative to each reference, interactions have the same outcomes relative to all observers. On the same grounds, it would seem to be a mistake to reason as if there were an absolute fact about Bob’s measurement outcome, concluding that this alleged fact cannot be expected to be correlated with the (relative) outcome of Alice’s measurement on Bob (cf. [57, p. 16f.]; [71, p. 8f.]; [72, p. 13–15]). The question of whether two observers get matching results is ill-posed if treated as an absolute question (cf. [1, 1666]; [30, pp. 2–4]). Nonetheless, we can compare perspectives, provided that we do it from the vantage point of some specified observer.

Emily Adlam, who has done more than anybody else to argue that classical RQM undermines intersubjective scientific practices, is well aware of this line of defence. But she does not think that a comparison of perspectives that is itself perspective-bound is sufficient to do science. In particular, she argues that “the results of a measurement by a third observer tells [sic] us nothing about the relationship between the subjective experiences of Alice and Bob” [71, p. 9]. Which subjective states of consciousness Alice and Bob go through, so the assumption that undergirds this remark, cannot possibly be relative to other systems. But it is not clear to us how this assumption could be justified. At first sight, one may wonder whether it rests precisely on the confusion of relativity with subjectivity that Rovelli has always cautioned against. Just as we can make sense of states of consciousness being relative to times or worlds, there is no reason in principle why they should not be relative to other parameters, too. If there is a genuine clash between RQM and scientific objectivity, it must lie elsewhere.

All this is not to say that there is no real question here. Experience shows that discussions between defenders and critics of classical RQM have a tendency to degenerate effortlessly into a sort of back-and-forth-table-tennis match with no clear winner:

Critic: There is just no way for Alice to find out about Bob’s perspective on things. All she can learn is how things stand relative to her.

Defender: Oh, but these things are not contradictory: Alice can measure Bob, and thereby find out what is the case relative to Bob relative to her. You just have to accept that facts about what is the case relative to Bob are themselves relative.

Critic: (sighs) \(\ldots \) Fine, perhaps I can accept that. But even then, the most Alice can get is an internally consistent account of things as they are relative to her. She does not get to learn how things stand relative to Bob, seen from his own perspective.

Defender: But of course she does! Alice can just ask Bob to tell her what is the case relative to him relative to him, and thereby find out what is the case relative to Bob relative to Bob relative to her. You just have to accept that...

Critic: (grunting)... that facts about what is the case relative to Bob relative to Bob are themselves relative, sure. But come on, you see what I mean! Ultimately, Alice only gets her own take on the facts, or the facts relative to others, or the facts relative to others relative to others...

Defender: I’m afraid I do not see that. Alice can find out what the facts are relative to others relative to others relative to others, too. You just have to accept that...

Critic: (orders a drink)

Is Alice confined to her own perspective in an exceptionable sense? The answer is not obvious. Matters are not helped by the fact that information acquisition is itself a physical process, such that whether or not somebody can or does gain access to some fact may itself be a relative question. RQM, we conclude, displays a feature characteristic for relativism quite generally: many people sense an incoherence, but it’s surprisingly difficult to catch hold of.

Whatever the right way to think about these matters, her doubts motivated Adlam to develop an updated version of RQM together with Rovelli. On a surface level, the key innovation is the introduction of a new postulate, ‘Cross-Perspective Links’, which says that the measurement of a system’s pointer accurately reveals the outcome said system has registered in an earlier interaction (unless, of course, the pointer has been tampered with in the meantime). What we have here, then, is an axiom that explicitly stipulates the possibility of communication across viewpoints. But for this axiom to function as intended (and to amount to a genuine novelty), absolute facts about the outcomes of interactions have to be assumed: “[W]e now regard the pointlike quantum events or ‘flashes’ as absolute, observer-independent facts about reality” [29, p. 11], Adlam and Rovelli write. Consequently, Extended Wigner no-go theorems, once cited in support of RQM, have turned into something to be circumvented (cf. [73, p. 32f.]). Evidently, we are moving away from relativism here. In fact, there is a case to be made that we are renouncing it altogether,^{Footnote 22} in the sense that there is nothing ‘out there’ in the world that gets relativised according to the new version of RQM. Let us explain.

RQM in the new guise maintains a mildly relational flavour insofar as it allows different observers to assign different quantum states to one and the same system (though cf. [65, pp. 14–16] for doubts). This is entirely in line with Adlam’s [73] contribution to the present issue, in which she defends the proposal that state vectors but not outcomes themselves be regarded as observer-dependent. But the relativity of quantum states is not in any way indication that their subject matter had been relativised; rather, it is a consequence of a certain reading of how they connect with the world on which the states assigned by different observers have different subject matters. In particular, it is not the case that Born probabilities are relativised. What we mean by that is that the quantum state one system S ascribes to another S’ is taken to encode the probabilities for S’ to manifest certain properties when interacting with S. So, Alice’s state is a tool for predictions about the behaviour of the target system in its interactions with Alice, and Wigner’s state is concerned with its behaviour in interactions with Wigner. If Alice and Wigner ‘disagree’ about the probability for, say, a z-spin measurement to yield outcome ‘up’, this is not because the probability p(‘up’|when subjected to z-spin measurement) takes on different values relative to different observers; rather, it is because Alice is talking about the probability p(‘up’|when subjected to z-spin measurement by Alice), and likewise for Wigner. Of course, in orthodox quantum theory, it is taken for granted that these two conditional probabilities coincide. But this is not a logical necessity, and it is untrue in Adlam-and-Rovelli-style RQM^{Footnote 23}, where these probabilities are taken to depend exclusively on the history of joint (direct or mediated) interactions between the respective target and reference systems. So: the point is not that one and the same conditional probability takes different values relative to different references, but that two clearly distinct conditional probabilities which are ordinarily assumed to coincide do not generally so coincide.

Hence, it seems to us correct to say that neither outcomes nor probabilities are really relativised on the new version of RQM. The only remaining place where we can look for ontic relativity is in the dynamical properties: Even if outcomes are absolute, one might maintain that properties are (first-order) observer-dependent, the idea being that the absolute fact about the outcome of an interaction between some \(S_1\) and \(S_2\) is an absolute fact about which property \(S_1\) took on relative to \(S_2\).^{Footnote 24} But on the view under consideration, it seems to us, even the first-order relativity of dynamical properties would hardly be more than a dispensable complication. Anything that could potentially be explained by a property’s being (merely) relative to Alice (for instance the fact that it has an impact only on the quantum state ascribed by Alice, but not on the quantum states assigned by other observers) could just as well be explained by its having manifested in an interaction with Alice - unless we categorically want to hang on to the notion that quantum states directly represent dynamical properties, that is. In her paper, though, Adlam makes it very clear that she sees no need for this notion. Indeed, she suggests that Wigner and Bell-Wigner scenarios should make us accept observer-dependent quantum states but not jettison the notion of an intrinsic, absolute ontic state of a system [73]. In her view, RQM-plus-CPL turns its back on “metaphysically radical non-absoluteness”, and in so doing makes a pronounced departure from extant varieties of quantum relativism.

As hardly needs emphasising, this marks a turning point in the history of RQM. This history started from the idea that the relativity of dynamical properties (and hence state vectors) is the key to understanding quantum theory. After a quarter of a century of pondering, developing, probing, and modelling, this idea has led us either to a view so vertiginous that some find it hard to make sense of, or to an account that seems to render relativity essentially obsolete.

In private communication, Rovelli informs us that he has not given up on RQM in its classical form, and that he is not personally convinced that it needs to be supplanted by the new, updated version. Which of them will enjoy greater popularity in the literature, and whether or not RQM will bid farewell to radical relativism, remains to be seen. This then is the story of how Relational Quantum Mechanics has reached a crossroads.

In the previous sections we provided an opinionated history of the development of RQM. This led us here. At the crossraods. It is time to take a closer look at this place. Rather than describing it ourselves, we will let the papers of this special issue paint the picture for the reader. That said, we do want to suggest a way of looking at these papers that helps both organizing the material and putting it in perspective. Such a perspective makes clear how they relate both to each other and to the broader argument and narrative of the present paper. We suggest we can group the contributions as follows—where some overlaps are explicitly mentioned:

• Foundational Issues: Papers in this group discuss foundational questions such as the measurement problem, the universality and completeness of RQM, relations between correlations, states, and perspectival facts and events, and even propose a new mathematical framework to sharpen such discussions. This group includes contributions from Di Biagio and Rovelli, Pienaar, Dussaud et al., Drezet, and Adlam.

• Ontological Issues: The second group focuses the discussion on ontological aspects of RQM, such as determinacy vs indeterminacy, absoluteness vs perspectivalism, foundationalism vs coherentism, and the like. It includes contributions by Adlam, Dorato and Morganti and Mariani, but also a somewhat comprehensive discussion of different ontological solutions in the last part of Oldofredi’s contribution.

• Comparison with Extant Interpretations: Finally, some papers mostly focus on comparisons between RQM and other extant interpretations. These include perspectival interpretations in general (Dieks), pragmatic interpretations (Healey), modal interpretations (Lombardi), and Bohmian Mechanics (Drezet).

We leave it to them to describe the lay of the land. For our part, with our feet planeted at the crossroads, we want to take a look ahead.

Having gained a sense of the past (the road we took) and the present (the crossoroads) we dare a glimpse into the crystal ball for the future: We present what we take to be fourteen and a half important (and partly interconnected) problems that may shape the future of RQM. These problems reach from the general to the specific, from the technical to the metaphysical, and in our list are—roughly speaking—ordered from the more foundational to the more far-reaching, rather than according to their relative urgency (which we leave to the reader to judge).

• The metaphysical Problem: If it is right that RQM, at least in its classical form, has to be cashed out in terms of perspectival facts, how ought we understand this notion? In the classification due to Fine [19], are there decisive reasons to favour fragmentalism, external relativism, or even privileged-perspective realism in the present context? And how does the iteration of relativity interact with these conceptions?

• The ontological problem: Is the fundamental ontology of RQM best understood in terms of events, in terms of systems, or in terms of something else altogether? If in terms of systems, what is their nature, and do arbitrary fusions of degrees of freedom make up a ‘system’ in the relevant sense? If in terms of events, what are they, if they cannot (or should not!) be conceptualised as the manifestation of properties between different systems?

• The Problem of Third-Party Interactions: Which is the most adequate ontological attitude towards interactions one is not directly involved in, and to the properties actualised in those? Are we right to suggest that Retro-Determination is the best fit for classical RQM, and which consequences would this have?

• The Problem of Wigner’s Friends: How does RQM position itself with regards to recent no-go theorems for observer-independent measurement outcomes? If it dissolves them, how? If it circumvents them, how?

• The Problem of Confirmation: Is it true that classical RQM is incompatible with the intersubjective pursuit of science and the confirmation of quantum theory, as Adlam and Healey have argued?

• The Problem of Interactions: How can the notion of an interaction, and with it the dynamics of RQM, be precisified? To what extent can RQM be made fit to solve initial value problems, or developed into a rigorous “means of locally navigating the set of quantum events" [29, p. 12]

• The Problem of Parts: How do mereological relations interact with relational properties? If a system has some property relative to some whole, does it thereby also possess that property relative to one of its parts, or vice versa, and under which circumstances? And, closely connected, The Problem of Combination (which we take from Adlam [75]): How are facts relative to fundamental physical systems related to facts relative to higher-level systems which they compose, or give rise to?

• The Problem of Probabilities: Which interpretation of probabilities should RQM be paired up with? And which implications does this have for our understanding of quantum states?

• The Problem of Generic Measurements: So far, the principles of RQM have always been illustrated using the example of ideal, non-disturbing measurements. How do property acquisition and state update generalise to more generic types of interactions, including so-called ‘interaction-free’, weak, and continuous measurements?

• The Problem of the Situated Agent: In the thoroughly relativist context of classical RQM, where anything to do with the dynamical states of physical things is always the case relative to a never-ending series of relata (if at all), how can a situated agent reason? What are the norms that govern their beliefs or assertions? Which facts relative to which series of relata should they take their perceptions to connect with, which facts their predictions to be about? Relatedly, does a system have a dynamical state relative to itself, and how can a system reason about measurements performed on itself by others?

• The Problem of Reconstruction: How does the interpretive framework of RQM relate to the ongoing attempts of reconstructing the quantum formalism from first principles, in particular Yang’s ‘Quantum Mechanics from Relational Properties’? To what extent can RQM serve as a motivation for their axioms? Which lessons do these attempts hold, and do they suggest changes to the tenets of RQM?

• The Problem of Reference Frames: How does RQM relate to recent research into internal quantum reference frames? Is Adlam [76] right to conjecture that it can provide a suitable interpretive home for the Page-Wootters formalism, and which lessons emerge from their joint consideration?

• The Problem of Generalization: Is the hope (cf. [29, p. 2]) that RQM can also be applied to quantum field theories and approaches to quantum gravity such as Loop Quantum Gravity justified? Which modifications, if any, should the interpretation undergo along the way?

Last not least, there is a meta-problem that has to be informed by and at the same time can be expected to have repercussions in the answers to all the others:

• The Problem of the Crossroads: How do the ‘classical’ version of RQM and its update due to Adlam and Rovelli compare in costs and benefits? Which one is more promising?

There is, then, a vast territory to be charted by physicists and philosophers. But whatever the answers to our questions turn out to be, whatever the fate of RQM as a viable paradigm for quantum physics, what we hope has become clear is that the relational viewpoint has had profound consequences for new ways to look at old problems, stimulating new questions, and suggesting out-of-the-box metaphysical outlooks. All signs are here that it will continue to do so, tomorrow and tomorrow and tomorrow. And this is where we leave things today.