Relational Quantum Mechanics (RQM) is the most recent among theinterpretations of quantum mechanics that are widely discussed today.It was introduced in 1996, with quantum gravity as a remote motivation(Rovelli 1996); interests has grown since, first very slowly, butsteadily, and has peaked during the last years (see Calosi and Riedel2024, also for a good account of the historical evolution of theinterpretation).

RQM does not interpret the confusion about quantum theory as a signthat what is necessary to render the theory intelligible is a newequation (as in De Broglie-Bohm theory), some not-yet observedphenomena (as in the physical collapse hypotheses), or the assumuptionof the existence of an unaccessible domain of reality (as the ManyWorlds’s universal quantum state.) Rather, it interprets quantumphenomena as an invitation to a radical update of the conceptualframework we use to think about reality.

RQM is a refinement of the textbook interpretation, where some aspectsof the role played by the “Copenhagen observer” (but notall of them) are not limited to the classical world, but can rather beplayed by any physical system. The interpretation rejects an onticconstrual of the quantum state: the quantum state play only anauxiliary role, akin to the Hamilton-Jacobi function of classicalmechanics. It is instead based on an ontology of physical systems andphysical variables, as is classical mechanics. The difference withclassical mechanics is double (a)variables only take value atdiscrete interactions and (b) the value a variable takes is onlyrelative to the (other) system affected by the interaction.Here “relative” is in the sense in which in classicalmechanics velocity is a property of a systemrelative toanother system. These relative events occur at discrete times, andconsist of physical variables taking on precise relative values; thesevariables may lack any value at all in intermediate times. At least insome readings, as discussed below, this leads to a radicalperspectival antifoundationism. The technical basis of RQM is thefollowing

Main Assumption:The probability distribution for (future) valuesof variables relative to a system \(S\) depend on (past) values ofvariables relative to the same system \(S\), but not on (past) valuesof variables relative to another system \(S'\).

The interpretation does not require, for its formulation, theassumption of a classical world. Measurement does not play anyfundamental role, and it does not require certain special systems tobe counted as ‘observers’. Instead, it assumes that anyphysical system can play the role that the Copenhagen’s observerassumes in bringing about values of variables at a given time. This ispossible without changing the predictions of quantum theory, thanks tothe Main Assumption, because the interference observed by a system\(S\) is not erased by the actualisation of variables relative to adifferent system \(S'\) (it can of course be suppressed bydecoherence). In the Wigner-Friend situation, the interferenceobserved by Wigner is compatible with Friend’s determinedobservation. In this way, RQM succeeds in making sense of a fullyquantum world without requiring hidden variables, many worlds,physical collapse mechanisms, or a special role for mind, agents, orsimilar.

The price to pay for this parsimony is a weakening of the conventional(“strong”) realism of classical mechanics where physicalvariables are assumed to have values which are non-relational andexist at every time. The fact that variables take value only atinteractions gives a sort of sparse event (or “flash”)ontology; the fact that they are labeled by the system to which theyrefer, adds a level of indexicality to the representation of theworld, and raises philosophical issues.

By itself RQM is metaphysically neutral, but it has a strongrelational stance that questions strong realism (Laudisa 2019), in asense discussed below. Because of this tinkering with realism, RQM hasbeen framed, in turn, in the context of various philosophicalperspectives, including constructive empiricism (van Fraassen 2009),neo-Kantism (Bitbol 2007 [Other Internet Resources], Bitbol 2010),anti-monism (Dorato 2016), structural realism (Candiotto 2017),Perspectival realism (Massimi 2022), metaphysical coherentism (Doratoand Morganti 2022) and anti-foundationalist coherentism. (See alsoBrown 2009, Wood 2010 [Other Internet Resources], and especially theextended discussion in Calosi and Riedel 2024.) The interpretation hasmany aspects in common with Dennis Dieks’ Perspectival QuantumRealism (Dieks 2022, Bene and Dieks 2002), with QBism (Fuchs 2001,2002 [Other Internet Resources]), with Healey’s pragmatistapproach (Healey 1989, 2023) and with the view of quantum theorydiscussed by Zeilinger and Bruckner (Zeilinger 1999, Brukner &Zeilinger 2003).

• 1. Main Ideas
  • 1.1 Values of physical variables
  • 1.2 Relative variables: “Different observers can give different accounts of the same set of events”
  • 1.3 Observer and measurement
  • 1.4 The wave function
  • 1.5. Quantum superposition: can a cat be half dead, half alive?
• 2. Related Issues
  • 2.1 Information
  • 2.2 Discreteness
  • 2.3 Comparison with other interpretations
  • 2.4 Representation
  • 2.5 Frauchiger-Renner experiment and locality
  • 2.6 Solipsism?
• 3. General Comments
  • 3.1 Reactions, criticisms, developments
  • 3.2 Relationality and realism
  • 3.3 The debate on the cross perspective link
• Bibliography
• Academic Tools
• Other Internet Resources
• Related Entries

1. Main Ideas

1.1 Values of physical variables

The starting point of RQM is that quantum mechanics is not about awave function or a quantum state \(\psi\); it is about values ofphysical variables. The basic ontology assumed by RQM, accordingly,includes only physical systems and variables that take values, as inclassical mechanics. For instance, a real fact is the position of aparticle having a certain value \(x\) at a certain time \(t\). Factsas this one (“the particle is at \(x\) at time \(t\)”) arecalled “events”, or “quantum events”. Quantumtheory is about such events. There are however two differences betweenfacts in quantum mechanics and facts in classical mechanics. Inclassical mechanics, there are two general assumptions that areabandoned in RQM:

(a) In classical mechanics it is assumed that all the variables of asystem have a value at every time. RQM, on the contrary, assumes thatin nature this is in not the case in general (Heisenberg 1925; Kochen& Specker 1967). Physical variables have values only at sometimes, and have no value at the other times. Events, in other words,are discrete. Variables have values when a system acts on anothersystem. More precisely, for a system \(S\) to have a variable \(A\)taking a valueis to interact with a second system \(S'\);the variable \(A\) characterizes the effect of a certain action on\(S'\). In RQM, this is what it means for a variable to have a value.That is, for a system to be described by a variable taking a valueis to affect another system in a certain manner, and nothingelse. This is the basic intuition that led Heisenberg to find the keyto quantum mechanics in 1925; there are questions that make sense inclassical mechanics, but have no significance in nature. For instance,the question “What is the \(y\)-component of the spin of anelectron when its \(z\)-component is \(\frac{1}{2} \hslash\)?”is meaningless: neither it admits an operational definition, nor is itneeded for a realistic understanding of nature.

(b) The second assumption of classical mechanics dropped in RQM isthat variables take absolute values, namely values independent fromany other systems. Instead, RQM assumes thatall (contingent)physical variables are relational. Contingent variables are thoserepresented by phase space functions in classical theory. Any valuethat these variables take is (implicitly or explicitly) labelled by asecond physical system. If the variable \(A\) of a system \(S\) takesa value in the interaction with a second systems \(S'\), the value ittakes isrelative to \(S'\). The actualisation of an eventitself is relative to a system. The concrete meaning of this is theassumption above, according to which future ways the system \(S\)affects \(S'\) depend (probabilistically) on the values that variablesof \(S\) have taken with respect to \(S'\), butfuture ways thesystem \(S\) affect a third system \(S''\) do not. The ensembleof all events relative to an arbitrary system \(S'\), together withthe probabilistic predictions these entail, is called the“perspective” of \(S'\).

Dropping these two assumptions breaks away from a venerable conceptualstructure that has long underpinned physics in particular and perhapsour worldview in general: the idea that the world can be though ascomposed by systems that at any time have variable properties bythemselves, irrespectively from any other system, and these propertiescan be describes by the values taken by variables characteristic ofthe system in itself.

The claim at the basis of RQM is that “different observers cangive different accounts of the same set of events” (Rovelli1996: 1643). Textbook quantum mechanics is a complete description ofthe perspective of a single system, but it disregards the effect ofthis system on the perspective of other systems. RQM emphasises thefact that any observer itself behaves as a quantum system, when actingon other systems. Vincenzo Fano (2024 [Other Internet Resources])gives a simple illustration of how RQM applies to common apparentlyparadoxical situation in quantum mechanic. The relation betweenperspectives is discussed below.

1.2 Relative variables: “Different observers can give different accounts of the same set of events”

Relative variables are variables whose value does not depend on asingle system, but rather on two systems. A well known example is thevelocity of an object in classical mechanics. The velocity isimplicitly or explicitly relative to a second object. There is no“velocity of a single object”, irrespectively on any otherobject, in classical mechanics. Other well-known examples are theelectric potential (only the potential of a conductor with respect toanother conductor has physical meaning) and position (only positionwith respect to some other object has physical meaning). Relationalquantum mechanics takes a further long step in this direction,assuming that we can make sense of quantum mechanics by assuming thatall physical variables are relational in this sense.

‘Relative’ does not mean subjective. Subjects, or agentsplay no special role in RQM. When we say that our speed is 11km/secondwith respect to the Sun, we are not attributing subjectivity to theSun. When we say that the distance between a signpost and a roadintersection is 100 meters, we are not thinking that a road’sintersection is an agent. In a naturalistic perspective, a person, anagent, a subject, are physical systems; the world they relate to isdescribed by the value of the variableswith respect to them.A person dwelling on the Earth sees the Cosmos rotating because theEarth is spinning; but the Cosmos rotates with respect to the framedefined by Earth irrespectively from the existence of persons on theEarth. To say that RQM requires subjects or agents is the same mistakeas saying that our explanation of the daily rotation of sun moon andstars around the Earth requires to take agency or subjectivity intoaccount: a nonsense. There is nothing subjective, idealistic, ormentalistic, in RQM.

1.3 Observer and measurement

In textbook presentations, quantum mechanics is about measurementoutcomes obtained when an “observer” makes a“measurement” on a quantum system. Such measurements arenot generic interactions between two systems. They are special kindsof interactions. They require that information is registered andstored. For this to happen, there must be decoherence and dissipation,hence a classical domain. RQM extends the interpretation of the theoryto the regimes where decoherence and dissipation are not sufficient tounderpin the “observer-measurement” interpretation. Whendecoherence is sufficient, the values of variables becomes“stable” (Di Biagio and Rovelli 2021): their label becomeirrelevant and measurments have determined outcomes within thatdecoherence domain.

According to RQM, therefore, quantum mechanics is not a theory of thedynamics of an entity \(\psi\), from which the world of our experiencesomehow emerges. It is instead a theory about the standard world ofour experience, described by values that conventional physicalvariables take at interactions, and about the transition probabilitiesthat determine which values are likely to be realized, given thatothers were. This is compatible with quantum phenomena, if therelative character of variables is taken into account.

1.4 The wave function

In RQM, the quantum state is a mathematical device that refers to twosystems, not a single one. It codes the values of the variables of thefirst that have been actualised in interacting with the second(Groenewold 1957); it therefore codes in particular anything we canpredict regarding the future values of these variables, relative tothe second system. The state \(\psi\) , in other words, can beinterpreted as a compendium of information accessible to a secondsystem, determined by a specific history of interactions. Understoodin this manner the quantum state is always and only arelativestate in the sense of Everett (1957). In this sense RQM isstrongly “Everettian”. It is so in a different sense thanthe Many Worlds interpretations, which includes a hypotheticaluniversal wave function of which the various relative states \(\psi\)are branches. The universal wave function plays no role in RQM (nor inany physical application of quantum theory.).

Several presentations of quantum theory interpret the wave function ofa system, or its quantum state \(\psi\), as properties of the systemas such. From the perspective of RQM, this is what generates theconfusion about quantum theory (Rovelli 2018). RQM is realist aboutquantum states in the weak sense that they represent somethingphysically real: for instance, after a procedure that we call“state preparation”, there is a matter of fact about whatthat preparation was; preparations giving distinct pure quantum statescorrespond to distinct physical states of affairs. These “statesof affaires”, however, are relative to the preparationapparatus, they are not states of the system alone. This, inparticular, renders RQM compatible with the ψ-Ontology theoremslike the PBR theorem for the reality of the wave function (Pusey,Barrett, & Rudolph 2012; Leifer 2014). The PBR theorem applies toRQM, construed as a theorem about relative states. The peacefulcoexistence between between RQM these theorems has been discussed in(Calosi and Oldofredi 2021).

On the other hand, RQM does not make use of the notion of theabsolute state of a system or of the idea – common inother interpretations – that the quantum state could represent“all there is” about that system. This “stronglyrealistic” interpretation of the state is given up in RQM. Inthis sense, the interpretation of the wave function in the context ofRQM is akin the interpretation of the Hamilton-Jacobi functional inclassical mechanics: a theoretical tool to facilitate the computationof the probabilities of future events on the basis of certain givenknowledge about a certain state of affairs. The relation between thewave function \(\psi\) and the Hamilton-Jacobi functional \(S\) ismore than an analogy, because in the semiclassical approximation thelater approximates the first \((\psi \sim \exp iS/\hslash)\). Thismathematical relation can be taken as an argument against a stronglyrealistic readings of \(\psi\), for the following reason. Theinterpretation of a quantity A in the mathematical apparatus of aphysical theory must be consisten with the interpretation of thequantity A reduces to in an approximation. The Hamilton-Jacobifunctions of, say, a classical particle has no strongly realisticinterpretation. The Hamilton-Jacobi function we explicitly use incalculations collapses and jumps with what we learn about the system,as does the quantum wave function.

Voiding the quantum states of its strongly realistic interpretationgives away with the mystery of quantum jumps and collapses. The factthat RQM state is relative to a system explains why it can jump as thetwo systems act on one another.

In classical mechanics we can dispense of the Hamilton-Jacobifunctional. This testifies for its lack of direct ontological weight.We can equally dispense with \(\psi\) in quantum theory. Evidence ofthis is that the full early development of the quantum mechanicalformalisms (Heisenberg 1925; Born & Jordan 1925; Dirac 1925; Born,Heisenberg, & Jordan 1926) predates the work where \(\psi\) wasintroduced (Schrödinger 1926). Quantum mechanics can beformulated without reference to the quantum state, as a theory ofprobabilities for sequences of events. The state \(\psi\) is aconvenient tool, not a necessary one.

Heilbron and Rovelli (2023) argue that Schrödinger’sdevelopment of wave mechanics, in spite of its wide utility, can beseen as conceptually misleading, because it has promoted a mistakenoveremphasis of the ontological role of \(\psi\) .

1.5. Quantum superposition: can a cat be half dead, half alive?

If \(\psi'\) and \(\psi''\) are two orthogonal quantum states of asystem, quantum mechanics assumes that the system can also be in thestate \(\psi = (\psi' +\psi'')/\sqrt{2}\). This is the superpositionprinciple, a cornerstone of the theory (Dirac 1930). If \(\psi'\) isthe state of a live cat and \(\psi''\) the state of a dead cat, then\(\psi\) is a state in which the cat is in a quantum superposition ofdead and alive; the theory predicts that this is a possible (relative)state of a cat. What does RQM say about situations such as this? Isthe cat in some sense half alive and half dead?

The existence of states like \(\psi =(\psi' +\psi'')/\sqrt{2}\)doesnot mean that we “see superpositions” (as sometimeswrongly stated): what we “see”, namely what we measure,according to textbook quantum theory, are eigenvalues of self-adjointoperators, not quantum states. Measured eigenvalues are alwaysunivocal, never “superimposed”. To be a superposition,rather, means two things. First, that if an observable has value\(a'\) in \(\psi'\) and value \(a''\) in \(\psi''\) then anyobservation of the system will give either \(a'\) or \(a''\), eachwith probability 1/2. Second, the probability distribution of theoutcomes of the measurement of any observable that is not diagonal inthe \((\psi'\), \(\psi''\)) basis will be affected by interference:that is, it will not be the mean of the average values of theobservable in \(\psi'\) and \(\psi''\). In RQM, this and nothing elseis the meaning of being in a quantum superposition.

We never see cats that are half alive and half dead because quantumtheory predicts that we never see this sort of things. It predictsthat we see cats either alive or dead. It also predicts that inprinciple we should be able to see interference effect between the twostates. These interference effects are strongly suppressed bydecoherence in the case of macroscopic systems (like cats), hence thetheory actually predicts that they are extremely hard to observe, inagreement with experience. A puzzle, on the other hand, appears if weask what the cat itself would perceive when we describe it in quantumsuperposition. Say the brain of the cat measures whether its heart isbeating or not. The theory predicts that the brain will find eitherthat it does or that it does not. In textbook quantum mechanics, thisimplies a collapse of \(\psi\) to either \(\psi'\) or \(\psi''\). Inturns, this implies that no further effects of interference betweenthese two states will happen. Andthis conclusion contradictsthe existence of interference effects (although small due todecoherence) predicted by quantum theory.This problem isresolved by RQM. It is solved by the Main Assumption: the way the cat,a quantum system, affects an external system, isnot affectedby the specific way the heart of the cat has affected its brain.

That is, the state of the cat with respect to the external world doesnot collapse when a part of the cat interacts with another.

2. Related Issues

2.1 Information

The early presentations of RQM were formulated in the language ofinformation theory. They were at the roots of the later development ofthe use of information theory to make sense of quantum theory (Calosiand Riedel 2024). The quantum state is a way of coding the informationthat an observing system \(S'\) may have about a quantum system \(S\),relevant for predicting future ways \(S\) can affect \(S'\). Thisinformation is determined by the ways \(S\) has affected \(S'\) in thepast. Furthermore, the hope was presented in (Rovelli 1996) that afull reconstruction of the quantum formalism on the basis of simpleinformational postulates was possible. Two main postulates wereproposed:

• (i) relevantinformation is finite for a system with compact phase space,
• (ii) new informationcan always be acquired.

The two postulates are not in contradiction with each other becausewhen new information is gathered some previously relevant informationbecomes irrelevant. “Relevant” here means that it affectsfuture probabilities. A moment of reflection shows that firstpostulate implies the characteristic discreteness of quantum theory,while the second is implied by Heisenberg’s uncertainties.Similar ideas were independently considered by Zeilinger and Bruckner(Zeilinger 1999; Brukner & Zeilinger 2003).

As emphasized in Dorato (2017), information is best not understood asa primary notion. It must be defined physically in terms of somethingelse; as such, it can play an important notion in “theories ofprinciple” in the sense of Einstein (1919). In RQM, theinformation is defined relationally as relative information (in thesense of Shannon) that a physical system has about another system.Relative information is physical correlation between two systems,namely a measure of the difference between the possible number ofstates of the combined system and the product of the number of statesof the two systems, due to the existence of physical constraints.Thus, we say that a variable \(O_A\) of a system has information abouta variable \(A\) of another system iff the values that \(A\) and\(O_A\)can take are correlated. In this case the outcome of ameasurment of \(O_A\) predicts the outcome of a measurement of \(A\),that is, in this sense, “\(O_A\)has information about\(A\)”.

In the spirit of Shannon, this is a weak definition of informationthat has no mentalistic, semantic, or cognitive aspects. Theinformational perspective of the early work in RQM has influenced thedevelopment of numerous later information theoretical approaches tothe foundations of quantum theory, as well as a number of laterattempts to derive the quantum formalism of the theory from physicallytransparent postulates. For an idiosycratic and a bit rambling, butwith intersting insights, account of the state of this program see(Stacey 2021 [Other Internet Resources]).

2.2 Discreteness

Discreteness is not an accessory aspect of quantum theory: it is itsmost characteristic feature (it gives the theory its name).Discreteness appears in two related ways in quantum theory.

First, the amount of information that can be gathered regarding thestate of a system which is in a finite region R of its phase space isfinite. For each degree of freedom, it is given by the Liouvillemeasure of R divided by the Planck constant. This is what causesdiscrete spectra. Continuous spectra require infinite phase spaces,and can be seen as effects of idealisations. The discreteness ofquantum mechanics is therefore expressed by the first of the twoinformational postulates.

Second, quantum mechanics describes the world in terms of values ofvariables at specific discrete times. This second aspect ofdiscreteness is directly accounted for by the sparse ontology of RQM.The history of a quantum particle, for instance, is neither acontinuous line in spacetime (as in classical mechanics), nor acontinuous wave function on spacetime. Rather, with respect to anyother system it is a discrete set of interactions, each localized inspacetime.

The discrete ontology of RQM seems to raise a difficulty: whatdetermines thetiming for the events to happen? The problemis the difficulty of establishing a specific moment when, say, ameasurement happens. The question is addressed in Rovelli (1998),observing that quantum mechanics itself does give a (probabilistic)prediction on when a measurement happens. This is because the meaningof the question whether or not a measurement has happened is toascertain whether of not a pointer variable \(O_A\) in the observingsystem \(S\) has become properly correlated with (namely, “hasinformation about”) the variable \(A\) of the system \(A\). Inturn, this is a physical question that makes sense because it can beposed empirically by measuring \(A\) and \(O_A\) and checking if theyare consistent. On the regress that this determines, see Section 3.3below.

2.3 Comparison with other interpretations

Textbook “Copenhagen”: To a good extentRQM is a completion of the standard textbook interpretation. Thedifference is that the latter assumes the existence of a classicalworld, or a classical observer, and describes the way quantum systemsaffect it in an interaction. The relational interpretation, on thecontrary, assumes that an account of these interactions is valid withrespect to any physical system. Thus, RQM is a sort of“democratised” version of Copenhagen, where some (but notall) roles of the single observer can be assumed by any physicalsystem. These are sufficient to define a consistent interpretation,without need of the decohetence and the dissipation required byconventional quantum measurements. From the perspective of RQM, thetextbook interpretation emerges when there is sufficent decoherence.

Many Worlds: Both RQM and the Many Worlds interpretation (seeVaidman 2018) are rooted in the work of Everett (1957). Both attemptto solve the mystery of quantum theory by adding a level ofindexicality. In RQM, variables have values with respect to otherphysical systems. In Many Worlds, variables have values with respectto branches of the universal wave function. In neither interpretationsthere is any a priori special role for measurement, or observers. Themain difference is the distinct ontological commitment: the ManyWorlds interpretation is based on the assumption that all relativestates are branches of a unique universal wave function, interpretedas a real entity, which obeys a single deterministic evolution law.The Many Worlds interpretation must work to recover Heisenberguncertainty (via branch indexicality), probabilities (via subjectiveinterpretation of probability), and discreteness, from this unique,deterministic, continuous universal wave function. RQM has all thiseasily in its foundation. On the other hand, the Many Worldsinterpretation is based on a (according to some, inflated, but)no-nonsense realist metaphysics, which is precluded by theperspectivism of RQM. The two can perhaps made closer by the simpleobservation that modality can always be transformed into multipleworld realismà la Lewis (1986), trading actuality forindexicality.

Hidden variables (Bohm): Hidden variable theories, of whichBohm theory (Bohm 1952) is the best available example, provide arealistic and deterministic interpretation of quantum mechanics. Thesimilarity between RQM and Bohm theory is in the realisticinterpretation of some variables, such as the position of a particle.The differences are two. The first is that on the Bohm theory it isposition that always has a definite value, whereas, on RQM, whatvariable acquires a value in an interaction depends on the nature ofthe interaction. The second is that on the Bohm theory position alwayshas a definite value, which changes in a continuous manner, whereas,on RQM, the ontology has the sparseness already discussed. In RQMthere is no analog of the extra equation assumed in Bohm theory.Drezet (2024) has discussed the relation between Bohm theory and RQM.

Physical collapse: Physical collapse theories like Ghirardi,Rimini, and Weber (1986) and Penrose (1996) are physicallydistinguishable from standard QM, which is instead assumed to becorrect up to contrary empirical indications, in RQM.

There are interpretations of quantum mechanics that are close to therelational one:

Zeilinger-Bruckner: The Relational Interpretation is close tothe view of quantum theory held developed by Zeilinger and Bruckner;in particular, similar postulates to the original ones of RQM wereindependently proposed in (Zeilinger 1999, Brukner & Zeilinger2003). These ideas generated some of the interesting mathematical workaiming at making the derivation of the formalism of quantum theoryfrom information theoretical postulates precise. For versions of thisprogram related to RQM see (Grinbaum 2005; Höhn 2017; Höhn& Wever 2017).

QBism: The emphasis on information in Rovelli (1996)influenced the birth of QBism (see Fuchs 1998: 3, 2001, 2002 [OtherInternet Resources]). There are similarities between RQM and QBism(Pienaar 2021b). One similarity is the emphasis on dropping questionsconsidered meaningless. The second is the use of the language ofinformation theory (Spekkens 2014). The difference is mostly in theway the subject holding information is treated. In QBism the ideas ofagent andexperience are fundamental (DeBrota 2018[Other Internet Resources]), while these ideas play no role in RQM. InRQM, the subject is fully naturalised: it is itself considered aphysical system that can be described by quantum theory. This leads toa stronger version of realism that QBism, and to the emphasis on therelational aspect of all variables. In QBism the emphasis is in theinformation about the world held by a single subject, taken asprimary. In RQM, the information is relative information (in the senseof Shannon) that a physical system has about another system; it is notprimary (see Dorato 2017): it is can be simply understood physicallyas a correlation between the two systems that can be observed by athird system. Steven French (2024, 2024b) has framed the relationbetween QBism and RQM in terms of the two versions of perspetivalism(‘perspectival₁’ and‘perspectival₂’) considered by MichelaMassimi’s Perspectival realism (Massimi 2022).

Richard Healey: Healey’s pragmatist approach (Healey1989) has in common with RQM the idea that the quantum state is not adescription of physical reality, not even incompletely. Its mainfunction is to be a (dispensable) tool for computing probabilities.The main difference is the emphasis on what quantum states arerelative to. For Healey’s pragmatist view, a quantum stateascription is relativeonly to the perspective of an actualor potential agent (Healey 2012). In RQM, values are relative to anyphysical system. Restricting quantum theory to its use by agents isnot a concern for Healey’s pragmatist philosophy; it is more soin a naturalistic perspective searching for an understanding of Naturethat remains significative also where no agents are around. This isthe same difference as between RQM and QBism, but Healey’sposition is closer to RQM than QBism because while the QBism’squantum state ascriptions depend on the epistemic state of the agent,for Healey the quantum state ascribed to a system depends only on thephysical circumstances defining the perspective of the agent.

Phenomenology: Steven French discusses RQM from aphenomenological perspective (2024b, 9.8) and observes that there isthe possibility of “an interesting accommodation [or RQM] withphenomenology” (2024b, pg 226) if RQM drops the insistence thatan observer cannot assign a quantum state to themselves and the RQMcan accomodate conscious observers.

Cavalcanti’s ‘Experimentalmetaphysics’: Cavalcanti’s formalization ofthe arguments connecting quantum predictions with general assumptionsabout the world (Cavalcanti 2008 [Other Internet Resources]) lead to aview very close to RQM.

2.4 Representation

The issue of the interpretation of quantum mechanics is related to theissue of the possibility of offering arepresentation in thesense of an intuitive account of what happens in the world. It can beuseful to give a simple-minded pictorial representation of theintuition sustaining different interpretations. Imagine at time\(t_1\) a radioactive atom is surrounded by Geiger counters and attime \(t_2\) one of the counters clicks, having detected a product ofthe decay. What has happened during the \(t_1\)-\(t_2\) interval?

• According totextbook quantum theory, the wave functionof a particle classically trapped in the nucleus leaks out of thenucleus symmetrically, filling the space surrounding the nucleus. Atthe moment of the detection this wave function magically disappearseverywhere except at the particular detector that clicks.
• According to theMany Worlds interpretation, alldetectors click. In fact, each detector clicks at every moment oftime, but the wave function of the universe branches continuously intoinnumerable branches: we, ourselves, happen to be in one particularbranch in which one particular detector clicks at one particulartime.
• According to theBohmiam interpretation, the wavefunction equally leaks uniformly in space, but in the meanwhile theassociated particle, guided by this wave function, zigzags around,until hitting a particular detector.
• According toPhysical Collapse interpretations, the wavefunction also leaks out uniformly, but when its effect on the heavyGeiger detectors begins to displace too much matter, the wave functioncollapses as in the textbook interpretation, but driven by ahypothetical dynamical process which has not yet been explicitlyobserved (Ghirardi 2018).
• What aboutRQM? In the spirit of Heisenberg, there is noactual wave function out there in nature, nor there is any fact of thematter aboutthe position of the particle respect to the Geigercounter at any moment between \(t_1\)and \(t_2\). The lack ofdetermination of variables in quantun theory, in particular in RQM,has been discussed in (Calosi and Mariani 2020). However, there may beother facts of the matter. For instance,the position of theparticle respect to some air molecule along the way. These, onthe other hand,have no bearing on the position of theparticle with respect to the Geiger counter, which actualises at time\(t_2\). The probabilistic distribution of this position does notdepend on the position of the particle with respect to the airmolecules.

2.5 Frauchiger-Renner experiment and locality

The Frauchiger-Renner thought-experiment (Frauchiger & Renner2018) can be read as an indirect support to RQM, since it makesconcrete the idea that “different observers can give differentaccounts of the same set of events”, as in the original RQMslogan. The experiment is discussed in the conceptual framework of RQMby Waaijer and van Neerven (2019 [Other Internet Resources]). But ifcourse it can be accounted by all interpretations.

The application of RQM to the EPR context and the problem of quantumnon locality has been initially discussed in Smerlak and Rovelli(2007) and (Laudisa 2001). Some of the claims of the earlierdiscussion about RQM being “local” have been questioned,pointing out that RQM should in any case be “forced to acceptsome form of non-locality in quantum phenomena”(Laudisa 2019: 227). See also Pienaar’s criticisms (2019) andthe discussion in Martin-Dussaud, Rovelli, and Zalamea (2019) and(Martin-Dussaud 2021), where a specific sense in which quantum theoryis non-local from the RQM perspective is clarified.

2.6 Solipsism?

Prima facie, RQM may seem to imply a form of perspectival solipsism(Rovelli 2024 [Other Internet Resources]), as the values of variablesrealized in the perspective of some system \(S\) are not necessarilythe same as those realized with respect to another system \(S'\).However, often this is not the case, as follows directly from quantumtheory itself. The key is to observe that any physical comparison isitself a quantum interaction. Suppose the variable \(A\) of \(S\) ismeasured by \(S'\) and stored into the variable \(A'\) of \(S'\). Thismeans that the interaction has created a correlation between \(A\) and\(A'\). In turn, this means that a third system measuring \(A\) and\(A'\) will find consistent values. That is: the perspectives of\(S'\) and \(S''\) agree on this regard, and this can be checked in aphysical interaction.

For instance: imagine experimenter \(S'\) measures the spin of theelectron \(S\), and writes the value of this spin on a piece of paper.In principle, experimenter \(S''\) can devise an experiment where shecan detect an effect due to interference between the two brancheswhere the spin of the electron (and the text) have one or the othervalue. But if \(S''\) measures the spin and reads the piece of paper,she will find that experimenter \(S'\) has seen the same spin asherself.

Why? Because quantum theory predicts so, as can be seen from thefollowing: with respect to \(S''\), the first interaction yields aquantum state of the form

Measuring the spin projects the state on one single branch of the two,and both branches lead to consistency. Therefore, as long as we do notchase subtle interference phenomena hidden behind decoherence, RQMimplies that we all ‘see the same world’.

3. General Comments

3.1 Reactions, criticisms, developments

Bas van Fraassen (2009) explores “the world of quantum mechanicsas RQM depicts it” (2010: 390), clarifying what is and what isnot relative to observers. He concentrates on the apparentlyparadoxical aspects of RQM. The limits on information that observerscan have, which can only be acquired through physical interaction,have surprising consequences for complex situations in which anobserver makes a measurement, a second observer makes measurements onthe first and its target, and even a third observer comes in andobserves a process involving the first two observers. Van Fraassenconcludes that all the consistency questions can be laid to rest, whenthe situation’s representation in RQM is properly understood. Onthe other hand, he also observes that if in RQM what the state of asystem relative to an observer is, is not itself relative to anything,then the question can be raised what relationships there are betweenthe state of a specific entangled system or its components relative todifferent observers. He proposes and additional postulate, weaklyrelating the description of the same system as given by differentobservers, which forbids the possibility of disturbing inconsistenciesallowed by the multiplication of perspectives. The idea of adding apostulate relating the description of the same system as given bydifferent observers has later been developed in Adlam & Rovelli(2023).

Laura Candiotto (2017) argues that the best philosophical frameworkfor RQM is Ontic Structural Realism (OSR) (Ladyman& Ross 2007;French & Ladyman 2011). Ontic structural realism is meant to be adefensible form of scientific realism (Ladyman 2019); it argues forthe priority of relations over substances, as self-subsistentindividual objects (Morganti 2011). For Candiotto, RQM is a realistictheory that assumes the notion of relation (the physical interactionbetween systems and instruments) as primitive; objects emerge asrelational “nodes” (French 2006), or intersections ofprocesses. The lack of observer-independence is not inability ofproviding an account of the structure of matter, because there are nointrinsic properties that can be assigned to systems independently oftheir interactions, therefore this structure is itself relational,hence in particular observer dependent. Relations via dynamicalprocesses of information exchange can be taken as the building blocksof the universe.

The relation between RQM and ontic structural realism has beenemphasized also by Mauro Dorato (2016). Dorato gives an extensiveevaluation of RQM, pointing out its main characteristics. Heemphasises then two aspects that characterise RQM. The first is arevisionary metaphysical account of quantum theory; that is: centralassumptions of common sense must go, if they contradict contemporaryphysical theories. Here, what is abandoned is the presupposition thatquantum systems have a non-relational, intrinsic nature. RQM’smetaphysics is revisionary also for a second reason. Analogously tothe many-worlds interpretation, RQM does not suggest changing theformalism of quantum theory—as alternative formulations of thetheory do—but rather, modifies the conceptual schemes with whichwe can interpret the formalism, and consequently, our metaphysics.Dorato observes that the relativisation of values implies arelativisation of the very notion of object or entity, if (i) havingsome intrinsic, non-purely dispositional properties is essential tothe identity of an object, and (ii) no entity can exist if it does nothave an intrinsic identity (see Nāgārjuna 1995). The onlyreality in RQM is given by events, which are the result ofinteractions between distinct quantum systems, but even these eventscan be described in a different way by different physical systems. Theinteraction cannot be described in a more precise way by aconstructive theory in Einstein’s sense (Einstein 1919) that canexplain the coming into being of a definite outcome without justassuming it as a fundamental fact. Dorato concludes that there is nomeasurement problem in RQM because RQM is implicitly formulated as atheory of principle. He also considers the issue of priority monism asdefined in Schaffer (2010): Shaffer claims that quantummechanics’ entanglement is evidence that the whole universe hasontological priority with respect to its parts. Dorato point out thatthe firm advocacy of relationalism of RQM has instead radicalanti-holistic consequences.

The second characteristic aspect of RQM pointed out by Dorato is that,consequently, the best way to capture the nature of not-yetinteracting quantum systems is to call into play a form ofdispositionalism: the only way to attribute some sort of intrinsicnessto the state-dependent properties of quantum systems is to attributethem dispositions to manifest in a certain way according to theinteractions they are subject to. Dispositionalism is present in manyother views of quantum mechanics (Dorato 2006) but fits particularlywell in the context of RQM. Unlike Qbists interpretations of quantumtheory, which are agents-centered, in RQM the relation “\(S\)manifest \(q\) relative to \(S'\)” is symmetric, and this is asimple consequence of the hypothesis that in RQM quantum systems and“observers” are on the same level. As a consequence of itsrelational and dispositional aspect, Dorato stresses the fact that inRQM there cannot be a universal flow of becoming, but only a local,worldline-dependent and relational one. This still counts as arelational form of becoming: no universal tide of coming into being,but a crisscross of ripples. Since a physical system can exemplify agiven succession of events only relatively to another system and notabsolutely, in RQM there cannot be cosmic time, so that also ingeneral relativity temporal succession of events cannot be regarded asa total order. In a sense, in RQM there is no quantum state of theuniverse, or a God’s eye point of view, since the cosmos canonly be described “from within a given perspective”.

Richard Healey has discussed RQM in two papers. In the first (2021),he questions possibility of reconciling the observer-relativity ofmeasurement outcomes with a basic norm of scientific objectivity, inthe context of a quantum theory of gravity. In the second (2022), heshifts to a more favorable view of main RQM thesis that the outcome ofa quantum measurement is to be viewed as a relative, not an absolute,fact and he compares RQM to his pragmatist view of quantum theory. Heargues that the version of RQM in Adlam & Rovelli 2023 solves hisprevious main objection to RQM (that its ontology of relative facts isincompatible with scientific objectivity and undercuts the evidentialbase of quantum theory) and brings RQM and his pragmatist view intoeven closer alignment.

Steven French (2024) discusses the relation between RQM and the“continental philosophy” account of quantum measurmentgiven by Fritz London and Edmund Bauer in 1939. Andrea Oldofredi(2021) has argued that RQM is easily compatible with scientificrealism, in the context of an ontology of properties (Oldofredi 2021).He has also discussed how precisely RQM solves the measurment problemin (Oldofredi 2022). Juan Sebastian Ardenghi and Olimpia Lombardi(2022) have discussed the relation between RQM and theModal‑Hamiltonian Interpretation, arguing that the twointerpretation complement each other. In (Martin-Dussaud, 2023) amathematical formalisation of the notion of relative facts isproposed.

3.2 Relationality and realism

The central move of RQM is to interpret all physical variables asrelational, namely as referring to two systems, not a single one, andto view them as realised only in interactions. Relationality has beenplaying an ever dominant role as our knowledge of the natural worldhas increased. Examples are the relational nature of velocity inclassical mechanics, of locality in general relativity, of thepotential in electromagnetism, of the gauge invariant observables innon-abelian gauge theories, and many others. RQM is a long stepfurther in this direction. Taken seriously, the philosophicalimplications of this overreaching relationally can be heavy. The mainone is a weakening of a strong version of realism.

There is nothing in RQM that contradicts the assumption that the worldis “out there”, irrespectively of our mental states, orperceptions. In this weak sense RQM is consistent with realism. ButRQM questions the assumption that each variables of each subsystem ofthe world has a single value at each and every time. In this strongersense, realism is questioned by RQM. The ontology of RQM is a sparseontology of relational quantum events, not derived from any unique“underlying” representation. This weakening of realism isin a direction similar to what happened with Galilean orEinstein’s relativity, which have shown that there is no fact ofthe matter in the velocity of a single object, or in the simultaneityof two space like separated events alone.

However, this is a radical step in this direction. In Laudisa (2019)it is pointed out that RQM gives no deeper account, or underlyingdynamical representation, of the main process: the actualisation ofquantum events at interactions. This is the process which in textbookquantum theory is called measurement and is accompanied by statereduction. Quantum mechanics gives probabilities for quantum events tohappen, not a story representing how they happen. This core aspect ofquantum theory is not resolved in RQM: it is taken as a fact of theworld. What RQM does resolve is the question of when this happens: anytime one system affects another one, it happens relative to this othersystem. What RQM does, is to show that this is not in contradictionwith the existence of interference effects. But the core discretenessof the quantum event actualisation is not “explained” inRQM: it is understood as the picture of how nature works according toquantum theory. This can be understood to be in spirit ofNewton’s famous observation “whatever is not deduced fromthe phenomena must be called a hypothesis; and hypotheses, whethermetaphysical or physical, or based on occult qualities, or mechanical,have no place in experimental philosophy. In this philosophyparticular propositions are inferred from the phenomena, andafterwards rendered general by induction” (Newton 1713).

The radicality of the step implied by RQM has been emphasized byTimotheus Riedel (2024). Riedel emphasizes the fact that RQM isnecessarilly committed to an “unrestricted iterationprinciple”, according to which facts about what the facts arefrom some particular perspective are themselves perspective-dependent,and so onad inf. This principle plays a crucial role inensuring the communicability and coherence of events acrossperspectives, but is incompatible with the orthodox reading ofrelativity in terms of relationality, and instead requires adoption ofa notion of perspectival facts. This follows from the fact that in RQMto say that a system \(S'\) has information about a system \(S\) is isitself a contingent property of the coupled system (\(S, S'\)), and assuch it can only be relative to some system (possibly \(S'\) itself).Concretely, this situation can be physically realized when ameasurment happens only if a certain quantum out come is realized,namely in the case of a superposition between a situation in which ameasurmenet has happened and one in which it hasn’t. Hence RQMassumes that there is no absolute meaning to a propsotion like Fact Ehas obtained. The viability of this radical persectivism (includingits RQM version) has been recently discussed by Peter Evans (2020) ina paper with the titlePerspectival objectivity Or: how I learnedto stop worrying and love observer-dependent reality.

This weakening of realism is the “price to pay” for therelational interpretation of quantum mechanics. It can be comparedwith the “price to pay” in other interpretations, such asthe inflated ontology and the distance between the ontology and theworld as we see it of the Many Worlds interpretation, the existence ofvariables unobservables in principle and the loss of Lorentzinvariance of Bohm theory, and so on.

An alternative to this radical perspectivalism is to reduce it torelativism (Riedel 2024), namely to assume that values of variablesare relative, but the fact that a variable has relative to a system isan absolute fact, which by itself is not relative to anything. Namelyto assume that the actualization of each unique quantum event is afundamental absolute physical event. This tamed version of RQM isoften implicitly assumed by commentators, and criticised. JacquesPienaar (2021) has given a sharp version of these criticisms in theform of five no-go theorems indicating that the balancing act betweenrelative values and absolute actualization of quantum event cannot besustanied. Related criticisms where raised in (Muciño 2022) and(Lawrence 2023). Responses, pointing to the fact that these paperscontain implicit assumptions rejected in RQM, were given in (Rovelli2021b [Other Internet Resources], Di Biagio & Rovelli 2022 andCavalcanti 2023).

The other side of the coin of each “price to pay” is thelesson we might gather from the empirical success of quantum theory:for the Many Worlds interpretation, for instance, the lesson is thereal existence of other branches, for Bohm theory is the realexistence of unobservable variables that pick a preferred referenceframe, and so on. For RQM, the lesson of quantum theory is that thedescription of the way distinct physical systems affect each otherwhen they interact (and not the way physical systems‘are’) exhausts all that can be said about the physicalworld. The physical world must be described as a net of interactingcomponents, where there is no meaning to ‘the state of anisolated system’, or the value of the variables of an isolatedsystem. The state of a physical system is the net of the relations itentertains with the surrounding systems. The physical structure of theworld is identified as this net of relationships. The notion ofsubstance that plays a major role in western philosophy might beinappropriate to account for this science; perhaps the idea of a“mutual dependency” (Nāgārjuna 1995) may offer arelevant philosophical cadre (Rovelli 2021).

3.3 The debate on the cross perspective link

Emily Adlam (2022) has argued that interpretations of quantummechanics that deny observer-independence challenge our presumption ofintersubjectivity regarding measurement outcomes and this can undeminethe possibility of the scentific project itself, which is based on thepossibility of such agreement. She argues that such observers areunable to escape their own perspective in order to learn anythingabout the perspectives of other observers and therefore be unable toconfirm the theory. The challenge has motivated her and Rovelli to addto RQM a specific postulate about the relation between perspevctves(Adlam & Rovelli 2023). They consider a ‘Cross-PerspectiveLink’ postulate, which states that the measurement of asystem’s pointer accurately reveals the outcome said system hasregistered in an earlier interaction (unless the pointer has beentampered with). This axiom stipulates the possibility of communicationacross viewpoints.

There are two ways to interpret this postulate. It can be interpretedstrongly, as an absolute statment about a relation betweenperspectives. Alternatively, it can be interpreted weakly, as astatement about what can be ascertained by a (possibly further)observer. In thsi case, the postulate leads only to the consistency ofphysical communication implied by the quantum formalism discussed in2.6 above.

The strong interpretation assumes that it is possible to take theensemble of all perspectives realistically by “regard[ing] thepointlike quantum events or ‘flashes’ as absolute,observer-independent facts about reality” [Adlam & Rovelli2023, Adlam 2024], even if this ensemble is not acessible in principleto anybody. Whether this option is a viable in RQM is an openquestion. It is challenged for instance by Riedel (2024)“unrestricted iteration principle”, and by specific no-gotheorems (Pienaar 2021). Blake Stacey (2022 [Other InternetResources]) has argued that the strong interpretation is step backsaway from the perspectivalism that characterizes the interpretation:it is “a disguised form of the projection postulate leading to a‘global collapse’ of the state of the interactingpair” (Lahti and Pelonpää 2023).

Interpreted weakly, the postulate is sufficient to guarantee theintersubjectivity between agents that enjoy a common decoherecedomain. They can pile up a sufficient number of facts that are stablein the sense of (DiBiagio and Rovelli 2021) and develop rationalscience by noticing probabilistic regularities and by induection, andtherefore develop and test physical laws. A community of scientificperception in agreement as to what constitutes the object of theinvestigation is therefore compatible with RQM ven in its fullperspectival version. On the other hand, this is not sufficient toclose off the possibility that with respect to a further observerexternal to this community the entire contingent world specificallydescribed by current science could be just a term in a quantumsuperposition. So interpreted, RQM does not challenge the rationalityof the scientific enterpreise, butdoes undermine thepossibility of ascertaining facts as absolutely true. Taken in thissense, RQM interprets quantum phenomena as an invitation to a radicalperspectivalism: with respect to some observer, we can always be likeFriend is for Wigner. For a recent extensive discussion of thesealteratives, see theFoundation of Physics Special Issue onRQM and especially the introduction by Calosi and Riedel (2024).

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Other Internet Resources

• Bitbol, M., 2007, “Physical Relations or Functional Relations? A non-metaphysical construal of Rovelli’s Relational Quantum Mechanics”, manuscript at the PhilSci Archive.
• Cavalcanti, Eric G., 2008, “The view from a Wigner bubble”, manuscript at arXiv.org.
• DeBrota, J.B., Stacey, B.C., 2018, “FAQBism”, manuscript at arXiv.org.
• Fano, Vincenzo, 2024, “Application of Relational Quantum Mechanics to Simple Physical Situations”, manuscript at PhilSci Archive.
• Fuchs, Christopher A., 2002, “Quantum Mechanics as Quantum Information (and Only a Little More)”, manuscript at arXiv.org.
• Relational Quantum Mechanics: Perspectives and Developments,Claudio Calosi guest editor, Special Issue ofFoundation ofPhysics [special issue available online].
• Rovelli, Carlo, 2021b, “A response to the Mucino-Okon-Sudarsky’s Assessment of Relational Quantum Mechanics”, manuscript at arXiv.org.
• Rovelli, Carlo, 2024, “Can Alice do science and have friends, in a relational quantum world? Solipsism and Relational Quantum Mechanics”, manuscript at arXiv.org.
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• Waaijer, Marijn and Jan van Neerven, 2019, “Relational Analysis of the Frauchiger—Renner Paradox and Existence of Records from the Past”, manuscript at arXiv.org.
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