# The Relational Dissolution of the Quantum Measurement Problems

Andrea Oldofredi Contact Information: University of Lisbon, Centre of
Philosophy, 1600-023 Lisbon, Portugal. E-mail<EMAIL_ADDRESS>
###### Abstract

The Quantum Measurement Problem is arguably one of the most debated issues in
the philosophy of Quantum Mechanics, since it represents not only a technical
difficulty for the standard formulation of the theory, but also a source of
interpretational disputes concerning the meaning of the quantum postulates.
Another conundrum intimately connected with the QMP is the Wigner friend
paradox, a thought experiment underlining the incoherence between the two
dynamical laws governing the behavior of quantum systems, i.e the Schrödinger
equation and the projection rule. Thus, every alternative interpretation
aiming to be considered a sound formulation of QM must provide an explanation
to these puzzles associated with quantum measurements. It is the aim of the
present essay to discuss them in the context of Relational Quantum Mechanics.
In fact, it is shown here how this interpretative framework dissolves the QMP.
More precisely, two variants of this issue are considered: on the one hand, I
focus on the “the problem of outcomes” contained in Maudlin, (1995)—in which
the projection postulate is not mentioned—on the other hand, I take into
account Rovelli’s reformulation of this problem proposed in Rovelli, (2022),
where the tension between the Schrödinger equation and the stochastic nature
of the collapse rule is explicitly considered. Moreover, the relational
explanation to the Wigner’s friend paradox is reviewed, taking also into
account some interesting objections _contra_ Rovelli’s theory contained in
Laudisa, (2019). I contend that answering these critical remarks leads to an
improvement of our understanding of RQM. Finally, a possible objection against
the relational solution to the QMP is presented and addressed.

_Keywords_ : Relational Quantum Mechanics; Wigner Friend Paradox: Measurement
Problem; Ontology

_Accepted for publication in Foundations of Physics_

###### Contents

  1. 1 Introduction
  2. 2 The Quantum Measurement Problems
    1. 2.1 The Problem of Outcomes
    2. 2.2 The Relational Solution
    3. 2.3 Unitarity vs. Collapse: Rovelli’s Formulation of the QMP
  3. 3 Relational QM and the Wigner’s Friend Paradox
    1. 3.1 The Relational Interpretation of the Paradox
    2. 3.2 Laudisa’s Criticisms to RQM
  4. 4 Discussion
  5. 5 Conclusion

##  1 Introduction

The Quantum Measurement Problem (QMP) is arguably one of the most debated and
discussed issues in the philosophy of Quantum Mechanics (QM), since it
represents not only a technical difficulty for the standard formulation of the
theory, but also a source of interpretational disputes concerning the meaning
of the quantum postulates. According to many scholars this is motivated by the
presence of physically ill-defined notions within the axioms of QM, as for
instance “measurement” and “observer”. More precisely, several authors argued
that standard quantum theory does not provide a physical and causal
explanation for the realizations of macroscopic measurement outcomes,
remaining _de facto_ silent about what kind of dynamical processes are
responsible for the actualization of particular experimental results (cf.
Bell, (1987), Bricmont, (2016), Maudlin, (1995) for more details). Other
authors claim that the QMP originates from the incoherence between the two
dynamical laws governing the behavior of quantum systems, i.e the Schrödinger
equation and the projection rule (cf. Rovelli, (2022)). The latter issue has
been notoriously investigated by Wigner, who proposed a thought experiment
highlighting the undesired consequences generated by this inconsistency (cf.
Wigner, (1995)).

Since the QMP is generally considered one of the major conundra of quantum
mechanics, and the Wigner friend paradox underlines a crucial defect of the
theory, every alternative interpretation aiming to be considered a sound
formulation of QM must provide an explanation to these problematic issues
associated with quantum measurements. In fact, in the literature concerning
the foundations of quantum theory, many essays have been written to show how
well-known interpretations of QM solve the QMP. Notable examples are provided
by Bohm, (1952), Holland, (1993), Dürr and Teufel, (2009) that explain in
great detail the resolution of the QMP offered by different approaches to the
pilot-wave theory, Ghirardi, (2016), Bassi and Ghirardi, (2003) who discussed
how macroscopic measurement outcomes are obtained from the Ghirardi-Rimini-
Weber dynamics, or Everett, (1957), Wallace, (2012) that show how the relative
state formulation of QM and the many-world interpretation respectively face
the measurement problem.

In the present essay I will discuss both the QMP—or better, different
formulations of the problem—and the Wigner friend scenario in the context of
Relational Quantum Mechanics (RQM), an interpretation of the standard quantum
formalism provided by Carlo Rovelli in the mid-nineties.111In Rovelli, (1996)
RQM is introduced for the first time; in this paper I assume that the reader
is familiar with its physical and metaphysical principles. For space reasons I
will not discuss them here; however, excellent introductions and presentations
of this interpretation are contained in Rovelli, (2016, 2018, 2022) and
Laudisa and Rovelli, (2019). This framework finds its motivations in “the
experimental evidence at the basis of quantum mechanics” that “forces us to
accept that distinct observers give different descriptions of the same events”
(Rovelli, (1996), p. 1638). Such a claim, which entails a novel perspective on
the interpretation of QM, finds its roots in Einstein’s idea behind special
relativity, i.e. that physical observations depends on the specific reference
frame in which these interactions occur.222Analyzing Rovelli’s papers on RQM
it clearly emerges how Einstein’s relativity theories and their axioms
influenced the relational interpretation of QM. For an interesting discussion
on this topic the reader may refer to Pienaar, 2021a  and Di Biagio and
Rovelli, (2021). Furthermore, these insights on the meaning of non-
relativistic quantum theory are also motivated by Rovelli’s reflections on
quantum gravity and general relativity—according to him, in fact, in these
theories the relational features of spacetime clearly emerge—and from the
ubiquitous presence of relational quantities in physics—from classical
mechanics and electromagnetism to quantum field theory and cosmology (cf.
Rovelli and Vidotto, (2014)).

The main novelty of Rovelli’s approach is to take seriously into account the
relational character of physics, applying it to the formalism of standard QM
taken at face value. This strategy entails remarkable consequences not only
for the worldview that RQM provides, but also for the way in which many
conceptual issues affecting quantum theory are solved—as we will see in the
following sections. According to this interpretative framework, in fact, the
notion of observer-independent state of physical systems is abolished in favor
of an observer-dependent description of reality. In RQM different observers
may provide distinct characterizations of the same sequence of physical
events, all of which are equally correct and non-contradictory. As a
consequence, the values of measurable properties are _relative to_ specific
observers. More generally, the relational character of Rovelli’s view implies
that the notion of an absolute reality should be abandoned:

> a quantum mechanical description of a certain system (state and/or values of
> physical quantities) cannot be taken as an “absolute” (observer-independent)
> description of reality, but rather as a formalization, or codification, of
> properties of a system _relative_ to a given observer. Quantum mechanics can
> therefore be viewed as a theory about the states of systems and values of
> physical quantities relative to other systems. […] Therefore, I maintain
> that in quantum mechanics, “state” as well as “values of a variable”—or
> “outcome of a measurement”—are relational notions in the same sense in which
> velocity is relational in classical mechanics” (Rovelli, (1996), pp.
> 1648-1649).

It is worth noting that in RQM the word “observer” refers to _every_ physical
object having a particular definite state of motion. Thus, in RQM “observers”
are not necessarily conscious beings: in this theoretical framework an
electron, an air molecule as well as a Geiger counter can equally play the
role of observers. Hence, conscious agents do not have a privileged status.
Referring to this, Di Biagio and Rovelli, (2021) point out that one should not
overestimate the relevance of this notion in relational QM: the theory is not
primarily concerned with observers, it is about events, i.e. physical facts
taking place in spacetime and relative to particular physical systems. Indeed,
RQM supports an event ontology recalling Wittgenstein’s idea for which the
world is the totality of facts333For simplicity, in the present essay I will
consider events and facts as synonyms. The subtle difference between these two
notions in RQM is not relevant for the purposes of this work and can be
overlooked., and not of things:

> the ontology of RQM is a sparse (“flash”) ontology of relational quantum
> events, taken as primitive, and not derived from any “underlying”
> representation (Laudisa and Rovelli, (2019)).

To this regard, recent analyses of the event ontology of RQM introduced the
distinction between relative and stable facts. As we will see in the remainder
of the present paper, this dichotomy will be relevant for our discussion
because it provides a deeper understanding of how relational QM actually works
in measurement situations.444For a new perspective about the event ontology of
RQM the reader may refer to Adlam and Rovelli, (2022), where the authors
introduce an additional interpretative postulate to the existing corpus of
principles shaping the theory. As a consequence of it, the authors argue that
observer-independent facts do exists although they are described by relational
quantum states. Due to spatial constraints I cannot discuss here in detail
this new interpretation of RQM, thus, it will not mentioned in the remainder
of the paper.

Against this background, the aim of the present essay is twofold: in the first
place, I show how this interpretative framework dissolves the QMP. More
precisely, two variants of this issue are considered: on the one hand, I focus
on the well-known “problem of outcomes” contained in Maudlin, (1995)—in which
the projection postulate is not mentioned—on the other hand, I take into
account Rovelli’s reformulation of this problem proposed in Rovelli, (2022),
where the tension between the Schrödinger equation and the stochastic nature
of the collapse rule is explicitly considered. While the former can be seen as
a problem of quantum theory without the projection postulate, the latter may
be interpreted as a conundrum implied by the obscure nature of the collapse
process.555I thank the anonymous referee for pointing out this distinction. In
the second place, I review how RQM explains the Wigner’s friend paradox,
taking also into account some interesting objections _contra_ Rovelli’s theory
contained in Laudisa, (2019). I contend that answering these critical remarks
leads to an improvement of our understanding of RQM.666In this essay Laudisa
critically discusses two open problems of relational QM: (i) the QMP and (ii)
the issue of locality. Here I will be concerned only with the former; for a
recent discussion of locality in RQM the reader may refer to Martin-Dussaud et
al., (2019), Pienaar, (2019), Adlam and Rovelli, (2022).

The paper is organized as follows: the two formulations of the QMP and the
solutions offered by RQM are presented in detail in Section 2. The Wigner’s
friend paradox and its relational explanation as well as Laudisa’s criticisms
are discussed in Section 3. In Section 4 a possible objection against the
relational solution to the QMP is presented and addressed. Finally, Section 5
concludes the essay.

##  2 The Quantum Measurement Problems

The present section aims at explaining how RQM solves two formulations of the
QMP; we will begin by taking into account the well-known “problem of outcomes”
as formulated in Maudlin, (1995), then we will consider Rovelli, (2022)
analysis of the measurement problem, where the inconsistency between the
Schrödinger dynamics and the collapse postulate is investigated.

###  2.1 The Problem of Outcomes

In order to present the first version of the QMP let us consider the standard
example of a pre-measurement situation of the observable $S_{z}$ on a system
$s$, where the latter is described by a wave function $\psi$ which is in a
superposition of two $z-$spin states
$|\uparrow\rangle_{z},|\downarrow\rangle_{z}$:

$\displaystyle\psi=a|\uparrow\rangle_{z}+b|\downarrow\rangle_{z}.$ (1)

Here $|\uparrow\rangle_{z}$ corresponds to the $z-$spin-up state,
$|\downarrow\rangle_{z}$ to the $z-$spin-down state, and the coefficients
$|a|^{2},|b|^{2}$ give the probability to find $s$ in the $z-$spin-up/down
state respectively. From QM, we assume that the wave function of a given
system contains all information about its state, providing its _complete_
description. In this particular example $\psi$ represents a superposition of
$z-$spin states, meaning that the superposition “$z$-spin-up _and_ $z$-spin-
down” is a consistent description of the state in which a quantum particle may
be (i.e. it is completely admitted by the theory’s formalism as a proper
physical state of a certain quantum object). This formal fact is usually taken
to entail that prior to a spin measurement the particle has _indefinite_
$z-$spin, being neither in the $z$-spin-up state _nor_ in the $z$-spin-down
state.

In addition, before the measurement we assume that the macroscopic
experimental device used to measure this quantity is in the ready state
$\Phi_{0}$, i.e. in a state pointing to a neutral direction, whereas the other
admissible pointer’s positions will be $\Phi_{1}$ that is associated with the
eigenvalue $+\hbar/2$, and $\Phi_{2}$ that is associated with $-\hbar/2$
respectively. Conforming to standard quantum theory we know that prior to the
observation of $S_{z}$ the states of the system and the apparatus are
independent, i.e. described by a product wave function. However, given the
evolution provided by the Schrödinger equation we obtain the macroscopic
superposition:

$\displaystyle(a|\uparrow\rangle_{z}+b|\downarrow\rangle_{z})\Phi_{0}\longrightarrow
a|\uparrow\rangle_{z}\otimes|\Phi_{1}\rangle+b|\downarrow\rangle_{z}\otimes|\Phi_{2}\rangle.$
(2)

Thus, assuming (i) that wave functions provide a complete, observer-
independent description of quantum systems, and (ii) that their dynamics is
uniquely and completely described by the Schrödinger evolution, the
microscopic superposition of states is amplified to the _macroscopic scale_ ,
as we can easily see from the r.h.s of equation (2). Hence, it follows that
also macroscopic objects can be in superpositions, contradicting empirical
evidence which speaks in favor of the uniqueness and definiteness of
measurement outcomes. This is in essence of the famous “problem of outcomes”,
a particular version of the measurement problem affecting quantum theory.
Following Maudlin, (1995), it may be schematically stated as follows:

  1. _P. 1_

Wave functions provide a complete description of quantum systems;

  2. _P. 2_

Wave functions evolve according to the unitary evolution provided by the
Schrödinger equation;

  3. _P. 3_

Measurements have a unique determinate outcome.

Remarkably, any pair of these propositions is consistent and entails the
falsity of the third one, but the conjunction of the three statements
generates inconsistencies with experimental evidence.777For a simple proof of
this fact the reader should refer to Maudlin, (1995), pp. 7-8. Interestingly,
it is possible to understand how the various interpretations of QM solve the
QMP by looking at what statement they reject. For instance, Bohmian mechanics
denies the first proposition, since in every account of the pilot-wave theory
the wave function does not exhaust the description of physical systems, which
is supplemented by additional variables (particles’ positions). Similarly,
spontaneous collapse theories discard the second proposition, since they
modify the Schrödinger equation and implement a non-linear dynamics, while
Everett’s relative state formulation of QM and the many worlds interpretation
reject the last sentence, given that according to these frameworks every
possible outcome is actualized in different branches of the wave function or
in different worlds respectively. In the remainder of the section we will see
how Rovelli’s theory dissolves the problem of outcomes.

###  2.2 The Relational Solution

In order to understand how RQM deals with the QMP let us follow the usual
strategy and see what propositions do not hold in the context of Rovelli’s
theory.

In the first place, proposition _P. 1_ expresses the idea that the usual
quantum mechanical wave function describes completely the inherent state of a
quantum system, which is taken to be perspective-independent. Trivially, this
is at odds with the basic tenets of RQM. However, such a statement can be
retained with little effort also in the latter theory, since it is true that
in RQM $\psi$ provides the maximal information available about physical
systems relative to specific observers. Therefore, by taking into account the
principle of relativization of states, we can rephrase Proposition 1 as
follows:

> _P. 1’_ The quantum mechanical wave function $\psi$ describes completely the
> state of a system $s$ _relative_ to an observer $O$.

The reformulation of the first statement of the measurement problem entails
that the same system may be described differently by distinct observers. More
specifically, _P. 1’_ implies that distinct wave functions are employed by
diverse observers in order to describe a certain physical system $s$; such
descriptions will be however equally correct. In addition, according to RQM—in
agreement with standard QM—the description of physical systems provided by
wave functions is complete, i.e. it does not require the introduction of
additional parameters as done e.g. in hidden variables theories. Hence, RQM
does not solve the measurement problem by rejecting _P. 1_.

Our analysis gets more interesting by considering Proposition 2. To this
regard, although the wave function in RQM dynamically evolves according to the
Schrödinger equation, the latter does not exhaust the dynamics of the theory,
since when interactions occur the unitary evolution is suppressed. Hence, the
complete dynamics of RQM includes the projection postulated, exactly as in
modern formulations of QM. Consequently, the above Proposition 2 is incorrect
in the context of Rovelli’s theory. To make an accurate statement concerning
the physical content of the latter we should write:

> _P. 2’_ Wave functions evolve according to Schrödinger evolution until a
> measurement is performed. When interactions occur the collapse rule
> suppresses the unitary dynamics.

It is worth stressing here that although RQM includes the projection postulate
among its laws, the interpretation of such a rule in the relational context is
completely different w.r.t. the usual one provided in standard QM. In fact, in
RQM the suppression of the unitary dynamics is not caused by stochastic
quantum jumps: since in Rovelli’s theory $\psi$ is not considered a real
object but rather a mere computational tool, nothing physical is literally
collapsing in measurements interactions (cf. Rovelli, (2016, 2022)).
Alternatively, given that $\psi$ “stores” the maximal information that a
certain observer may have respect to a physical system to compute future
predictions, the collapse of the wave function is interpreted as an
information update relative to a certain agent concerning the value of some
magnitude measured on a particular system.888The interpretation of the
collapse postulate in RQM is similar to that provided by QBism. For discussion
cf. Pienaar, 2021b . The wave function, then, does not have any ontological
significance in RQM, contrary to standard quantum theory.999The ontological
status of the wave function in RQM has been discussed in several places, the
reader may refer to Smerlak and Rovelli, (2007), Rovelli, (2016), Laudisa and
Rovelli, (2019), Oldofredi, (2020).

In this respect, Rovelli’s views are close to the Heisenberg picture, which is
about the change of physical variables in time. Indeed, contrary to the
Schrödinger picture, where the wave function describes completely the state of
a system and evolves unitarily, in the Heisenberg picture $\psi$ just encodes
information about past interactions, and it changes only as a result of
another future interaction. Referring to this, Smerlak and Rovelli claimed
that in RQM “[w]hat evolves with time are the operators, whose expectation
values code the time-dependent probabilities that can be computed on the basis
of the past quantum events” (Smerlak and Rovelli, (2007), p. 431).101010As a
consequence in RQM also the notion of “wave function of the universe” present
in several interpretations of quantum theory—as for instance in Everett’s
relative state formulation of QM, the Many worlds interpretation, Bohmian
mechanics, _etc._ —is rejected.

In addition to these remarks about the interpretation of $\psi$—which explain
why the collapse postulate does not generate conceptual conundra—it is
relevant to note that the exact details about the mechanisms causing the
suspension of the unitary dynamics cannot be available in RQM. The reason is
the following: if information is given in terms of correlation, a system
cannot be correlated with itself, in turn exact information about the
machinery which generates the suspension of the Schrödinger evolution are not
accessible:

> Since between times $t_{1}$ and $t_{2}$ the evolution of $s$ is affected by
> its interaction with $O$, the description of the unitary evolution of $s$
> given by $O$ breaks down. The unitary evolution does not break down for
> mysterious physical quantum jumps, due to unknown effects, but simply
> because $O$ is not giving a full dynamical description of the interaction.
> $O$ cannot have a full description of the interaction of $s$ with himself
> ($O$), because his information is correlation, and there is no meaning in
> being correlated with oneself (Rovelli, (1996), pp. 1666-1667).

This fact should be simply considered as a descriptive limit of RQM, and not
an ontological drawback affecting this framework (more on this issue in the
next section).111111Cf. Dorato, (2016) for a good discussion of this issue.
Thus, it is the suppression of the unitary evolution via the collapse rule
that allows RQM to overcome the problem of outcomes, however, in this
theoretical framework such a postulate does not cause additional
interpretational troubles.

Although we have seen that RQM rejects Proposition 2, it is interesting to
note that also Proposition 3—which prescribes that measurements have a unique,
observer-independent outcome—does not carry over within such a theory. In
fact, _P. 3_ is true in RQM only _relative to_ an observer $O$ that measures a
certain magnitude on a given system $s$. The agent $O$ will certainly obtain a
unique, definite value via the interaction with the observed system. However,
in virtue of the principle of relativity of states, another observer $W$ may
ascribe a different state to the whole experimental situation, as we will see
in the next section. Referring to this, however, it should be underlined that
the requirement of internal consistency establishes that if $W$ interacts with
the complex system formed by $s+O$—provided that $O$ does not destroy the
information obtained measuring a certain observable on $s$—they will obtain
the same result registered by $O$. On the other hand, without a direct
interaction these two observers will in general assign different
representations of the same sequence of physical events. Therefore, in the
relational context the following is true:

> _P. 3’_ Measurements performed on a system $s$ have a unique determinate
> outcome relative to a specific observer $O$ that performed the observation.

Concerning the rejection of _P. 3_ , it is interesting to observe that RQM
behaves differently from both the many-worlds interpretation as well as from
Everett’s original proposal, which are the main solutions to the QMP refuting
Proposition 3. Contrary to the former, in a relational context there are no
splitting of worlds; Rovelli’s theory, in fact, is single-world interpretation
of the quantum formalism.121212Another crucial difference between these two
interpretations is that in RQM the wave function of the universe, which play a
central ontological role in MWI, does not exist. More interesting is the
difference existing between Everett’s and Rovelli’s perspectives. The first
thing to highlight is that Everett aimed at solving the QMP by getting rid of
the collapse postulate from the principles of QM, proposing a version of
quantum theory that he defined “pure wave mechanics”. According to this view,
every possible outcome of a certain measurement is actualized in different
branches of the wave function—which is the central object of the theory.
Interestingly, each branch of $\psi$ corresponds to the relative state of a
particular observer, which is itself part of the quantum mechanical
description of physical situations. Referring to this, Barrett, (2018)
underlines that Everett “believed that he could deduce the standard
statistical predictions of quantum mechanics (…) in terms of the subjective
experiences” of such observers.

As we have already seen, things are remarkably different in RQM where (i)
_not_ every possible measurement result is actualized, (ii) wave functions do
not split in different branches representing subjective experiences of some
agents, and (iii) the projection postulate is retained. Taking into account
the $z-$spin measurement employed to discuss Maudlin’s formulation of the QMP,
in fact, an observer $O$ performing the observation of the quantity $S_{z}$ on
a system $s$ will obtain only one definite result. The relativization of
states in Rovelli’s theory claims that another observer $W$ may assign a
different description of the same sequence of physical events, as we will see
in detail in the next section.

Thus, RQM provides a different strategy to solve the problem of outcomes
w.r.t. these well-known and established interpretations of QM.

###  2.3 Unitarity vs. Collapse: Rovelli’s Formulation of the QMP

Before concluding our discussion, we have to take into consideration another
approach to the QMP contained in Rovelli, (2022). According to Rovelli, the
essence of the measurement problem lies in the alleged incoherence between the
unitary evolution of the Schrödinger equation and the collapse postulate, he
then reformulates the issue as follows.

It is well-known that the probability amplitude $W(b(t),a)$ for a certain fact
$b$ to happen at time $t$ evolves according to the linear and unitary dynamics
provided by the Schrödinger equation. On the other hand, the collapse rule
affirms that the probability changes only when a measurement is performed,
i.e. when a certain fact occurs. The contradiction between these two laws of
QM arises, Rovelli contends, “because of quantum interference: interference
effects in the unitary evolution are cancelled by the projection” (Rovelli,
(2022), p. 1058).

In order to express this point more formally one can consider the following
situation: suppose a particular fact $a$ happened, and one among possible
facts $b_{i}$ (with $i=(1,\dots,N)$) may occur, then

> [b]y composition of probabilities, we expect the probability $P(c)$ for a
> further fact $c$ to happen to be given by
>
> $\displaystyle P_{collapse}(c|a)=\sum_{i}P(c|b_{i})P(b_{i}|a),$
>
> where $P(b|a)$ is the probability for $b$ to happen, given $a$. From the
> relation between probability and amplitude
>
> $\displaystyle P_{collapse}(c|a)=\sum_{i}P|W(c,b_{i})|^{2}|W(b_{i},a)|^{2}.$
> (3)
>
> But since quantum probabilities are squares of amplitudes and amplitudes
> sum, linear evolution requires
>
> $\displaystyle
> P_{unitary}(c|a)=|W(c,a)|^{2}=|\sum_{i}W(c,b_{i})W(b_{i},a)|^{2}$
> $\displaystyle\neq\sum_{i}|W(c,b_{i})|^{2}|W(b_{i},a)|^{2}=P_{collapse}(c|a)$
>
> (_ibid._ , pp. 1058-1059).

Thus, Rovelli concludes, the probability for the fact $c$ is different in the
case one considers the unitary dynamics or the collapse rule, and this is in
virtue of the quantum interference phenomena. Provided that we have already
seen that the collapse postulate does not generate conceptual issues in RQM,
we can still ask the following: what is the relational strategy to avoid this
undesired inconsistency concerning quantum probabilities? The answer is very
simple and has to be found in the labelling of facts (which will be explained
in more detail in the next section). According to the principles of RQM,
physical events happen relative to certain systems functioning as observers,
so that generally (3) does not hold in the case that facts $b_{i}$ and $c$ are
labeled w.r.t. different agents, since the probability amplitudes $W(b,a)$
“determine probabilities _only_ if $a$ and $b$ are relative to the same
system”.

Recalling the third person scenario from Rovelli, (1996)—which is used by
Rovelli in order to show how the relativization of states works—we can easily
exemplify the above discussion. Suppose that the quantity $S_{z}$ is measured
on the system $s$ by an agent $O$ inside their lab. The interaction between
$s$ and $O$ causes the suppression of the unitary evolution—and therefore the
suppression of interference effects—generating a unique, definite outcome for
the system $s$ with respect to the observer $O$. Thus, the actualization of a
particular value between $\pm\hbar/2$ is a fact relative to $O$, but not
relative to another observer $W$ who is outside the room. Consequently, the
probability for the actualization of a certain value for the magnitude $S_{z}$
w.r.t. $W$ will still involve interference effects. However, taking into
account (i) the processes of wave function collapse and decoherence that
occurred during the interaction between $s$ and $O$ and (ii) the system formed
by $O$ and the environment in which the observation took place, the
actualization of a specific experimental outcome can be considered a stable
fact also for $W$. This entails that if agent $W$ interacts directly with the
complex system $s+O$, $W$ will obtain results that are consistent with those
found by the agent $O$. Thus, we can safely conclude this section claiming
that RQM provides a detailed answer also to this formulation of the QMP.

Interestingly, in the last paragraph we anticipated some details which are
relevant in order to understand how RQM explains the Wigner’s friend paradox
to which we now turn.

##  3 Relational QM and the Wigner’s Friend Paradox

After having discussed how Rovelli’s theory dissolves the QMP, in this section
I am firstly going to show how this interpretative framework explains the
Wigner’s friend scenario, and secondly how it is possible to provide an answer
to the interesting objections contained in Laudisa, (2019) against RQM—showing
that these criticisms do not threat its internal coherence.

The Wigner friend paradox is a prominent though experiment proposed by Eugene
Wigner to show the inconsistency between the two fundamental laws of quantum
theory, i.e. the linear, deterministic Schrödinger equation and the stochastic
collapse postulate (cf. Wigner, (1995)). Such an argument can be summarized in
a few words as follows.

Suppose that a friend of Wigner $O$ is performing a measurement of the
$z-$spin on a quantum particle $s$ in their laboratory. Let’s also assume that
$s$ is not in an eigenstate of $S_{z}$, so that before the observation—at some
arbitrary initial time $t_{1}$—the system is in the superposition encountered
in the previous section:

$\displaystyle a|\uparrow\rangle_{z}+b|\downarrow\rangle_{z}.$ (4)

Now, at a later time $t_{2}$ the agent $O$ performs the measurement of $S_{z}$
on $s$; consequently, according to the standard formulation of QM the state of
the observed system collapses in one of the possible eigenstates of the
measured quantity—for the sake of the argument, let’s stipulate that $O$ finds
the $z-$spin-up state $|\uparrow\rangle_{z}$ upon measurement. Hence, this
sequence of physical events E relative to $O$ can be formalized as follows:

$\displaystyle\left.\begin{aligned} t_{1}\longrightarrow t_{2}\\\
a|\uparrow\rangle_{z}+b|\downarrow\rangle_{z}\longrightarrow|\uparrow\rangle_{z}\end{aligned}\right\\}\textbf{E}$
(5)

Now, Wigner ($W$) is outside the laboratory and describes the experimental
situation into the room by using standard QM, knowing that $O$ will measure
the $z-$spin of $s$. In this thought experiment $W$ is an external observer,
and the lab should be considered for all practical purposes an isolated
system. Consequently, from the linear dynamics of the Schrödinger equation it
follows that according to $W$’s perspective the system $s+O$ is in a
superposition of states:

$\left.\begin{aligned} t_{1}\longrightarrow t_{2}\\\
(a|\uparrow\rangle_{z}+b|\downarrow\rangle_{z})\otimes|O-ready\rangle\longrightarrow
a|\uparrow\rangle_{z}\otimes|O_{\uparrow}\rangle+b|\downarrow\rangle_{z}|O_{\downarrow}\rangle\end{aligned}\right\\}\textbf{E'}$
(6)

Remarkably, $W$ assigns a superposition state to the laboratory, although $O$
recorded a definite result after the $z-$spin measurement. It is only when $W$
asks directly to $O$ which outcome they obtained that the macroscopic
superposition E’ breaks. Nonetheless, well before $W$ asked his question, the
state of the system $s$ was already definite, i.e. the superposition (4) was
already decohered in the laboratory. Thus, Wigner concludes, the state after
the interaction between $s$ and $O$ was already either
$|\uparrow\rangle_{z}\otimes|O_{\uparrow}$ or
$|\downarrow\rangle_{z}\otimes|O_{\downarrow}\rangle$, and not the one
represented by the r.h.s. of (6). Here is the contradiction in Wigner’s words:

> the state described by the wave function
> $a(|\uparrow\rangle_{z}\otimes|O_{\uparrow}\rangle)+b(|\downarrow\rangle_{z}\otimes|O_{\downarrow}\rangle)$
> describes a state that has properties which neither
> $|\uparrow\rangle_{z}\otimes|O_{\uparrow}\rangle$ or
> $|\downarrow\rangle_{z}\otimes|O_{\downarrow}\rangle$ has. […] [T]he wave
> function
> $a(|\uparrow\rangle_{z}\otimes|O_{\uparrow}\rangle)+b(|\downarrow\rangle_{z}\otimes|O_{\downarrow}\rangle)$
> (which also follows from the linearity of the equations) appears absurd
> because it implies that my friend was in a state of suspended animation
> before he answered my question (Wigner, (1995), p. 256, notation adapted).

Wigner’s aim was to show that QM, in virtue of its incoherent laws, generates
contradictory descriptions of the same reality. According to him, in order to
resolve the tension existing between the dynamical postulates of quantum
theory, and to make sense of them, the notion of consciousness, or of a
conscious mind, should be introduced into the quantum picture in order to
break the superposition of states described above. In Wigner’s view, the
mind—or more generally a being with consciousness—cannot be in a superposition
of states, and thus it assumes a privileged status in quantum theory.131313For
further details on Wigner’s view cf. Wigner, (1995).

###  3.1 The Relational Interpretation of the Paradox

Wigner’s argument generated intense discussions among the experts working on
the foundations of quantum theory, and it is still vividly discussed to the
present day.141414Cf. Frauchiger and Renner, (2018), Bong et al., (2020),
Allard Guérin et al., (2021). Indeed, it is well known how the most popular
interpretations of QM solve this paradox and its new extensions (cf. for
instance Lazarovici and Hubert, (2019)). Referring to this, it is worth noting
that Rovelli, (1996) explained how RQM works discussing a physical situation
which is formally and logically equivalent to the Wigner friend scenario—what
Rovelli called the “Third Person Problem”. Let us then discuss the latter in
order to understand the relational interpretation of Wigner’s thought
experiment.

In the context of RQM the two sequences of events E and E’ encountered above
represent two different yet equally correct descriptions of the same physical
situation. Following the principles of the theory, in fact, E and E’ provide
diverse characterizations of the experimental context under consideration,
since they are relative to two distinct observers $O$ and $W$ respectively.
According to the former, the system $s$ possesses a sharp value for $S_{z}$,
whereas conforming to the latter (i) $s$ is _not_ in the state
$|\uparrow\rangle_{z}$, and (ii) the measuring device does not indicate any
sharp value of the $z-$spin. Indeed $W$ describes the complex system $s+O$ in
a macroscopic superposition of states.

Since RQM affirms that different observers can provide distinct descriptions
of the same sequence of physical events, it follows that _both_ descriptions E
and E’ are equally valid and not contradictory. Thus, one concludes that the
notion of “state of a system” must always be relative to another physical
system. In particular, in relational QM a certain object has a definite value
for a quantity _only relative_ to another observer. It follows, then, that the
notions of “quantum state”, “measurement outcome” and “value of a variable”
are purely relational concepts in this context. Consequently, _contra_ Wigner,
in RQM there is no need to introduce conscious agents to resolve the tension
created by the different descriptions of events E and E’, since they are both
correct characterizations of a relational reality. This is, in essence, the
message conveyed by the third person problem.151515Three main consequences can
be drawn from our discussion. Firstly, in RQM the separation between observed
system and observer cannot be univocally determined, _bona pace_ Wigner—in our
example agent $O$ observes $s$, but it is part of the composite observed
system $s+O$ according to Wigner’s perspective (more abut this issue in
Section 4). Secondly, as we already underlined, according to Rovelli’s theory
there is no privileged observer since all physical systems are equivalent:
“[n]othing a priori distinguishes macroscopic systems from quantum systems. If
the observer $O$ can give a quantum description of the system $s$, then it is
also legitimate for an observer $W$ to give a quantum description of the
system formed by the observer $O$” (Rovelli, (1996), p. 1644, notation
adapted). Thirdly, RQM provides a _complete_ description of the world, because
there is neither a deeper theory, nor hidden parameters describing how an
absolute reality behaves, as we have already pointed out in the previous
section studying the first proposition of the problem of outcomes.

Interestingly, the relational solution of the Wigner friend paradox can be
explained even more precisely with the aid of recent developments about
Rovelli’s theory contained in Di Biagio and Rovelli, (2022) and Rovelli,
(2022); particularly useful for us is the distinction between _relative_ and
_stable_ facts.

According to Di Biagio and Rovelli relative facts can be generally defined as
the interaction of a certain physical system—in our example $s$—with another
system, in the case at hand $O$.161616It is worth recalling that such
interactions involve wave function collapses. More precisely, if in virtue of
the interaction occurred between $s$ and $O$, the variable representing the
final state of $O$ depends on the value of $S_{z}$ measured on $s$, then such
a value constitutes a fact _relative_ to the agent $O$, as Di Biagio and
Rovelli, (2022) claim (p. 3). These authors call $O$ a “context” for the
actualization of a specific value of $S_{z}$ for $s$, thus, “[t]he interaction
with the context determines the fact that a certain variable has a value in
that context” (_ibid._). In this particular case, we can also say that the
post-collapse actualization of a particular value for $s$ constitutes a
_stable_ fact for $O$.171717According to these authors stable facts are a
proper subset of relative facts, i.e. all stable facts are also relative, but
the converse does not hold: not every relative fact is stable. The definition
of stable facts provided by Di Biagio and Rovelli is the following: knowing
that one among $N$ possible mutually exclusive facts $a_{i}$ with
$i=(1,...,N)$ occurred, the probability $P(b)$ for another fact $b$ to happen
is given by

$\displaystyle P(b)=\sum_{i}P(b|a_{i})P(a_{i}),$ (7)

where $P(a_{i})$ represents the probability that $a_{i}$ has happened, and
$P(b|a_{i})$ is the conditional probability for the occurrence of the fact $b$
given $a_{i}$. In our example we are considering a fact about the system $s$
relative to the agent $O$, thus, fact $b$ corresponds to the pointer variable
pointing in the $z-$spin-up direction, knowing that fact $a$ represents the
post-collapse actualization of $|\uparrow\rangle_{z}$. Notably, these two
facts are relative to $O$, consequently this formula holds:

$\displaystyle P(b^{(O)})=\sum_{i}P(b^{(O)}|a_{i}^{(O)})P(a_{i}^{(O)}).$ (8)

We can therefore conclude that the actualization of a definite value for the
magnitude $S_{z}$ measured on $s$ is a stable fact for $O$. In general,
however, for any observer $W\neq O$ (8) is not valid; this in turn implies
that

$\displaystyle P(b^{(W)})=\sum_{i}P(b^{(W)}|a_{i}^{(O)})P(a_{i}^{(O)})$ (9)

does not always holds.181818In those particular cases in which (9) holds for
also for another observer $W$, then we can say that $a_{i}^{(O)}$ is stable
also for $W$. In the context of the Wigner friend scenario, the failure of the
above equation for $W$ is due to the presence of interference effects: since
the composite system $s+O$ can be considered for all practical purposes
isolated for $W$, Wigner will represent the facts relative to the system $s+O$
according to (6). Nonetheless, as Di Biagio and Rovelli underline,
probabilities computed from that superposed state violate (9), and therefore
the actualization of the state
$|\uparrow\rangle_{z}\otimes|O_{\uparrow}\rangle$ is not a stable fact for
$W$:

> Equation (7) holds only if $b$ and $a_{i}$ are facts relative to the same
> system, but fails in general if used for facts relative to different systems
> (Di Biagio and Rovelli, (2022), p. 3, equation number adapted).

Remarkably, what makes a relative fact stable is quantum decoherence, an
ubiquitous phenomenon that occurs as soon as a large number of quantum systems
are involved. This is relevant for our discussion since via decoherence it is
possible to show how the actualization of $|\uparrow\rangle_{z}$ relative to
$O$ can be a stable fact also for Wigner. In order to achieve this result one
has to consider two systems $O$ and $E$—where $E$ represents the environment
in which the measurement of $S_{z}$ took place—and the variable corresponding
to the possible final states of $O$, let us call it $L_{O}$ for simplicity.
Let $O_{a_{i}}$ be the eigenvalues of $L_{O}$. According to standard QM, the
generic state of the complex system $O+E$ can be written as:

$\displaystyle|\psi\rangle=\sum_{i}c_{i}|O_{a_{i}}\rangle\otimes|E_{i}\rangle,$

where $E_{i}$ represent the normalized states of the environment. Now, suppose
that $W$ does not interact with $E$, as in the Wigner friend scenario. The
probability of a possible fact relative to $W$ resulting _from the
interaction_ between $W$ and $E$ can be computed via the density matrix
obtained tracing over $E$:

$\displaystyle\rho=\textrm{tr}_{E}|\psi\rangle\langle\psi|=\sum_{i}|c_{i}|^{2}|O_{a_{i}}\rangle\langle
O_{a_{i}}|.$

Finally, establishing that $P(O_{a_{i}}^{(E)})=|c_{i}|^{2}$ we obtain

$\displaystyle
P(b^{(W)})=\sum_{i}P(b^{(W)}|O_{a_{i}}^{(E)})P(O_{a_{i}}^{(E)})$

meaning that the probabilities for facts relative to $W$ computed from the
possible values of $L_{O}$ satisfy equation (9). This result has remarkable
implications: (i) the value of the variable $L_{O}$—corresponding to the final
state of the agent $O$ after the observation of $S_{z}$—is _stable for
$W$_191919Here I am simplifying the physical description of the actual
situation since small interference effects should be taken into consideration.
For a more detailed account of this discussion see Di Biagio and Rovelli,
(2022) Section 3., (ii) events concerning the systems $O$ and $E$ can generate
a stable fact for another observer that has not yet interacted with them.
Consequently, we can claim that also for $W$ the state of $O$ has effectively
collapsed into one of the possible measurement outcomes (with probability
$P(O_{a_{i}})=|c_{i}|^{2}$) although $W$ did not interact with $O$.

An interesting question, then, is to ask how different perspectives may
coexist without generating contradictions. We have already answered to this
issue studying the second proposition of the problem of outcomes, however, let
us give another, more specific reply. Recently, Di Biagio and Rovelli, (2021)
stressed that one of the interpretative postulates of RQM is the following:
“[i]n the Wigner’s friend scenario, if $W$ measures $s$ on the same basis on
which $O$ did, then appropriately interacts with $O$ to ‘check the reading’ of
a pointer variable (i.e. by measuring $O$ in the appropriate ‘pointer basis’),
the two values found are in agreement”.202020A similar idea was already stated
in Rovelli, (1996) as follows: “if $W$ knows that $O$ has measured $S_{z}$,
and then she measures $S_{z}$, and then she measures what $O$ has obtained in
measuring $S_{z}$, consistency requires that the results obtained by $W$ about
the variable $S_{z}$ and the pointer are correlated” (p. 1652, notation
adapted). This ensures that if these two agents interact their results will
agree, provided that $O$ does not destroy the information obtained after the
measurement of $S_{z}$ by performing another observation of a magnitude
incompatible with $z-$spin. Alternatively stated, if $W$ measures the state of
the complex system $s+O$, he will break the superposition in (6) and will
found the state $|\uparrow\rangle_{z}\otimes|O_{\uparrow}\rangle$—proviso that
$O$ did not performed another measurement destroying the information obtained
measuring $S_{z}$. Then, if $W$ asks to $O$ which result they obtained, the
answer will be $|\uparrow\rangle_{z}$, so that the descriptions of $W$ and $O$
will match. This is in virtue of the decoherence process that took place
within the lab, that “stabilized” the measurement outcome.

###  3.2 Laudisa’s Criticisms to RQM

Having discussed the relational explanation of the Wigner friend though
experiment, let us now take into account the major objections against RQM
contained in Laudisa, (2019). In the first place, Laudisa correctly points out
that the physical situation considered in the third person scenario is
identical to the Wigner friend paradox; however, he underlines that Wigner’s
aim was not to demonstrate the relational character of quantum theory, but
rather to show a fundamental ambiguity about _when_ the unitary dynamics
provided by the Schrödinger equation “should stop holding”.

In the second place, Laudisa interestingly claims that “in indexing states
relative to observers, RQM attempts to dissolve the inconsistency that appears
to follow from the linear dynamics of the states involved in a typical QM
measurement process” (Laudisa, (2019), p. 222). However, he says, such a move
is problematic since the sequence E described by (5) “overlooks the
correlation” between the possible states of the system $s$ and those of the
observer $O$ that is created before a definite measurement outcome is selected
by the collapse process. More precisely, Laudisa argues that the correct
dynamical history of what happens in the laboratory should go first from the
superposed state $a|\uparrow\rangle_{z}+b|\downarrow\rangle_{z}$ to the
entangled state
$a|\uparrow\rangle_{z}\otimes|O_{\uparrow}\rangle+b|\downarrow\rangle_{z}\otimes|O_{\downarrow}\rangle$,
and only after, in virtue of collapse, to the state $|\uparrow\rangle_{z}$.
However, Laudisa remarks, the first step of this dynamical process “leads
immediately to the description E’:

$\displaystyle\left.\begin{aligned} t_{1}\longrightarrow t_{2}\\\
(a|\uparrow\rangle_{z}+b|\downarrow\rangle_{z})\otimes|O-ready\rangle\longrightarrow
a|\uparrow\rangle_{z}\otimes|O_{\uparrow}\rangle+b|\downarrow\rangle_{z}\otimes|O_{\downarrow}\rangle\end{aligned}\right\\}\textbf{E'}$

Consequently, he concludes that it is not true that the sequences of events E,
E’ are different, as Rovelli’s theory entails. The sequence E’, then, “is not
a different sequence w.r.t. to E, but simply the same sequence under the
(standard) assumption that the correlation between $O$ and $s$ is taken
_explicitly_ into due account” (_ibid._ , p. 222).

Finally, and more importantly, Laudisa argues that in the third person
scenario there is an element of ambiguity concerning Wigner’s perspective.
According to RQM, $W$ describes the complex system $s+O$ without performing
any action on it, although according to Rovelli, (1996) the only way to obtain
information in RQM is via interaction. Thus, Laudisa argues, it is reasonable
to claim that the relational theory

> inherits from standard QM the ordinary way to describe the kind of
> interaction that is suitable to account for measurement, namely through the
> tensor product coupling. But in this case, we couple $\cal{H}_{W}$ to
> $(\mathcal{H}_{S}\otimes\cal{H}_{O})$ so as to obtain
> $\cal{H}_{W}\otimes\mathcal{H}_{S}\otimes\cal{H}_{O}$, and in turn we obtain
> the sequence (with the obvious interpretation for the states
> $|W-ready\rangle,|W_{\uparrow}\rangle$ and $|W_{\downarrow}\rangle$:
>
>
> $\displaystyle(a|\uparrow\rangle_{z}+b|\downarrow\rangle_{z})\otimes|O-ready\rangle\Longrightarrow$
> (10) $\displaystyle
> a|\uparrow\rangle_{z}\otimes|O_{\uparrow}\rangle\otimes|W_{\uparrow}\rangle+b|\downarrow\rangle_{z}\otimes|O_{\downarrow}\rangle\otimes|W\downarrow\rangle$
>
> which is completely consistent with E and E’, provided that now the system
> under scrutiny is $W+s+O$ and no more $s+O$.
>
> To sum up: the “third person problem” is allegedly one of the cornerstones
> of RQM, and the main argument underlying it is meant to support the shift to
> a fundamental relativization of states of quantum physical systems to
> observers. The formulation itself of the problem, however, seems to be based
> on a basic ambiguity, affecting the very description of a measurement
> process provided by different observers. If one tries to remove the
> ambiguity by sharpening the description, the alleged difference between E
> and E’ appears to evaporate and the motivation for the relativization gets
> considerably weaker (_ibid._ , pp. 222-223, equation and notation adapted).

Laudisa’s objections are very well articulated and go directly to the heart of
RQM discussing some potential difficulties of this interpretative framework.
In fact, it is essential to explain how RQM is able to overcome these
criticisms in order to show that this theory is not affected by the conceptual
ambiguities mentioned above. Thus, let us consider them in order.

In the first place, it should be noted that in his works on RQM Rovelli never
stated that Wigner’s friend paradox was constructed to show the relational
character of quantum theory. In fact, although it is true that the third
person problem and Wigner’s thought experiment employ the same logical
structure—and thus are formally equivalent—the explanations for the very same
scenario provided by these two authors pull in opposite directions. On the one
hand, Wigner argued that (i) there exists a fundamental tension (or even worse
an incoherence) between the dynamical laws of quantum theory, and (ii) the cut
between quantum system and classical observer is ambiguous in the standard
formulation of QM. As is known, he suggested to resolve these issues with the
introduction of a conscious mind whose role is to cause the suppression of the
unitary dynamics and, thereby, to define clearly the moment in which the wave
function should collapse. In this manner, the vagueness about the demarcation
between observed system and observer is resolved as well. On the other hand,
Rovelli showed a direct application of the principle of relativization of
states—one of the core interpretative postulates of RQM—via the third person
problem. As already stated, in Rovelli, (1996) such a scenario has a central
explanatory and heuristic function, since it illustrates that endorsing the
metaphysical assumptions of relational QM and taking the formalism of quantum
theory at face value, one is led to the relativity of states. Against this
background, it is relevant to underline that RQM rejects one of the implicit
premises of the Wigner’s friend thought experiment, namely that there exists a
unique, absolute reality which is described inconsistently by agents $O$ and
$W$. Hence, contrary to Wigner’s conclusions, according to RQM there is no
contradiction between the descriptions provided by these two different
observers. Moreover, according to Rovelli there is no incoherence between the
laws of QM, since $\psi$ has no ontological significance in RQM, as we have
seen in Section 2. In addition, as already stressed, given that in RQM every
physical system can play the role of observer and observed system, the issue
of the arbitrary distinction between the two simply vanishes without
introducing consciousness in QM.

In the second place, contrary to Laudisa’s claim, I argue that the sequences
of physical events E and E’ are different in the context of RQM. Taking into
account the sequence (5), agent $O$ measures at some arbitrary initial time
$t_{1}$ the quantity $S_{z}$ on the system $s$, and finds at a successive
final time $t_{2}$ a determinate value for the $z-$spin in virtue of the
collapse process occurred in the laboratory that suppressed the superposition
of states (4). The obtained measurement outcome is a fact relative to $O$.
From standard QM we know that before the measurement $s$ is in a superposition
of states and $O$ is in a neutral state $|O-ready\rangle$, their state in fact
is: $(a|\uparrow\rangle_{z}+b|\downarrow\rangle_{z})|O-ready\rangle$.
Successively, when their physical interaction begins, the state of the system
and the state of $O$ get correlated
($a|\uparrow\rangle_{z}\otimes|O_{\uparrow}\rangle+b|\downarrow\rangle_{z}\otimes|O_{\downarrow}\rangle$),
until at some final time $t_{2}$ the projection rule breaks the superposition
and $O$ eventually obtains a definite value for the measured quantity—in our
example $|\uparrow\rangle_{z}$—and consequently $O$ will see the pointer of
the experimental apparatus pointing in the $z-$spin-up direction.

This situation is remarkably different for observer $W$, since his description
terminates at $t_{2}$ with the superposition of states
$a|\uparrow\rangle_{z}\otimes|O_{\uparrow}\rangle+b|\downarrow\rangle_{z}\otimes|O_{\downarrow}\rangle$,
where no definite eigenvalue for $S_{z}$ has been obtained. Laudisa’s
objection in my opinion overlooks the following point: although the
superposition in (6) appears also in the sequence E, in the latter case this
is just a _dynamical transition_ to arrive at the final state in which $O$
obtains a sharp value for the quantity $S_{z}$ measured on $s$. Alternatively
stated, the dynamical histories that take place according to $O$ and $W$ are
not both governed by a unitary evolution contrary to Laudisa’s view: from the
laboratory’s perspective the Schrödinger dynamics is suppressed by a
stochastic collapse of the wave function which in turns allows agent $O$ to
find the system $s$ in a definite $z-$spin state, and thereby, to record a
sharp value for the measured quantity $S_{z}$. Thus, although the two
sequences have partial structural similarity, they denote different states of
affairs, since the perspectives of the observers $O$ and $W$, and their
information about the measure of the $z-$spin on $s$ do not agree. In fact,
albeit the actualization of a particular eigenvalue of $S_{z}$ is a stable
fact for Wigner in virtue of decoherence, this is not a fact relative to him.
Hence, we can conclude that $\textbf{E}\neq\textbf{E'}$. Moreover, Laudisa is
implicitly assuming that $O$ must include themselves into their description of
the sequence (5); however, this is not the necessarily case: $O$ is merely
describing what happens to $s$ relative to their own perspective, without
including themselves into the sequence of physical events occurring in the
lab—this is why the superposition (6) does not appear explicitly in E, but it
is present in E’ where $O$ is part of the observed system.

Finally, let us try to shed light on the alleged ambiguity present in RQM
treatment of the quantum measurement process. Referring to this, it is worth
noting that the sequence of events represented by (5) constitutes not only a
fact relative to $O$, but also a stable fact for $W$ in virtue of the
decoherence processes taking place in the lab. However, since Wigner has not
yet interacted with the complex system $s+O$, he assigns a relative state to
$s+O$ in which interference effects are still present. In other words, the
actualization of a definite value for $s$ is not a fact relative to $W$. The
distinction between relative and stable facts, hence, shows that there is no
ambiguity in the description of physical events from the perspectives of $O$
and $W$. Consequently, we conclude by saying that sequences E and E’ represent
different states of affairs in RQM. In addition, as already pointed out a few
lines above, considering the sequence (5) one notes that $O$ is _not_ involved
in the description of the physical events occurring in the lab. This is
because (5) represents a set of facts relative to $O$; furthermore, $O$ is
never in a superposed state from their own perspective within the room. Only
taking into account another agent $W$, $O$ becomes part of the observed system
$s+O$. Applying the same logic, equation (10) is not describing Wigner’s
perspective, since $W$ is not himself part of his description of what happens
in the lab between $s$ and $O$.212121It should be noted that also in the
original Wigner’s friend scenario, Wigner is not part in the description of
the experimental situation taking place in the lab. Thus, Laudisa’s equation
(10) seems to refer to the perspective of a super-observer $Q$, who is
observing the tripartite system $W-s-O$, and not to $W$’s perspective.

In sum, we can conclude that there is no fundamental ambiguity in the
relational explanation of the Wigner friend thought experiment as well as in
the relativization of states.

##  4 Discussion

Having explained how RQM dissolves the Wigner’s friend paradox as well as the
QMP, one may raise the following objections: “(i) the relational solution to
these issues is not satisfactory because the theory employs physically ill-
defined notions as “observer” and “measurement”, and (ii) RQM does not specify
what objects determine the actualization of measurement outcomes, i.e. it does
not provide a clear ontology for the microscopic regime”.222222This objection
can be found e.g. in Laudisa, (2019), as underlined in Rovelli, (2022), p.
1066. In the latter essay Rovelli responds arguing that RQM rejects a strong
form of realism where physical objects have well-defined values for their
properties at all times. Moreover, he continues, not only in relational QM
there is no such a thing as the wave function of the universe, but also “there
is no coherent global view available”. Referring to this, Laudisa and Rovelli,
(2019) claim that if “by realism we mean the assumption that the world is “out
there”, irrespectively of our mental states, or perceptions, there is nothing
in RQM that contradicts realism. But if by realism we mean the stronger
assumption that each variables of each subsystem of the world has a single
value at each and every time, then this strong version of realism is weakened
by RQM”.

These are common criticisms to RQM which deserve to be addressed and
discussed. For the sake of precision, it should be noted that such objections
implicitly assume that the physical description of the quantum regime must be
given employing an object-oriented ontology that specifies the elementary
objects of RQM—what John S. Bell would call the “beables” of the theory—and
how these entities dynamically evolve in space and time.

In order to answer the above criticisms, it is sufficient to look closely at
the principles of RQM and how they works, keeping in mind that such
interpretative framework implements a completely different metaphysical view
w.r.t. local beables theories. As we already pointed out, contrary to the case
of standard QM, in Rovelli’s view the notion of “observer” is clearly defined:
every physical object that can have a state of motion—i.e. that can interact
with other systems—can be an observer. It is a logical consequence, therefore,
that any physical system can be an observer as well as an observed system. A
clear example of this fact is given by the different roles played by agent $O$
in the Wigner’s friend scenario. Hence, in RQM any given measurement
situation—more clearly, any interaction—determines without ambiguities which
system is observed and which system is observing. Moreover, as already
stressed, an observer is not necessarily a conscious being, as clarified by
Smerlak and Rovelli:

> [a]n observer, in the sense used here, does not need to be, say “complex”,
> or even less so “conscious”. An atom interacting with another atom can be
> considered an observer. Obviously this does not mean that one atom must be
> capable of storing the information about the other atom, and consciously
> computing the outcome of its future interaction with it; the point is simply
> that the history of its past interaction _is_ in principle sufficient
> information for this computation (Smerlak and Rovelli, (2007), p. 430).

Taking into account the notion of measurement, RQM simply says that any
physical interaction between two or more systems constitutes an observation.
Thus, it is fair to claim that there is no vagueness concerning the
theoretical and observational terms appearing within the principles of the
theory. Nonetheless, it must be stressed again that RQM does not provide a
story or a justification of the dynamical processes causing a certain
actualization of a particular quantum event, i.e. a wave function collapse. As
Laudisa and Rovelli, (2019) explain, “quantum mechanics gives probabilities
for quantum events to happen, not a story representing how they happen. This
core aspect of quantum theory is not resolved in RQM: it is taken as a fact of
the world. What RQM does resolve is the question of when this happens: any
time one system affects another one, it happens relative to this other system.
What RQM does, is to show that this is not in contradiction with the existence
of interference effects. But the core discreteness of the quantum event
actualization is not ‘explained’ in RQM: it is understood as the picture of
how nature works according to quantum theory”.232323It goes without saying
that for many authors this feature of RQM constitutes an inherent defect of
the theory, and thus, a justified motivation to discard it. It should be
noted, however, that other well-known, established interpretations of the
quantum formalism involving either a branching process, or a relativization of
states seem to have a descriptive limit similar to RQM. For instance, the many
worlds interpretation does not explain the physical details responsible for
the branching process. Analogously, Everett’s interpretation requires that in
measurement situations every possible outcome is actualized in relative states
corresponding to different branches of the wave function. However, the details
concerning the actualization of determined records in such relative states are
not provided.

Finally, let us discuss what kind of ontology is implemented by RQM. As
anticipated at the outset of this section, the theory does not employ an
object-oriented ontology where the macroscopic reality is somehow reduced to
the dynamical evolution of a given class of objects equipped with
noncontextual properties. On the contrary, RQM as originally conceived in
Rovelli, (1996) implements an event ontology.242424This kind of ontology has a
robust philosophical basis, for a general introduction the reader may refer to
Casati and Varzi, (2020). According to this proposal, events are physical
interactions occurring among two (or more) systems. These interactions in turn
change the values of some properties instantiated by physical systems relative
to other systems functioning as observers. Thus, conforming to this event
based formulation of RQM, the world is just “an evolving network of sparse
relative events, described by punctual relative values of physical variables”
(Laudisa and Rovelli, (2019)), as we saw in section 1.

Interestingly, recent developments of RQM have been helpful in clarifying the
ontological content of this theory and proposing alternative metaphysical
readings. In addition to the already mentioned papers by Di Biagio and
Rovelli, let us mention other approaches present in literature:

  * •

Candiotto, (2017) contends that RQM is best appreciated in terms of an
objectless metaphysics of relations without relata. In her view Rovelli’s
theory should be considered an instantiation of the ontology proposed by ontic
structural realism according to which the fundamental building blocks of
nature are relations, not objects. Underlining the centrality of relations in
RQM, Candiotto affirms that in this theory there are no objects entering into
a given relation: it is the latter that generates objects. Hence, she
concludes that the natural framework to cast relational quantum mechanics and
to understand its metaphysical content is a radical form of structural
realism;

  * •

Contrary to Candiotto’s view, Oldofredi, (2020) claims the notion of physical
object can be retained in RQM implementing an ontology of
properties.252525Such ontologies not only have a long and prestigious
philosophical tradition, but also they are endorsed by several authors in the
contemporary philosophy of quantum mechanics, as for instance in da Costa et
al., (2013), Lombardi and Dieks, (2016) and Kuhlmann, (2010). According to
this proposal, physical systems in RQM can be defined as a mereological fusion
of properties, where (i) the intrinsic attributes characterizing a certain
species of particles have observer-independent values (e.g. mass and charge),
(ii) the extrinsic qualities take definite values relative to particular
observers (e.g. position, spin along a given axis, _etc._), and (iii) not
every observable defining a certain system can have a definite value due to
their contextual nature. Consequently, from the perspective of mereological
bundle theory, one can properly speak about material objects in motion in
spacetime, whose attributes vary in relation to different observers. This
interpretation entails that RQM can be made compatible with moderate
structural realism;

  * •

In Calosi and Mariani, (2020) it is argued that metaphysical indeterminacy
offers a new perspective on the metaphysics of RQM. On the one hand, it is
shown that indeterminacy can underwrite a full-blooded realistic attitude
towards non-interacting quantum systems. On the other hand, it is suggested
that RQM provides example of genuine metaphysical indeterminacy. As far as
non-interacting quantum systems are concerned;

  * •

Dorato, (2016) argues instead that isolated systems in RQM can be interpreted
as objects having dispositions that are manifested through interactions with
other physical systems. Such manifestations are responsible for observer-
dependent measurable properties;

These examples clearly suggest that RQM can be provided with a sound
metaphysics and a well-defined ontology; thus, we completed our answer to the
objection considered at the beginning of this section.262626One may easily
rephrase the relational solution to the Wigner friend paradox and the QMP in
terms of the various proposals mentioned in this section; however, this
exercise is left to the reader.

In sum, although this theory entails a radical departure from commonly
accepted physical intuitions and a new perspective about reality, we can
conclude that the technical and ontological issues affecting standard quantum
theory find a solution in RQM.

##  5 Conclusion

In this essay we discussed how RQM dissolves the QMP and how it explains the
Wigner’s friend paradox, answering also to interesting objections raised by
Laudisa. In particular, we have seen (i) which propositions composing the
“problem of outcomes” are at odds w.r.t. the metaphysical assumptions of
Rovelli’s theory, and (ii) that there is no fundamental tension between the
Schrödinger dynamics and the collapse postulate in the context of RQM.
Moreover, it has been shown how the relativization of states actually works in
the context of Wigner’s thought experiment, stressing the relevance of the
distinction between relative and stable facts for the explanation of this
alleged paradox. Finally, we briefly mentioned various proposals for the
interpretation of RQM, claiming that this theoretical framework can be
considered a metaphysically sound formulation of quantum theory.

Although in this paper we argued that RQM is not affected by the well-known
conundra plaguing standard QM, a lot of work remains to be done in the context
of this framework. Future research will include a clarification of the nature
of quantum probabilities involved within this interpretation, as well as a
detailed discussion about the status of macroscopic superpositions. Moreover,
it will be interesting to extend RQM to the quantum theory of fields. These
exciting questions will be addressed in future works.

Acknowledgements: I warmly thank the Guest Editor of this special issue
Claudio Calosi for having invited me to contribute. My sincere thanks go also
to the referee of this paper, whose comments and remarks improved the quality
of the essay. AO is grateful to the Fundaç$\tilde{\mathrm{a}}$o para a Ciência
e a Tecnologia (FCT) for financial support (Grant no. 2020.02858.CEECIND).

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