Relational Quantum Mechanics

Historical Context and Theoretical Foundations

Relational Quantum Mechanics (RQM) represents a fundamental reconceptualization of the mathematical formalism of quantum theory. Introduced by theoretical physicist Carlo Rovelli in a seminal 1996 preprint, RQM posits that the state of a quantum system is not an absolute, objective property of the system in isolation ¹²³. Instead, the quantum state is entirely relational; it is a mathematical description of the relationship between a specific observer and the observed system ¹. Unlike traditional interpretations that attempt to explain the counterintuitive phenomena of quantum mechanics by postulating multiple universes, adding hidden variables, or invoking spontaneous physical collapse mechanisms, RQM accepts the standard mathematical framework of quantum theory as complete while discarding classical metaphysical assumptions regarding the absolute nature of physical properties ¹³⁴.

Origins in Early Quantum Theory

To understand the motivations behind RQM, it is necessary to examine the historical development of quantum mechanics. In 1925, Werner Heisenberg introduced matrix mechanics, a formulation based entirely on observable quantities and discrete transitions ²⁵. Shortly thereafter, in 1926, Erwin Schrödinger developed wave mechanics, introducing the continuous wave function ($\psi$) ². While the two mathematical frameworks were proven to be equivalent, Schrödinger's formulation became dominant because differential equations were more familiar to physicists of the era ².

According to the relational interpretation, the conceptual step of endowing Schrödinger's wave function with ontological weight - treating it as a real, physical entity - was a historical misstep that generated decades of interpretational confusion ²³. RQM argues that the wave function does not represent the "actual stuff" of the universe ². Instead, it is an epistemic tool utilized to track the history of interactions between systems, directly analogous to the Hamilton-Jacobi function in classical mechanics ³⁶.

The Analogy with Special Relativity

The conceptual architecture of RQM is heavily inspired by the paradigm shift initiated by Albert Einstein's special theory of relativity ¹²⁷. Prior to the development of special relativity, physicists struggled to interpret Lorentz transformations because they implicitly assumed the existence of an observer-independent, absolute framework of time and space ¹. Einstein resolved these theoretical paradoxes by demonstrating that time, length, and simultaneity are not absolute, but are strictly relative to the reference frame of the observer ¹⁸.

Rovelli applied this exact epistemic maneuver to quantum mechanics. He suggested that the paradoxes of quantum formalism - such as Schrödinger's cat and the measurement problem - arise from the persistent, incorrect assumption that a physical system possesses an absolute, observer-independent state ¹. In classical mechanics, properties like velocity and electric potential are already understood to be relational; an object has no absolute velocity, only a velocity relative to another specified object ⁴⁸. RQM extends this relationality to all physical variables, including position, momentum, and spin ⁴⁹.

Information Theory as a Physical Substrate

The development of RQM was also deeply influenced by physicist John Archibald Wheeler's concept of "It from Bit," which proposed that information theory could serve as the foundational language of quantum mechanics ¹²⁶. In the context of RQM, the term "information" does not imply consciousness, semantic meaning, or human knowledge. Instead, it is defined in the strict physical sense of Claude Shannon's information theory ³⁶⁸.

Information in RQM is a measure of the physical correlation established between two systems resulting from a physical interaction ³⁶⁸. When two systems interact, the degrees of freedom of one system become correlated with the degrees of freedom of the other. The state vector of conventional quantum mechanics is therefore understood as a bookkeeping device that encodes this relative information, allowing one system to predict the probabilities of future interactions with another specific system ⁶¹⁰.

The Ontology of Relational Quantum Mechanics

Any interpretation of quantum mechanics must establish a coherent ontology - a fundamental account of the entities and properties that constitute reality. RQM proposes a sparse, relational ontology that departs significantly from both the classical worldview and alternative quantum interpretations ²⁶¹¹.

Sparse Relative Events and Interactions

In RQM, continuous trajectories and persistent, absolute properties are viewed as illusions of the macroscopic limit ¹¹². The fundamental fabric of reality consists of discrete quantum events, sometimes referred to in the literature as "flashes" ⁶⁹¹¹¹¹. A quantum event occurs strictly during a physical interaction between two systems ³⁹. It is only in the course of an interaction that a physical variable actualizes and assumes a definite value ³⁹¹².

Crucially, this actualization is entirely relative to the interacting systems. If a variable of system $S$ takes a definite value during an interaction with system $S'$, that value is actualized strictly relative to $S'$ ³⁴. To a third, non-interacting system $S''$, the variable remains indefinite, and the composite system of $S$ and $S'$ is described as being in an entangled superposition ¹⁴⁹. Because physical variables lack values at intermediate times between interactions, the ontology of RQM is considered "sparse" ³⁶¹². Reality is modeled as an evolving network of punctual relative values actualized at discrete interaction nodes ⁶¹².

Naturalization of the Observer

Historically, the founders of quantum mechanics utilized the concept of the "observer" heavily, which led to persistent misunderstandings that human consciousness, subjectivity, or biological agency plays a functional role in collapsing the quantum wave function ⁵¹⁵¹⁶. RQM decisively severs the link between the observer and consciousness, offering a fully naturalized account of observation ³⁴⁶.

In the relational framework, the terms "observer" and "observed" are strictly interchangeable labels applied to any arbitrary physical system ¹⁴. An electron interacting with a photon constitutes an observation just as validly as a human physicist looking at a digital readout ¹¹¹. Every physical interaction is a "measurement" that produces definite values relative to the interacting systems ¹¹¹¹¹. By democratizing the role of the observer to encompass any physical system, RQM eliminates the need for a mystical boundary between the quantum and classical worlds, avoiding the dualism that plagues orthodox interpretations ³⁴¹¹.

Rejection of the Universal Wave Function

Because RQM defines a quantum state strictly as the relative correlation between two distinct physical systems, the theory conceptually forbids the possibility of an external, overarching observer ¹. Consequently, there is no meaning in speaking of the "state" of the entire universe ¹.

To assign a state to the universe would require ascribing a correlation between the universe and some other physical observer outside of it, which is a logical impossibility since any physical observer must, by definition, form part of the universe ¹. In RQM, the universal wave function plays no role, and the theory is constructed entirely from the localized, relative perspectives of interacting subsystems ³.

Comparative Analysis of Quantum Interpretations

To fully comprehend the nuances of Relational Quantum Mechanics, it is necessary to contrast it with the other dominant interpretations of quantum formalism. Each interpretation chooses a different conceptual sacrifice to resolve the measurement problem ⁸¹¹.

Orthodox Copenhagen and Consistent Histories

RQM is frequently described as a "democratized" completion of the standard textbook Copenhagen interpretation ³⁴¹¹. The orthodox Copenhagen view successfully utilizes the mathematical formalism but relies on a "shifty split" (the Heisenberg cut) between the quantum system being measured and the classical, macroscopic measuring apparatus doing the observation ¹¹¹⁵¹³. RQM accepts the Copenhagen premise that properties are realized in measurement, but rejects the necessity of a unique classical domain ⁴¹¹.

When compared to the Consistent Histories approach, RQM shares similarities in its rejection of a single objective narrative. Consistent Histories posits that there are "consistent" sets of events to which classical probabilities can be assigned, but these values are framework-dependent ¹¹⁸. Rovelli explicitly noted the compatibility between RQM and Consistent Histories, pointing out that RQM takes the framework-dependence of Consistent Histories to its logical conclusion: different observers do not have to agree on a single consistent history, as facts are strictly relational ¹⁸.

Everettian Many-Worlds and De Broglie-Bohm

Both RQM and the Many-Worlds Interpretation (MWI) are deeply rooted in the work of Hugh Everett III, specifically his "relative state" formulation published in 1957 ³⁶¹⁴. Both frameworks attempt to solve the measurement problem by introducing indexicality - the idea that properties are relative ⁴⁶¹¹. However, their ontological commitments are diametrically opposed.

MWI reifies the universal wave function, proposing that every possible outcome of a quantum interaction branches into a physically real, parallel universe, resulting in massive ontological inflation ³⁶¹⁵. RQM avoids this bloat. In RQM, there is only one world, but the facts within it are relative to the subsystems interacting within it; the wave function is merely a tracking tool, not a multiverse generator ³¹⁸.

Conversely, De Broglie-Bohm pilot-wave theory introduces hidden variables to restore classical realism and determinism ³⁶¹⁶. It posits that particles possess absolute, well-defined positions at all times, guided by an invisible, non-local pilot wave ¹⁶¹⁴¹⁶. RQM strictly forbids hidden variables, maintaining that quantum mechanics is a complete theory, and denies the existence of absolute, unmeasured properties ¹⁹¹⁷.

Quantum Bayesianism (QBism)

Quantum Bayesianism shares significant conceptual overlap with RQM, as both propose that reality is shaped relative to observers and treat the wave function as an epistemic tool for calculating probabilities rather than an objective feature of reality ³⁶¹⁶¹⁸.

The divergence lies primarily in their definition of the observer and the nature of information. QBism restricts the role of the observer to a "rational decision-making agent" capable of holding subjective beliefs and updating those beliefs upon experiencing an empirical outcome ⁶⁸¹⁸. In QBism, the probabilities are personal and subjective ⁸¹⁶. RQM rejects this anthropocentric and epistemic restriction. In RQM, information is Shannon correlation between arbitrary physical systems - no rational agency, cognition, or subjective belief is required ³⁶⁸.

Empirical Tests and Quantum Paradoxes

Because different interpretations of quantum mechanics share the same underlying mathematical formalism, they generally yield identical empirical predictions, making experimental differentiation notoriously difficult ²²⁴. However, recent theoretical breakthroughs and advancements in quantum technology have allowed physicists to operationalize historical thought experiments, placing severe pressure on interpretations that rely on absolute macroscopic facts.

The Wigner's Friend Scenario

The necessity of relational facts is best illustrated by the "Wigner's Friend" thought experiment, originally formulated by Eugene Wigner in 1961 to highlight the contradictions inherent in absolute wave function collapse ¹⁹²⁰²¹.

In this scenario, Wigner places his Friend inside an isolated laboratory. The Friend measures a quantum system, such as a photon in a superposition of horizontal and vertical polarization ²¹²⁸. According to standard quantum mechanics, the Friend observes a definite outcome. Relative to the Friend, the wave function has collapsed, and a definite fact has been established ¹²¹²⁸.

However, Wigner stands outside the isolated laboratory. Because Wigner has not yet interacted with the laboratory interior, standard quantum mechanics dictates that he must describe the entire laboratory - the photon, the measuring apparatus, and the Friend - as evolving unitarily in a massive, entangled superposition ²¹²⁸²². Wigner can theoretically perform a complex interference measurement on the entire laboratory to prove that the superposition still exists ²⁰²¹²².

If quantum facts are absolute, a logical contradiction arises: a single event cannot be both definitively realized (to the Friend) and in an indeterminate superposition (to Wigner). RQM resolves this paradox seamlessly by abandoning the requirement for absolute facts. The photon is polarized relative to the Friend, and the laboratory is in a superposition relative to Wigner. Both observers provide accurate, complete accounts of reality from their respective physical standpoints ¹¹⁶¹⁹.

The 2019 Six-Photon Experiment

For decades, Wigner's Friend remained a purely theoretical construct. However, in 2019, Massimiliano Proietti and colleagues at Heriot-Watt University successfully instantiated an extended Wigner's Friend scenario in a physical laboratory setting using state-of-the-art quantum photonics ¹⁹²²²³.

The researchers utilized a complex setup involving pairs of entangled photons from a source ($S_0$) distributed to simulated "Friends" who performed local measurements using entangled sources ($S_A, S_B$) and type-I fusion gates ²¹²². The measurement records were heralded using superconducting nanowire single-photon detectors (SNSPD) ²². From the "inside" perspective, the Friends registered definite facts ²¹²⁴. The external "Wigners" (Alice and Bob) then performed non-classical interference measurements on the total photon systems using 50/50 beam splitters ²¹²².

By analyzing the measurement records, Proietti et al. demonstrated a violation of a Bell-type (Clauser-Horne-Shimony) inequality by five standard deviations ²³²⁵. This massive statistical violation proved that the realities experienced by the Friends (who saw definite outcomes) and the Wigners (who observed unbroken entanglement) were simultaneously verifiable yet fundamentally irreconcilable in any absolute sense ¹⁹²⁰²². The study concluded that, assuming standard principles of locality and free choice hold, the scientific community must accept that quantum theory is intrinsically observer-dependent ²⁸²³²⁵. This empirical finding offers profound indirect support for the sparse ontology proposed by Relational Quantum Mechanics ²⁵.

The Frauchiger-Renner Theorem

Theoretical support for the relational perspective was further bolstered by the Frauchiger-Renner theorem, published in 2018. Daniela Frauchiger and Renato Renner constructed a complex, nested version of the Wigner's Friend paradox ¹⁶³³²⁶. The thought experiment forces observers, who are modeled as quantum systems themselves, to use quantum mechanics to reason about the knowledge and observations of other observers within the system ³³²⁶.

Frauchiger and Renner proved that if one assumes that quantum mechanics is universally applicable to all systems, that observers can consistently rely on the observations of other agents, and that measurement outcomes represent absolute, single facts about the world, a logical contradiction inevitably occurs ³³²⁶²⁷. The agents arrive at mutually exclusive certainties regarding the outcome of an experiment ³³²⁸.

To resolve the paradox, at least one of the core assumptions must be abandoned. While some physicists use the Frauchiger-Renner theorem to argue for physical collapse theories, proponents of RQM point to it as a mathematical proof that the existence of absolute, observer-independent macroscopic facts is a false premise ¹²¹⁶²⁶. The paradox dissolves entirely within the RQM framework, as facts are valid only relative to the specific agent observing them, forbidding the absolute logical chaining of incompatible relative facts ¹²¹⁶. Recent literature has also expanded this via the GHZ-Mermin scenario, highlighting the logical contextuality at the heart of the paradox ²⁶.

The Intersubjectivity Problem and Solipsism

Despite its logical elegance in resolving measurement paradoxes, RQM's radical denial of absolute facts invites severe philosophical and physical scrutiny. If the physical state of a system - and indeed, the occurrence of physical events themselves - is relative only to the observer involved in the interaction, RQM teeters precariously close to epistemic solipsism ⁶¹¹¹⁶.

Critiques of Absolute Relativity

In 2021, physicists Jacques Pienaar and Časlav Brukner published rigorous critiques of RQM ⁷²⁹³⁰. Pienaar formulated a series of "no-go" theorems aimed at the internal consistency of RQM, arguing that the relationality in RQM is far more extreme than the relationality in Einstein's relativity ⁷³¹.

In relativity, observers moving at different velocities will disagree on the duration of an event or the distance between objects, but they perfectly agree on the absolute existence of the spacetime events themselves. In early formulations of RQM, however, the facts themselves are relative. Pienaar demonstrated that, based on RQM's original axioms, observers have no absolute method for comparing their perspectives ⁷³¹. If Alice makes a measurement and Bob measures Alice to ask what she saw, they are merely establishing a new relative correlation between Bob and Alice, potentially trapping observers within their own inaccessible, subjective informational bubbles ⁷¹¹⁴⁰. This lack of intersubjective agreement threatens the foundational methodology of empirical science itself ³².

The Cross-Perspective Link Postulate

Recognizing that a physical theory must permit scientists to compare data and reach intersubjective agreement, philosopher Emily Adlam and Carlo Rovelli proposed a formal addendum to the theory in 2022 and 2023: the Postulate of Cross-Perspective Links (CPL) ⁶⁴⁰³².

The CPL postulate explicitly bridges the gap between isolated relative facts. It states that if an observer Alice measures a variable of a system $S$ and stores that information in her physical variables, then if a second observer Bob subsequently measures Alice's physical variables to ascertain her information, Bob's measurement result will reliably match Alice's original measurement result (provided the information was not destroyed by decoherence) ⁴⁰³².

This postulate acts as a guarantee of communicability ⁶¹⁶. It ensures that while information is generated relationally in an isolated interaction, that information is encoded physically in the observer and can be faithfully accessed by third parties ¹⁶⁴⁰. The CPL allows RQM to construct a stable, shared macroscopic reality out of a substrate of quantum interactions, satisfying the requirement for scientific objectivity without invoking an overarching absolute wave function ⁴⁰³².

Contemporary Debates and Theoretical Schisms

While the Cross-Perspective Link was designed to save RQM from solipsism, it triggered intense contemporary debate regarding the internal consistency of the theory, resulting in a schism within the RQM literature up through 2025 and 2026.

The Hidden Variable Contradiction

A fierce critique of the CPL postulate was leveled by physicists Jay Lawrence, Marcin Markiewicz, and Marek Żukowski between 2023 and 2025 ¹⁷³³⁴³. They analyzed the CPL within the context of the Wigner's Friend paradox. If Bob (Wigner) measures Alice (the Friend) and is guaranteed by the CPL to receive an outcome matching Alice's earlier internal measurement, then Alice's relative fact is causally dictating Bob's subsequent measurement outcome ¹⁷.

Lawrence et al. demonstrated that within the standard quantum formalism, Bob is measuring an entangled superposition. For Bob's outcome to be predetermined by Alice's internal relative fact, Alice's fact must be acting as a hidden variable ¹⁷³³. However, Rovelli's original axioms for RQM expressly forbid hidden variables, positing that standard quantum mechanics is fundamentally complete ¹¹⁷. Lawrence and colleagues argue that merging the CPL with the quantum formalism results in an "internally inconsistent hidden variable theory," concluding that RQM, modified by the CPL, can no longer be considered a valid interpretation of quantum mechanics ¹⁷³³⁴³.

Orthodox Relationalism Versus Modified Frameworks

The mathematical friction introduced by the CPL has led to a proposed bifurcation of the relational framework in recent literature ⁴⁴³⁴. In 2025 and 2026, Emily Adlam articulated a distinction between "Orthodox RQM" (abbreviated as RRQM) and the modified Adlam-Rovelli RQM (ARQM*) ³⁴³⁵.

Orthodox RRQM adheres strictly to the radical relationalism of the original 1996 proposal: all physical facts are infinitely relativized to physical systems, ensuring complete compliance with the standard quantum formalism at the cost of persistent vulnerability to the solipsism critique ⁴⁴³⁴³⁵.

Conversely, ARQM accepts the CPL and concedes that to guarantee intersubjective agreement, the theory must postulate the existence of some absolute, non-relational facts ⁴⁴³⁴. Specifically, the quantum events (the actualization of outcomes between an observer and a system) are treated as absolute, observer-independent occurrences that anchor reality, even though the quantum states used to predict them remain relational ⁴⁰⁴⁴³⁵. Because these absolute facts cannot be derived purely from the standard quantum formalism, ARQM explicitly surrenders the assumption that quantum mechanics is a complete theory of nature, proposing instead that the absolute aspects of reality lie outside the current mathematical framework ³⁴.

Relational Quantum Dynamics

The ongoing refinement of relational theories has also spawned broader interpretations, such as Relational Quantum Dynamics (RQD), proposed in 2025 ³⁶. RQD builds upon the core tenets of RQM but explicitly integrates the emergence of spacetime and the role of highly integrated informational systems ³⁶. RQD proposes five interlocking principles, treating time and space not as external parameters, but as emergent structures constructed from patterns of quantum entanglement and relational information exchange ³⁶. RQD explicitly addresses the Frauchiger-Renner paradox and Bell's theorem by replacing absolute facts with context-dependent truths, attempting to unify quantum mechanics and emergent macroscopic physics within a single informational web ³⁶.

Philosophical and Cosmological Implications

The evolution of Relational Quantum Mechanics carries implications that extend far beyond the measurement problem, influencing the philosophy of science and the search for a unified theory of physics.

Ontic Structural Realism

Philosophically, RQM aligns seamlessly with Ontic Structural Realism (OSR), a framework championed by philosophers such as Steven French and James Ladyman, and applied extensively to RQM by Laura Candiotto ¹²¹⁶³⁶. Traditional Western metaphysics, tracing back to Parmenides, privileges "substance" or "entities" with intrinsic properties, treating the relations between those entities as secondary ³⁷.

OSR and RQM invert this hierarchy. In RQM, the relations are the fundamental constituents of reality; the "objects" (relata) emerge solely as nodes in a network of interactions ⁹¹²³⁷. There is no "thing-in-itself" sitting in isolation possessing mass, spin, or position; these properties are irreducible two-place relations between systems ³⁷. The world is an interconnected informational web, making RQM a structurally realistic but non-substantive ontology ⁹³⁶.

Spatiotemporal Emergence and Quantum Gravity

Carlo Rovelli's primary domain of research is Loop Quantum Gravity (LQG), and RQM was initially conceived with quantum gravity as a remote motivation ³⁶. In classical general relativity, spacetime is a dynamic, continuous field. In efforts to quantize gravity, spacetime itself must be subjected to quantum rules.

RQM provides an ideal conceptual substrate for quantum gravity. If physical systems do not possess absolute states in space and time, but rather realize sparse properties relative to one another during interactions, then spacetime itself is not a pre-existing stage. Instead, spacetime geometry emerges from the network of quantum correlations ⁹¹²³⁶. In an RQM-compatible quantum gravity framework, a physical process does not occur in a spacetime region; the relational process is the spacetime region ¹². Spatiotemporal relationalism and quantum mechanical relationalism merge, suggesting that time and space are macroscopic manifestations of an underlying structure of discrete, relative quantum informational exchanges ⁹¹²³⁶. Furthermore, recent analyses of RQM in the context of higher-dimensional Quantum Field Theory (QFT) suggest that relational interpretations inherently require a Wilsonian approach, where physical descriptions are fundamentally tied to the specific measuring scale of the observer ³⁸.