⚛️ quantum physics

The Reference System Loophole

The paper argues that Extended Wigner's Friend theorems, including the Local Friendliness theorem, contain an overlooked "loophole" arising from the necessity of reference systems to define measurement outcomes, which allows for the preservation of both quantum mechanical predictions and Local Friendliness without contradiction.

Original author: Emily Adlam

Published 2026-11-03

📖 6 min read🧠 Deep dive

CC BY 4.0

Original author: Emily Adlam

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the author. For technical accuracy, refer to the original paper. Read full disclaimer

In the strange world of quantum mechanics, particles can exist in multiple states at once, a phenomenon known as superposition. This is not just a theoretical quirk; it is a fundamental rule that governs how the universe works at its smallest scales. However, a long-standing puzzle arises when we ask what happens when a person, or an observer, looks at these particles. Standard quantum theory suggests that the act of measurement forces the particle to choose a single state. But what if that observer is themselves inside a sealed room, observed by someone else outside? This is the heart of the "Wigner's Friend" thought experiment, a scenario that has challenged physicists for decades. It asks whether a measurement outcome is a single, absolute fact for everyone, or if it can be different depending on who is looking. Recent work has extended this idea into rigorous mathematical proofs, known as "no-go theorems," which suggest that if quantum mechanics is universally correct, then at least one of our most basic assumptions about reality—such as the idea that events happen absolutely or that information cannot travel faster than light—must be false. These theorems have forced scientists to choose between abandoning the idea that observed events are absolute or accepting that quantum mechanics breaks down in complex situations.

A new paper by Emily Adlam proposes a different path, one that avoids these difficult choices by introducing a subtle but crucial distinction often overlooked in these experiments. The author argues that the paradoxes arise because we assume the result an observer sees inside a lab is the same thing an outside observer measures. Adlam suggests that to truly understand what is happening, we must recognize that a measurement outcome is not a standalone fact; it is a relationship that depends on a reference system. Just as a direction like "up" only makes sense if you know what "up" is relative to, a measurement result only has meaning when tied to a specific frame of reference. In the context of these experiments, the paper suggests that the "result" the friend sees inside the lab and the "result" the outside observer measures are actually two different variables. The friend sees a definite outcome relative to their own internal equipment, while the outside observer measures a relationship between the friend's equipment and their own.

The core of Adlam's argument is that these two perspectives do not have to be identical to preserve the laws of physics. In the standard version of the experiment, the outside observer performs a special type of measurement that checks the entire state of the friend's lab without disturbing it. This measurement reveals that the friend and the particle are in a superposition, a state where they are effectively in two places or states at once. The paradox occurs because we try to force the friend's definite internal experience to match the outside observer's superposition. Adlam shows that if we accept that the friend's internal experience is a fact relative to their own lab, but the outside observer's measurement is a fact relative to the outside lab, the contradiction disappears. The outside observer can still see the quantum superposition and the strange correlations it produces, while the friend inside still experiences a single, clear result. The two descriptions are not fighting each other; they are simply describing different relationships.

This approach relies on the idea that certain properties, like the orientation of a laboratory, are not absolute facts but are relative. When the friend measures a particle, their entire laboratory, including their measuring devices, becomes entangled with the particle. From the outside, the lab is in a superposition of different orientations. However, inside the lab, the friend always sees a single, definite orientation because their experience is tied to their own internal frame. The paper demonstrates that this distinction allows the predictions of quantum mechanics to remain correct for the outside observer, who sees the expected quantum correlations, without forcing the friend to have a vague or undefined experience. The friend always knows what they saw, and the outside observer always sees the quantum weirdness, but they are not describing the same single variable.

The author addresses several potential objections to this idea, particularly regarding how the two observers could end up with different orientations in the first place. One might wonder how a sealed lab could suddenly lose its alignment with the outside world. The paper argues that this is a natural consequence of the extreme isolation required for the outside observer to perform their special measurement. To keep the lab in a quantum superposition, it must be completely cut off from the outside world, including any gravitational or physical signals that would normally keep it aligned. In this isolated state, the act of measurement inside the lab causes the lab's orientation to become indefinite relative to the outside, even though it remains definite for the person inside. This is not a violation of physical laws but a feature of how quantum systems behave when they are perfectly isolated.

Furthermore, the paper explores whether this solution works for other types of measurements, not just those involving spin or direction. The author argues that it does, because almost any physical quantity we measure is actually a relationship that requires a reference. Even something as simple as the distance between two objects or the time on a clock is not an absolute fact but a value relative to a standard. The paper suggests that because all our measurements are essentially comparisons to a reference system, the loophole applies universally. Whether we are measuring the position of a particle or the state of a complex machine, the result is always a relationship between the system and the observer's frame. This means the solution is not limited to a specific type of experiment but is a fundamental feature of how observation works in a quantum universe.

The significance of this work lies in what it preserves. By accepting that measurement outcomes are relative to a reference system, the paper allows us to keep the idea that events are absolute for the person experiencing them, while also keeping the idea that information cannot travel faster than light and that quantum mechanics works everywhere. It avoids the need to say that reality is fundamentally unstable or that our memories and communications are unreliable. Instead, it offers a way to understand the universe where both the inside and outside perspectives are valid, but they are describing different aspects of the same physical situation. This approach does not claim to have solved every mystery of quantum mechanics, but it provides a coherent way to resolve a specific, long-standing paradox without giving up on the core principles of science. It suggests that the confusion in these experiments comes not from a failure of physics, but from a failure to properly account for the role of the reference frame in defining what a measurement actually is.

Technical Summary: The Reference System Loophole in Extended Wigner's Friend Theorems

Problem Statement
The paper addresses the "Local Friendliness" (LF) no-go theorem (Bong et al., 2020), which demonstrates a contradiction between the predictions of unitary quantum mechanics and a set of plausible assumptions collectively termed "Local Friendliness." These assumptions include:

Absoluteness of Observed Events: Measurement outcomes are absolute, single events not relative to any observer.
Locality: Measurement outcomes on one side do not depend on the choice of measurement settings on the other side (parameter independence).
No-Superdeterminism: The choice of measurement settings is independent of the hidden variables determining the outcomes.

The theorem posits that if quantum mechanics is universally correct, these assumptions cannot all hold simultaneously. Standard responses often involve denying the "absoluteness of observed events," a move the author argues is epistemologically problematic as it implies instability in memory and communication. The paper identifies a previously unappreciated "loophole" in the derivation of the LF inequalities: the implicit assumption that the variable describing an observer's internal measurement outcome is identical to the variable describing that outcome relative to an external reference frame.

Methodology and Theoretical Framework
The author proposes a resolution based on the distinction between two types of variables in the context of the Bong et al. experiment (involving observers Alice, Chidi, Bob, and Divya):

$A_I$ (Internal Outcome): The value Alice observes relative to her own internal reference system (e.g., "spin parallel to my axis").
$A_E$ (External Outcome): The value of the spin relative to Bob's external reference system (e.g., "spin parallel to Bob's axis").

The core argument relies on the symmetry properties of physical variables. The author posits that variables associated with symmetry transformations (such as spatial orientation under rotation) are not absolute facts but must be relativized to a reference system.

State Description: When Alice measures a spin, she obtains a definite outcome ( $A_I$ ). However, relative to Bob, the combined system of Alice and the particle evolves unitarily into a superposition where Alice's laboratory (and thus her reference axis) is entangled with the spin. In this superposition, $A_I$ is definite in both branches, but the orientation of Alice's axis relative to Bob ( $R_{AB}$ ) is indefinite.
Variable Definition: The external outcome is defined as $A_E = A_I \times R_{AB}$ . Because $R_{AB}$ is indefinite (or stochastic) relative to Bob until a specific measurement is performed, $A_E$ does not have a well-defined value on every run of the experiment where Bob performs a "supermeasurement" (which erases $A_I$ 's record).

The author utilizes the partial/complete observables formalism (Rovelli, 2002) to generalize this. "Partial observables" (quantities like spin direction or position) vary under symmetry transformations and require a reference system. "Complete observables" (relational facts) are invariant and definite. The author argues that measurement outcomes ( $A_I$ ) correspond to complete observables (definite facts for the observer), while the variables used to test quantum correlations ( $A_E$ ) are partial observables that require relativization.

Key Contributions and Results

Identification of the Loophole: The paper demonstrates that the LF inequalities are derived by assuming a single probability distribution exists over four variables ( $A, B, C, D$ ) that simultaneously satisfies quantum predictions. The author shows that if $A$ and $C$ are interpreted as internal outcomes ( $A_I, C_I$ ), they are absolute, but the quantum predictions (which rely on correlations between entangled spins) apply to the external outcomes ( $A_E, C_E$ ). Since $A_E$ depends on the stochastic variable $R_{AB}$ , there is no single joint probability distribution over $A_I, B, C_I, D$ that is required to match the quantum predictions for $A_E, B, C_E, D$ .
Preservation of Assumptions: By distinguishing $A_I$ $A_{I}$ from $A_E$ $A_{E}$ , the author shows that one can maintain:
- Absoluteness of Observed Events: Alice always sees a definite outcome ( $A_I$ ).
- Locality and No-Superdeterminism: The correlations between $A_I$ and other variables do not need to satisfy the specific quantum constraints that lead to the contradiction, because the quantum constraints apply to $A_E$ .
- Unitary Quantum Mechanics: Bob can still observe interference and standard quantum correlations for the variables $A_E$ and $C_E$ because the superposition of Alice's orientation relative to Bob is preserved.
Toy Model: A simple model is presented where $A_I$ and $C_I$ are generated as random, uncorrelated variables. The external outcomes ( $A_E, C_E$ ) are then generated to match quantum predictions by adjusting the reference relation variables ( $R_{AB}, R_{CD}$ ). This model satisfies Local Friendliness while reproducing quantum statistics for the observed pairs.
Generalization to Other Variables: The author argues this loophole is not limited to spin. Using the partial/complete observables framework, it is argued that any variable Alice can measure is a "partial observable" subject to symmetry transformations (including time translations and diffeomorphisms). However, the author explicitly notes that a version of the Bong et al. experiment performed using a superposition of distinct conscious states could not be resolved by the reference system loophole. The author suggests that since such superpositions have not been demonstrated, and if conscious experiences supervene on complete observables (which cannot be directly measured), the loophole remains applicable to all physically realizable versions of the experiment.

Response to Objections

Distinct Measurements: The paper argues that Bob cannot measure both the supermeasurement outcome ( $B$ ) and the reference orientation ( $R_{AB}$ ) simultaneously. Measuring $R_{AB}$ (e.g., by checking if the lab flipped) would decohere the superposition required for $B$ . Thus, $A_E$ and $B$ are never simultaneously well-defined, preventing the derivation of the LF inequalities.
Conservation Laws: The apparent "jump" in Alice's orientation relative to Bob does not violate conservation of angular momentum or energy because these laws hold within a single reference frame. The transition from a superposition of orientations to a definite orientation is a quantum measurement event, not a classical physical trajectory requiring energy input.
Quantum Reference Frames (QRF): The author clarifies that this proposal is distinct from existing QRF formalisms. Standard QRF assumes a well-defined transformation between frames, whereas this loophole relies on the indefiniteness of the relation between frames during the experiment, a scenario not fully modeled by current QRF approaches which do not account for single definite outcomes.

Significance and Claims
The paper claims that the "Reference System Loophole" offers a way to resolve the EWF paradoxes without sacrificing the absoluteness of observed events, locality, or the universality of quantum mechanics (in a first-person sense).

Epistemological Advantage: It avoids the "unattractive" implications of denying absoluteness of events (e.g., memory instability), offering a more conservative resolution that preserves standard scientific epistemology.
Theoretical Integration: The approach naturally integrates concepts from symmetry, reference frames, and general relativity (diffeomorphism invariance) into the measurement problem. It suggests that only "partial observables" (symmetry-variant quantities) are subject to quantum superposition, while "complete observables" (invariant facts) remain definite.
Scope: The author asserts that this loophole works for any EWF experiment involving measurable variables that are partial observables, with the specific exception of experiments involving superpositions of distinct conscious states, which the loophole cannot resolve.

The paper concludes that this approach provides a principled, physically motivated alternative to denying the absoluteness of events, suggesting that the contradiction in EWF theorems arises from a category error in conflating internal measurement outcomes with external relational variables.

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