Are free choices absolute, when internalized in Wigner's friend?

This paper argues that, within extended Wigner's friend scenarios based on the Pusey–Barrett–Rudolph theorem, the absoluteness of free choices cannot be maintained under a specific notion of locality, mirroring recent challenges to the absoluteness of observed outcomes.

The Gist

The Big Question: Are Your Choices "Real" to Everyone?

Imagine you are in a locked room making a decision—say, flipping a coin to decide between pizza or tacos. To you, the moment you flip the coin, the choice is made. It's a solid, real fact.

But what if someone outside the room (let's call them the "Super-Observer") could describe your entire room, including you and the coin, as a giant, swirling cloud of possibilities? In this quantum world, the Super-Observer might say, "You haven't actually chosen yet; you are in a superposition of both choosing pizza and choosing tacos."

This is the heart of the famous "Wigner's Friend" thought experiment. For a long time, physicists have argued about whether the person inside the room (the Friend) has a single, absolute reality, or if the reality depends on who is looking at it.

The New Twist: What About Free Will?

This paper, written by Laurens Walleghem, asks a new, tricky question: If we accept that the "Friend's" reality might be relative (depending on who looks), does that also mean their free choices are relative?

Usually, we think of "free choice" as something absolute. If I choose to wear a red shirt, that choice happened. It's a fact. But this paper argues that in the quantum world, if we treat the Super-Observer's view as valid, then your free choices might not be absolute facts either. They might be "relative" to the observer.

The Story: The Locked Rooms and the Magic Dice

To prove this, the author sets up a complex game involving four characters: Alice, Bob, Charlie, and Debbie, plus a Super-Observer named Wigner.

1. The Setup: Alice and Bob are in two separate, sealed labs. They are like "Friends" in the original story.
2. The Choice: Inside their labs, Alice and Bob make a "free choice." Let's say they each pick a number: 0 or 1.
   • Analogy: Imagine they each roll a magic die. To them, the die lands on a specific number.
3. The Message: They encode this number into a tiny quantum particle (a qubit) and send it out of their labs to Charlie and Debbie.
4. The Outside View: Wigner is outside. He can choose to do one of two things:
   • Option A (The "Ask"): He opens the labs and asks Alice and Bob, "What number did you pick?" (This reveals their choice).
   • Option B (The "Magic Scan"): He keeps the labs sealed and performs a special, complex quantum measurement on the entire labs at once. This is like scanning the whole room to see if the "swirling cloud" of possibilities interferes with itself in a specific way.

The Paradox: The Impossible Puzzle

The paper uses a famous logic puzzle called the PBR Theorem (named after Pusey, Barrett, and Rudolph) to show a contradiction.

Here is the logic in plain English:

• Assumption 1 (Absolute Events): We assume that when Alice picks a number, it is a single, absolute fact for everyone.
• Assumption 2 (Local Agency): We assume that Alice's choice is only influenced by things in her past, not by what Charlie or Debbie do far away later.

The Conflict:
The author shows that if you combine these two assumptions with the rules of quantum mechanics, you get a logical impossibility.

1. If Wigner chooses to "Ask" (Option A), he confirms that Alice picked a specific number (e.g., 0).
2. If Wigner chooses to "Scan" (Option B), the math of quantum mechanics says that if Alice had picked 0, a certain outcome is impossible (probability is zero).
3. However, because of the way the game is set up, Charlie and Debbie (who are far away) can perform measurements that prove Alice must have picked 0 in a way that makes Wigner's "Scan" outcome possible.

The Result:
You end up with a situation where:

• Alice definitely picked 0.
• But if she picked 0, the Super-Observer's special scan cannot happen.
• Yet, the scan does happen.

This is a contradiction. It's like saying, "I definitely ordered a pizza," but "If I ordered a pizza, the pizza delivery truck could not possibly exist," while simultaneously seeing the truck arrive.

The Conclusion: Choices Are Relative

Since the math of quantum mechanics is solid, one of our assumptions must be wrong. The paper argues that the assumption that needs to go is the absoluteness of free choices.

The Takeaway:
If you accept that a Super-Observer can describe a person in a lab as a quantum wave, you have to accept that the person's "free choice" isn't a single, absolute fact for the whole universe.

• To Alice, she made a choice.
• To Wigner (the Super-Observer), Alice's choice is part of a larger, entangled wave that hasn't "collapsed" into a single fact yet.

The paper suggests that free choices might be "relational." Just as a shadow looks different depending on where the light is, a "choice" might look different depending on who is observing it. It doesn't mean free will doesn't exist, but it means it might not be the absolute, universal fact we think it is.

Summary in a Metaphor

Imagine you write a secret note in a locked diary.

• To you: The note is written. It's a fact.
• To a magician outside: The diary is still a "cloud of possibilities" containing every possible note you could have written.

This paper argues that if the magician's view is valid, then your act of writing the note wasn't an absolute event for the whole universe. The "choice" to write the note is relative to who is looking at the diary. If you try to force the idea that your choice is absolute for everyone, the laws of physics break down.

Technical Summary

Technical Summary: "Are free choices absolute, when internalized in Wigner's friend?"

Problem Statement
The paper addresses a foundational challenge in quantum theory regarding the measurement problem and the consistency of reasoning between different observers. Specifically, it investigates the "Local Friendliness" (LF) no-go theorem, which establishes a contradiction under two assumptions: the Absoluteness of Observed Events (AOE) (outcomes are absolute, single-valued events) and Local Agency (free choices/interventions are only correlated with events in their future lightcone). While recent extended Wigner's friend (EWF) arguments have used these assumptions to challenge the absoluteness of measurement outcomes, this work asks whether the same logic applies to free choices themselves. The central question is: If a superobserver (Wigner) models an observer's (Friend's) "free choice" unitarily within a sealed lab, can that choice be considered an absolute, single-valued event independent of the superobserver's perspective?

Methodology
The authors construct an extended Wigner's friend scenario that integrates the Pusey–Barrett–Rudolph (PBR) theorem with the LF framework. The protocol involves:

1. Agents: Two friends (Alice and Bob) in sealed labs, a superobserver (Wigner), and two external observers (Charlie and Debbie).
2. Initial Setup: Alice and Bob each make a "free choice" ($a, b \in \{0, 1\}$). These choices are encoded into qubits ($T_A, T_B$) sent to Charlie and Debbie, while the choice itself is recorded in the state of their respective labs ($L_A, L_B$). The joint state of the labs and qubits is modeled as an entangled superposition (e.g., $|00\rangle + |11\rangle$).
3. External Measurements: Charlie and Debbie measure the received qubits ($T_A, T_B$) in either the computational ($Z$) or Hadamard ($X$) basis, depending on their settings ($x, y$).
4. Superobserver Measurement: Wigner chooses a setting $z$.
   • If $z=0$, Wigner reveals the friends' choices (measuring labs in the computational basis).
   • If $z=1$, Wigner performs a joint entangled measurement on the labs ($L_A \otimes L_B$) in the PBR basis ($\{|\xi_1\rangle, |\xi_2\rangle, |\xi_3\rangle, |\xi_4\rangle\}$), which is incompatible with the basis encoding the friends' choices.
5. Logical Derivation: The authors assume AOE and Local Agency apply to the friends' choices ($a, b$) even when they are not revealed (i.e., when $z=1$). They derive a contradiction by showing that if $a$ and $b$ are absolute, the probabilities of Wigner's outcomes in the PBR measurement must satisfy specific zero-probability constraints that are mutually exclusive with the non-zero probability of the friends' choices being revealed in a compatible context.

Key Contributions

• Extension of LF Arguments: The paper extends the scope of Local Friendliness no-go theorems from the absoluteness of observed outcomes to the absoluteness of free choices.
• Internalization of Free Choice: It introduces a model where a superobserver treats an observer's "free choice" as an internalized quantum variable (a unitary evolution of the lab) rather than an exogenous parameter. This challenges the standard view of free choices as purely external inputs.
• PBR-Based Scenario: Unlike previous EWF arguments relying on Bell nonlocality or contextuality alone, this work utilizes the PBR theorem's logic regarding the reality of quantum states to derive a contradiction specifically regarding the nature of the choice variable.
• Generalization: The argument is generalized to arbitrary choice amplitudes (not just equal probabilities), demonstrating robustness across different initial superposition states.

Results
The authors derive a "no-go theorem" for the absoluteness of free choices under the Local Agency assumption.

• The Contradiction: By applying AOE and Local Agency, the authors show that the joint probability distribution for the friends' choices ($a, b$) and Wigner's PBR outcomes ($w$) must satisfy a set of conditions (Eq. 13) where all possible outcomes for a specific configuration of revealed choices have zero probability.
• The Violation: However, standard quantum mechanics predicts that the scenario where the friends make specific choices and Charlie/Debbie measure in specific bases occurs with non-zero probability (Eq. 15).
• Conclusion: The conjunction of Local Agency and the assumption that free choices are absolute (single-valued events independent of the superobserver) leads to a logical contradiction. Therefore, within this framework, free choices cannot be absolute in the same way measurement outcomes are assumed to be in standard LF arguments.

Significance and Claims
The paper claims that resolutions to extended Wigner's friend paradoxes which reject the absoluteness of outcomes (relational approaches) must also incorporate a relational nature of free choices.

• Reconceptualizing Agency: The work suggests that if one accepts the unitary modeling of observers by superobservers, the concept of "free choice" as an exogenous, absolute variable is incompatible with quantum universality and locality.
• Fine-Tuning Implications: If one wishes to maintain the absoluteness of free choices, the paper implies that such a resolution would require "fine-tuned" choices (in addition to fine-tuned measurement outcomes) to avoid the contradiction.
• Operational Rethinking: The authors do not argue against the existence of free choice but against its absoluteness when internalized in a physical description. They invite a rethinking of how free choices are defined and operationalized in physics, particularly in scenarios involving superobservers.

The paper concludes that similar arguments can be constructed using other nonlocality or contextuality models, but the PBR-based scenario provides a distinct and rigorous pathway to questioning the absoluteness of the agent's input settings.