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Limits of Absoluteness of Observed Events in Timelike Scenarios: A No-Go Theorem

Sumit Mukherjee, Jonte R. Hance

TL;DR

The paper advances Wigner’s Friend-type reasoning by formulating a timelike, time-ordered analogue called the Causal Friendliness Paradox, where locality is replaced by Axiological Time Symmetry (ATS) and Absoluteness of Observed Events (AOE) is studied under No Retrocausality (NRC) and Screening via Pseudo Events (SPE). It proves a CHSH-type no-go inequality under these assumptions and shows quantum mechanics violates it, implying at least one assumption must be abandoned. The authors then develop a weaker, operational form of AOE via Existence of Marginals (EOM) and Operational Mediation (OM)/OPEM, demonstrating that quantum violations persist even without a full joint distribution, though discarding Absoluteness of Pseudo Events (APE) undermines the no-go by allowing algebraic maximal correlations. Overall, the work reinforces the non-classical nature of observed events in timelike quantum scenarios, clarifies the role of pseudo-events, and suggests avenues for further foundational and experimental exploration of Wigner’s Friend-inspired paradoxes. The analysis blends formal no-go theorems with operational relaxations, highlighting the robustness of quantum violations against classical notions of absolute events in time-ordered settings, and offering a path to testable predictions in causal, nonlocal quantum foundations.

Abstract

Wigner's Friend-type paradoxes challenge the assumption that events are absolute -- that when we measure a system, we obtain a single result, which is not relative to anything or anyone else. These paradoxes highlight the tension between quantum theory and our intuitions about reality being observer-independent. Building on a recent result that developed these paradoxes into a no-go theorem, namely the Local Friendliness Theorem, we introduce the Causal Friendliness Paradox, a time-ordered analogue of it. In this framework, we replace the usual locality assumption with Axiological Time Symmetry (ATS), and show that, when combined with the assumptions of Absoluteness of Observed Events (AOE), No Retrocausality (NRC), and Screening via Pseudo Events (SPE), we obtain a causal inequality. We then show that quantum mechanics violates this inequality and is therefore incompatible with at least one of these assumptions. To probe which assumption might be incompatible, we then examine whether AOE in its entirety is essential for this no-go result. We propose a weaker, operational form of AOE that still leads to inequalities that quantum mechanics violates. This result shows that even under relaxed assumptions, quantum theory resists reconciliation with classical notions of absolute events, reinforcing the foundational significance of Wigner's Friend-type paradoxes in timelike scenarios.

Limits of Absoluteness of Observed Events in Timelike Scenarios: A No-Go Theorem

TL;DR

The paper advances Wigner’s Friend-type reasoning by formulating a timelike, time-ordered analogue called the Causal Friendliness Paradox, where locality is replaced by Axiological Time Symmetry (ATS) and Absoluteness of Observed Events (AOE) is studied under No Retrocausality (NRC) and Screening via Pseudo Events (SPE). It proves a CHSH-type no-go inequality under these assumptions and shows quantum mechanics violates it, implying at least one assumption must be abandoned. The authors then develop a weaker, operational form of AOE via Existence of Marginals (EOM) and Operational Mediation (OM)/OPEM, demonstrating that quantum violations persist even without a full joint distribution, though discarding Absoluteness of Pseudo Events (APE) undermines the no-go by allowing algebraic maximal correlations. Overall, the work reinforces the non-classical nature of observed events in timelike quantum scenarios, clarifies the role of pseudo-events, and suggests avenues for further foundational and experimental exploration of Wigner’s Friend-inspired paradoxes. The analysis blends formal no-go theorems with operational relaxations, highlighting the robustness of quantum violations against classical notions of absolute events in time-ordered settings, and offering a path to testable predictions in causal, nonlocal quantum foundations.

Abstract

Wigner's Friend-type paradoxes challenge the assumption that events are absolute -- that when we measure a system, we obtain a single result, which is not relative to anything or anyone else. These paradoxes highlight the tension between quantum theory and our intuitions about reality being observer-independent. Building on a recent result that developed these paradoxes into a no-go theorem, namely the Local Friendliness Theorem, we introduce the Causal Friendliness Paradox, a time-ordered analogue of it. In this framework, we replace the usual locality assumption with Axiological Time Symmetry (ATS), and show that, when combined with the assumptions of Absoluteness of Observed Events (AOE), No Retrocausality (NRC), and Screening via Pseudo Events (SPE), we obtain a causal inequality. We then show that quantum mechanics violates this inequality and is therefore incompatible with at least one of these assumptions. To probe which assumption might be incompatible, we then examine whether AOE in its entirety is essential for this no-go result. We propose a weaker, operational form of AOE that still leads to inequalities that quantum mechanics violates. This result shows that even under relaxed assumptions, quantum theory resists reconciliation with classical notions of absolute events, reinforcing the foundational significance of Wigner's Friend-type paradoxes in timelike scenarios.

Paper Structure

This paper contains 16 sections, 4 theorems, 48 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Wigner's Friend Scenarios and their implications
  3. The Wigner's Friend paradox
  4. Extended Wigner Friend Scenarios
  5. Causal Friendliness Paradox
  6. The Causal Friendliness Scenario
  7. The Causal Friendliness No-Go Theorem
  8. Proof of the Causal Friendliness No-Go Theorem
  9. Role of Pseudo Events in the Causal Friendliness Paradox
  10. Replacing psi-ontic reproducibility with lambda-mediation
  11. Can we weaken the AOE assumption?
  12. Impossibility of discarding the Absoluteness of Pseudo Events
  13. Discussions and outlook
  14. Comparing to Related Results
  15. Implications of the findings for interpretational issues
  16. ...and 1 more sections

Key Result

Theorem 1

Consider the scenario we give in Section Subsect:NewScenario, with Charlie and Alice acting before Debbie and Bob. Let $a,b,c,d\in\{\pm1\}$ denote the outcomes of Alice, Bob, Charlie, and Debbie, respectively, and let $x,y\in\{0,1\}$ denote the measurement settings of Alice and Bob. Assume: Given these Assumptions, the observed correlations satisfy the inequality: where $\langle A_{x} B_{y} \ran

Figures (3)

  • Figure 1: The extended Wigner's Friend Scenario for the Local Friendliness no-go theorem.
  • Figure 2: Time-ordered measurement scenario for Causal Friendliness no-go theorem.
  • Figure 3: Causal influence diagram for the Causal Friendliness scenario. The rectangular entities are those that are in direct control of the observer, while the circles represents events that are not in direct control. The arrows represents the order of the events conveying the cause-effect relationships between the events. Red coloured shapes indicate the Pseudo Events while the blue one are Truly-Observed Events.

Theorems & Definitions (11)

  • Definition 1: Operational Time Symmetry
  • Theorem 1: Causal Friendliness No-Go Theorem
  • Lemma 1
  • proof
  • Lemma 2: (Alice(Bob) cannot depend on Bob's(Alice's) choice of measurement beyond $c,d$
  • proof
  • Theorem 2: Operational Pseudo Event Mediation (OPEM)
  • proof
  • Definition 2: Existence of Joint Probability Distributions (EJPD)
  • Definition 3: Absoluteness of Truly-Observed Events (ATOE)
  • ...and 1 more