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arXiv:2107.13937 · Physical Review A

Causal reappraisal of the quantum three-box paradox

Paweł Błasiak, Ewa Borsuk

Published Jan 10, 2022• 2 citations
arXivHTMLPDF

Abstract

The quantum three-box paradox is a prototypical example of some bizarre predictions for intermediate measurements made on pre- and postselected systems. Although in principle those effects can be explained by measurement disturbance, it is not clear what mechanisms are required to fully account for the observed correlations. In this paper, this paradox is scrutinized from the causal point of view. We consider an array of potential causal structures behind the experiment, eliminating those without enough explanatory power. A distinction is made between the propagation in the system of just the measurement outcome and the information about the full measurement context. We also discuss the consequences of the realist position in which preexisting values are revealed by measurements. Interestingly, the answers depend crucially on whether the original version of the paradox is considered or its extension where the third box is allowed for inspection too. This illustrates the richness of the paradox which is better appreciated from the causal perspective.

DOI
10.1103/physreva.105.012207

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The quantum three-box paradox is a prototypical example of some bizarre predictions for intermediate measurements made on pre- and postselected systems. Although in principle those effects can be explained by measurement disturbance, it is not clear what mechanisms are required to fully account for the observed correlations. In this paper, this paradox is scrutinized from the causal point of view. We consider an array of potential causal structures behind the experiment, eliminating those without enough explanatory power. A distinction is made between the propagation in the system of just the measurement outcome and the information about the full measurement context. We also discuss the consequences of the realist position in which preexisting values are revealed by measurements. Interestingly, the answers depend crucially on whether the original version of the paradox is considered or its extension where the third box is allowed for inspection too. This illustrates the richness of the paradox which is better appreciated from the causal perspective.
Quantum mechanics describes the relation between different measurement contexts in terms of superpositions of the potential measurement outcomes. This relation between measurement contexts makes it impossible to determine context independent realities. Here, I illustrate the problem using three path interferences that implement the three box paradox and show that the representation of the final measurement outcome as a superposition of intermediate paths describes well-defined coherences between seemingly empty paths.
Many quantum paradoxes based on a realistic view of weak values were discussed in the last decades. They lead to astonishing conclusions such as the measurement of a spin component of a spin-1/2 particle resulting in $100\ensuremath{\hbar}$, the separation of a photon from its polarization, and the possibility of having three particles in two boxes without any two particles being in the same box, among others. Here, we show that the realistic view of the weak values present in these (and other) works is equivalent to a realistic (and highly controversial) view of quantum measurements, where a measurement reveals the underlying reality of the measured quantity. We discuss that all quantum paradoxes based on weak values simply disappear if we deny these realistic views of quantum measurements and weak values. Our work thus aims to demonstrate the strong assumptions and the corresponding problems present in the interpretation of these quantum paradoxes.
Quantum measurement is widely regarded as paradoxical due to the apparent role of observers, wave function collapse, and mutually inconsistent descriptions of reality. We argue that these paradoxes are not intrinsic to quantum mechanics, but arise from a category error: treating observer-dependent inferences as observer-independent physical facts.We introduce a causality-first framework in which quantum states represent open causal structures, and measurement corresponds to a scale-dependent transition to causal closure. No privileged observer, stochastic collapse mechanism, or many-worlds ontology is required. Within this framework, celebrated paradoxes such as Wigner’s Friend and the Frauchiger–Renner no-go theorem dissolve, as their contradictions rely on an implicit violation of causal consistency.Our proposal does not modify quantum dynamics nor introduce new postulates. Instead, it clarifies when quantum processes may enter causal chains. The result is a realist, observer-independent account of measurement that preserves standard quantum theory while eliminating its most persistent conceptual pathologies.
Abstract This paper proposes a novel framework that reinterprets the observer in quantum mechanics as a physical system governed by causal integration principles. By modeling the observer as an active participant in the measurement process—rather than a passive external entity—we show that quantum collapse can emerge as a natural consequence of the observer’s internal causal structure and information processing constraints. This framework avoids the ad-hoc postulates of standard quantum theory and provides a consistent, ontologically grounded account of measurement. Crucial experimental tests are proposed to validate the predictions of this model, including modified double-slit experiments and precision measurements of quantum correlations. These experiments aim to distinguish between the predictions of our causal integration model and those of conventional quantum mechanics, thereby opening new avenues for experimental investigation into the foundations of quantum theory.
The quantum three-box paradox considers a ball prepared in a superposition of being in any one of three boxes. Bob makes measurements by opening either box 1 or box 2. After performing some unitary operations (shuffling), Alice can infer with certainty that the ball was detected by Bob, regardless of which box he opened, if she detects the ball after opening box 3. The paradox is that the ball would have been found with certainty by Bob in either box if that box had been opened. Resolutions of the paradox include that Bob’s measurement cannot be made non-invasively or else that realism cannot be assumed at the quantum level. Here, we strengthen the case for the former argument by constructing macroscopic versions of the paradox. Macroscopic realism implies that the ball is in one of the boxes prior to Bob or Alice opening any boxes. We demonstrate the consistency of the paradox with macroscopic realism, if carefully defined (as weak macroscopic realism, wMR) to apply to the system at the times prior to Alice or Bob opening any boxes but after the unitary operations associated with preparation or shuffling. By solving for the dynamics of the unitary operations and comparing with mixed states, we demonstrate agreement between the predictions of wMR and quantum mechanics: the paradox only manifests if Alice’s shuffling combines both local operations (on box 3) and nonlocal operations, on the other boxes. Following previous work, the macroscopic paradox is shown to correspond to a violation of a Leggett–Garg inequality, which implies failure of non-invasive measurability if wMR holds.
Quantum mechanics predicts experimental outcomes with extraordinary precision, yet its conceptual foundations remain unsettled. Persistent paradoxes—superposition, tunneling, nonlocal correlations, and measurement—suggest not a failure of the theory, but a mismatch between physical processes and the dimensional limits of observation. This work proposes that many quantum paradoxes arise from dimensional projection errors: systematic misinterpretations that occur when observers confined to three spatial dimensions attempt to describe processes involving higher-dimensional structure. By treating quantum probabilities as consequences of observer limitation rather than intrinsic randomness, the framework restores determinism without altering any established predictions of quantum mechanics. The result is not a replacement of quantum theory, but a coherent reinterpretation that dissolves paradoxes into perspective effects. In this restricted yet profound sense, Einstein was right again.