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arxiv: 2607.00198 · v1 · pith:FUP55CM2new · submitted 2026-06-30 · 🪐 quant-ph

Wavefunctions localization, and the Wigner's Friend Paradox in a Framework of Discrete-Space Hypothesis

W. A. Z\'u\~niga-Galindo This is my paper

Pith reviewed 2026-07-02 18:29 UTC · model grok-4.3

classification 🪐 quant-ph
keywords Wigner's Friend paradoxp-adic numberswavefunction collapsediscrete spacequantum mechanicsnon-local Hamiltoniansrealism
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The pith

Wavefunction localization in p-adic space resolves the Wigner's Friend paradox by giving independent definite readings to both parties.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper embeds quantum mechanics in the hybrid space R × Q_p, treating p-adic numbers as a model of discrete microscopic space. In this setting the Schrödinger equation with non-local Hamiltonians causes wavefunctions to localize onto compact supports during measurement, turning collapse into a dynamical process that produces definite pointer readings. Both Wigner and his Friend are modeled as classical apparatuses that each trigger this localization independently, removing any conflict between their accounts of reality. The approach stays consistent with existing no-go theorems because it introduces no reasoning agents capable of recording outcomes.

Core claim

Within the framework of quantum mechanics on L2(R × Q_p), wavefunction collapse is a dynamical consequence of the Schrödinger equation, leading to localization on compact supports. Modeling both Wigner and his Friend as classical apparatuses results in each producing a definite reading through independent applications of this mechanism, thereby eliminating the paradox. The framework upholds the absoluteness of observed events without requiring observer independence.

What carries the argument

Wavefunction localization onto compact supports in L2(R × Q_p) induced by non-local Hamiltonians during measurement interactions.

If this is right

  • Each classical apparatus produces a definite pointer reading independently.
  • No information exchange between subsystems is required for collapse.
  • The framework is consistent with no-go theorems from extended Wigner's Friend scenarios.
  • The absoluteness of observed events holds without observer independence.
  • Realism is permitted at the cost of locality due to intrinsic non-locality.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If localization occurs dynamically, similar mechanisms might address other measurement problems in quantum mechanics without extra postulates.
  • Discrete-space models at small scales could be explored for consistency with other quantum paradoxes.
  • Numerical simulations of the toy model could check whether localization always produces unique pointer states.

Load-bearing premise

The Schrödinger equation with non-local Hamiltonians on the hybrid space produces wavefunction localization onto compact supports as a dynamical consequence of measurement interactions.

What would settle it

An explicit calculation for the toy model of a particle in a box showing that wavefunctions do not localize onto compact supports under the non-local Hamiltonian would falsify the dynamical collapse claim.

read the original abstract

We present a resolution of the Wigner's Friend paradox within a framework of quantum mechanics (QM) on the hybrid space RxQ_{p}, where Q_{p} denotes the field of p-adic numbers, regarded as a model of discrete microscopic space at the Planck-Bronstein scale. In this framework, wavefunction collapse is not an independent postulate but a dynamical consequence of the Schr\"odinger equation with non-local Hamiltonians: wavefunctions localize onto compact supports during measurement interactions, producing definite pointer readings without the intervention of observers or the exchange of information between subsystems. We model both Wigner and his Friend as classical apparatuses and show that each produces a definite reading through independent applications of the collapse mechanism, thereby eliminating the conflict between their descriptions of reality. The framework is consistent with the principal no-go theorems in finite- and infinite-dimensional Hilbert spaces associated with extended Wigner's Friend scenarios -- including those of Frauchiger-Renner, Brukner, Bong et al., and Gu\'erin et al. -- since it requires no agents capable of recording or reasoning about outcomes, thereby vacating the observer-dependent assumptions that drive those theorems. We illustrate the collapse mechanism explicitly through a toy model of a particle in a box, comparing the standard description with the new one. The non-locality intrinsic to QM on L2(RxQ_{p}) permits realism at the cost of locality, and the Absoluteness of Observed Events holds in our framework without requiring observer independence.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims to resolve the Wigner's Friend paradox in a framework of QM on the hybrid space ℝ × ℚ_p (with ℚ_p modeling discrete space at the Planck-Bronstein scale). It asserts that wavefunction collapse emerges dynamically from the Schrödinger equation with non-local Hamiltonians, causing localization onto compact supports during measurement interactions and yielding definite pointer readings for classical apparatuses without observer intervention or information exchange. Both Wigner and his Friend are modeled as classical apparatuses obtaining independent definite readings, eliminating the paradox; the framework is stated to be consistent with no-go theorems (Frauchiger-Renner, Brukner, Bong et al., Guérin et al.) because it requires no agents capable of recording or reasoning about outcomes. A toy model of a particle in a box is used to illustrate the mechanism, and the approach is said to permit realism at the cost of locality while preserving the Absoluteness of Observed Events.

Significance. If the dynamical localization mechanism were rigorously derived as a general consequence of the non-local Hamiltonian on L²(ℝ × ℚ_p) for measurement interactions, the framework would offer a concrete way to obtain definite outcomes from unitary evolution alone, thereby addressing observer-dependent paradoxes while remaining consistent with no-go results by eliminating the need for reasoning agents. The approach would also provide an explicit trade-off between realism and locality in a hybrid continuous-p-adic space, with potential implications for foundational questions in quantum mechanics.

major comments (2)
  1. [Abstract] Abstract (and the framework description): the central claim that 'wavefunction collapse is not an independent postulate but a dynamical consequence of the Schrödinger equation with non-local Hamiltonians' and that 'wavefunctions localize onto compact supports during measurement interactions' is asserted without an explicit general derivation or theorem establishing that localization occurs for the relevant class of interactions and initial states on L²(ℝ × ℚ_p). The toy model is cited as illustration but does not supply the required general mechanism; without this derivation the independent collapse for each apparatus (and thus the resolution of the paradox) does not follow from the stated dynamics.
  2. [Abstract] The modeling of Wigner and Friend as classical apparatuses that each produce definite readings 'through independent applications of the collapse mechanism' rests on the unshown dynamical localization; if the localization does not follow automatically, the claimed elimination of conflict between their descriptions cannot be established.
minor comments (2)
  1. [Abstract] The abstract states consistency with no-go theorems because the framework 'requires no agents capable of recording or reasoning about outcomes'; this should be cross-referenced to the specific assumptions of each cited theorem (Frauchiger-Renner, etc.) to make the vacating of observer-dependent assumptions explicit.
  2. [Abstract] Notation for the hybrid space (RxQ_p) and the Hilbert space L2(RxQ_p) should be standardized throughout; the p-adic component is introduced as a model of discrete space but its precise embedding into the measurement interaction Hamiltonians is not detailed in the provided abstract.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments. Below we respond point by point to the major comments.

read point-by-point responses

  1. Referee: [Abstract] Abstract (and the framework description): the central claim that 'wavefunction collapse is not an independent postulate but a dynamical consequence of the Schrödinger equation with non-local Hamiltonians' and that 'wavefunctions localize onto compact supports during measurement interactions' is asserted without an explicit general derivation or theorem establishing that localization occurs for the relevant class of interactions and initial states on L²(ℝ × ℚ_p). The toy model is cited as illustration but does not supply the required general mechanism; without this derivation the independent collapse for each apparatus (and thus the resolution of the paradox) does not follow from the stated dynamics.

    Authors: The localization follows from the non-local structure of the Hamiltonian on L²(ℝ × ℚ_p), where the p-adic factor restricts the support during interactions; the toy model of the particle in a box supplies an explicit instance of this dynamics for a representative measurement interaction. The manuscript does not contain a theorem covering every possible interaction and initial state on the hybrid space. We will revise the abstract and framework description to state more precisely that the mechanism is demonstrated for the class of interactions relevant to the apparatuses considered, rather than asserted as fully general. revision: partial

  2. Referee: [Abstract] The modeling of Wigner and Friend as classical apparatuses that each produce definite readings 'through independent applications of the collapse mechanism' rests on the unshown dynamical localization; if the localization does not follow automatically, the claimed elimination of conflict between their descriptions cannot be established.

    Authors: Each apparatus is treated as a classical system whose interaction with the quantum particle is governed by the same non-local Hamiltonian. Because the localization is a direct consequence of that Hamiltonian acting on the hybrid space, the two apparatuses undergo independent localizations and obtain independent definite readings. No additional postulate or information exchange is required; the conflict is thereby removed within the framework. revision: no

Circularity Check

1 steps flagged

Localization and collapse presented as dynamical consequence but built into non-local Hamiltonian framework by construction

specific steps
  1. self definitional [Abstract]
    "In this framework, wavefunction collapse is not an independent postulate but a dynamical consequence of the Schrödinger equation with non-local Hamiltonians: wavefunctions localize onto compact supports during measurement interactions, producing definite pointer readings without the intervention of observers or the exchange of information between subsystems. We model both Wigner and his Friend as classical apparatuses and show that each produces a definite reading through independent applications of the collapse mechanism, thereby eliminating the conflict between their descriptions of reality."

    The hybrid-space framework is introduced with non-local Hamiltonians on L²(ℝ × ℚ_p) chosen to produce localization onto compact supports. The claimed resolution (independent definite readings eliminating the paradox) then follows immediately from this built-in dynamical feature, making the 'consequence' equivalent to the framework definition rather than a derived result from the Schrödinger equation alone.

full rationale

The paper's central resolution rests on wavefunction localization to compact supports occurring automatically from the Schrödinger equation on L²(ℝ × ℚ_p) with non-local Hamiltonians, allowing independent definite readings for Wigner and Friend without extra postulates. This is asserted in the abstract as following directly from the dynamics. However, the framework itself is defined via choice of those non-local Hamiltonians precisely to induce compact-support localization during measurements (as illustrated only by a toy model). The independent collapse outcomes therefore reduce to a property of the model definition rather than an independent derivation, producing partial circularity in the load-bearing step. No general theorem equating arbitrary interactions to localization is quoted, but the toy model and consistency claims provide some independent content, preventing a higher score.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The central claim rests on the physical relevance of the hybrid space and the dynamical localization property; these are introduced without independent empirical support.

free parameters (1)
  • prime p
    Choice of prime defining the p-adic field Q_p is required to set the discrete-space model.
axioms (2)
  • domain assumption The Schrödinger equation with non-local Hamiltonians on L2(R x Q_p) produces localization onto compact supports as a dynamical consequence of measurement interactions
    This is the load-bearing assumption that replaces the usual collapse postulate.
  • ad hoc to paper Space at the Planck-Bronstein scale is modeled by the hybrid R x Q_p
    Postulated to justify discreteness without further derivation.
invented entities (1)
  • hybrid space R x Q_p no independent evidence
    purpose: Model of discrete microscopic space enabling non-local dynamics and localization
    New postulated structure introduced to support the collapse mechanism; no independent evidence supplied.

pith-pipeline@v0.9.1-grok · 5809 in / 1668 out tokens · 33405 ms · 2026-07-02T18:29:13.929343+00:00 · methodology

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Reference graph

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