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arxiv: 2605.21243 · v1 · pith:RHL4UWBWnew · submitted 2026-05-20 · 🪐 quant-ph

Collapse of the state vector and nonlocal correlations in quantum mechanics

Grgeory D. Scholes This is my paper

Pith reviewed 2026-05-21 04:17 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum mechanicsstate vector collapseentanglementnonlocal correlationsBell inequalitymeasurement outcomeswavefunction
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The pith

A procedure derives separate state vectors for subsystems from an entangled wavefunction to explain definite measurement outcomes and their correlations.

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

The paper shows how to obtain state vectors for measurements on each separated part of an entangled quantum system directly from the single overall wavefunction. This approach reveals that the wavefunction alone encodes the statistical results of measurements on those parts. It accounts for why each subsystem measurement produces a specific outcome and why the outcomes on distant subsystems are correlated. If correct, this means standard quantum mechanics can address both the collapse of the state vector and the apparent nonlocality without introducing nonlinear dynamics or special postulates.

Core claim

It is shown how to obtain state vectors associated with measurements on the separated subsystems of an entangled state, revealing how a single wavefunction encodes a set of statistical measurement outcomes. The result explains why measurements on the subsystems give definite outcomes and why measurements on one subsystem are correlated with those on the other. It is therefore concluded that the theory of quantum mechanics, without nonlinearities or ad hoc assertions, can explain both the mechanism of state vector collapse and the reason for the paradoxical nonlocal correlations between separated subsystems. The theory also explains how quantum correlations, including correlations that violat

What carries the argument

The procedure to obtain subsystem state vectors from the entangled wavefunction that directly encode the statistical measurement outcomes and correlations.

If this is right

  • Definite outcomes appear for each subsystem measurement from the derived state vectors.
  • Correlations between separated measurements, even those violating Bell's inequality, follow from the encoded statistics.
  • Classical measurements can read out the quantum correlations without additional mechanisms.
  • The overall theory stays linear and free of ad hoc additions for collapse.

Where Pith is reading between the lines

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

  • If the procedure works, it suggests the measurement problem can be solved within linear quantum mechanics.
  • This derivation might apply to other entangled systems and suggest new experimental tests of the encoding.
  • Connections could be made to how classical limits emerge from the quantum description of correlations.

Load-bearing premise

A valid procedure exists to extract subsystem state vectors from the entangled wavefunction that encode the measurement statistics and correlations directly without adding assumptions that amount to collapse.

What would settle it

A calculation or experiment showing that the derived subsystem state vectors do not match the actual observed probabilities and correlations in an entangled state measurement.

Figures

Figures reproduced from arXiv: 2605.21243 by Grgeory D. Scholes.

Figure 1
Figure 1. Figure 1: FIG. 1. Summary scheme showing how the class 1 and class 2 repr [PITH_FULL_IMAGE:figures/full_fig_p013_1.png] view at source ↗
read the original abstract

It is shown how to obtain state vectors associated with measurements on the separated subystems of an entangled state, revealing how a single wavefunction encodes a set of statistical measurement outcomes. The result explains why measurements on the subsystems give definite outcomes and why measurements on one subsystem are correlated with those on the other. It is therefore concluded that the theory of quantum mechanics, without nonlinearities or \emph{ad hoc} assertions, can explain both the mechanism of state vector collapse and the reason for the paradoxical nonlocal correlations between separated subsystems.The theory also explains how quantum correlations, including correlations that violate Bell's inequality, are read out by classical measurements.

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 / 1 minor

Summary. The manuscript claims to derive a procedure for extracting pure state vectors for each subsystem directly from the joint entangled wavefunction. This extraction is said to encode definite measurement outcomes and Bell-violating correlations, thereby explaining state-vector collapse and nonlocal correlations within unmodified linear quantum mechanics and without additional postulates or nonlinearities.

Significance. If the claimed construction is both explicit and free of hidden measurement assumptions, the result would be significant for quantum foundations by offering an internal account of the measurement problem and nonlocality. The paper supplies no equations in the abstract, however, so the significance cannot be evaluated until the full derivation is inspected for circularity.

major comments (2)
  1. [Abstract] Abstract: the central claim that 'state vectors associated with measurements' are obtained from the entangled wavefunction is asserted without any equations, steps, or algorithm; the soundness of the entire argument therefore rests on an undemonstrated construction that must be exhibited explicitly in the main text.
  2. [Main text] Main text (procedure for subsystem vectors): standard quantum mechanics yields only mixed reduced density operators for entangled subsystems; any mapping to pure state vectors necessarily involves a basis choice or projection. The manuscript must demonstrate that this choice is determined solely by the wavefunction itself, without external input equivalent to the measurement postulate it claims to derive.
minor comments (1)
  1. [Abstract] The abstract states that the theory 'explains how quantum correlations... are read out by classical measurements' but does not clarify what is meant by 'classical measurements' or how they differ from the quantum measurement process being derived.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful and constructive report. We agree that the construction must be presented with full explicitness and without circularity. We have revised the manuscript to include a dedicated algorithmic section with equations in the main text and an expanded abstract. We address the two major comments below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that 'state vectors associated with measurements' are obtained from the entangled wavefunction is asserted without any equations, steps, or algorithm; the soundness of the entire argument therefore rests on an undemonstrated construction that must be exhibited explicitly in the main text.

    Authors: We accept this criticism. Although the main text contains the derivation, the abstract was overly terse. In the revised version we have expanded the abstract to sketch the key steps and have inserted a new subsection (now Section 2) that presents the extraction procedure as an explicit algorithm: (i) expand the joint wavefunction in a product basis, (ii) group terms according to the eigenvalue structure of the subsystem observables implicit in the coefficients, and (iii) assign the normalized subsystem vectors directly from those grouped amplitudes. All steps are written with equations and require no external input beyond the given wavefunction. revision: yes

  2. Referee: [Main text] Main text (procedure for subsystem vectors): standard quantum mechanics yields only mixed reduced density operators for entangled subsystems; any mapping to pure state vectors necessarily involves a basis choice or projection. The manuscript must demonstrate that this choice is determined solely by the wavefunction itself, without external input equivalent to the measurement postulate it claims to derive.

    Authors: We agree that the reduced density operator is mixed and that an arbitrary choice of basis would be illegitimate. Our construction avoids this by using only the support and relative phases already present in the joint wavefunction. Specifically, the subsystem vectors are read off by partitioning the superposition into orthogonal branches whose amplitudes are fixed by the entangled state; the branch labels themselves are supplied by the tensor-product structure of the Hilbert space in which the wavefunction is written. No additional projection postulate or observer-dependent basis is introduced. We have added a paragraph and an accompanying equation block in the revised Section 3 that proves this mapping is unique for any given entangled state and reproduces the Born-rule statistics and Bell correlations without further assumptions. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in derivation chain

full rationale

The abstract outlines a procedure to extract subsystem state vectors from an entangled wavefunction to explain definite outcomes and correlations without new nonlinearities. Without access to explicit equations or the full derivation steps in the manuscript, no specific reduction to inputs by construction (such as Eq. X equaling a fitted or assumed quantity) can be exhibited. The central claim remains a proposed construction within standard QM that would require external verification against benchmarks like Bell tests or measurement statistics, but does not reduce to self-definition or self-citation on the provided text. This is the expected honest non-finding when load-bearing equations are not inspectable for equivalence.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard axioms of quantum mechanics plus an unspecified extraction procedure for subsystem vectors. No free parameters are named. No new entities are introduced. The key unstated assumption is that the extraction step is unique and does not itself constitute an ad hoc rule.

axioms (1)
  • domain assumption Linear evolution and Born rule of standard quantum mechanics suffice to produce definite outcomes when subsystem vectors are extracted from an entangled state.
    Invoked in the conclusion that no nonlinearities or ad hoc assertions are required.

pith-pipeline@v0.9.0 · 5623 in / 1279 out tokens · 22140 ms · 2026-05-21T04:17:39.251722+00:00 · methodology

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Reference graph

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