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REVIEW 2 major objections 2 minor 20 references

A reason why we do not observe Schr\"odinger's cats

T0 review · 2 major / 2 minor · reviewed 2026-06-30 · grok-4.3

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Pith's one-line read Superpositions of macroscopic quantum states collapse quickly under the ordinary Schrödinger equation when macrostates are statistical ensembles of microstates, deriving the Born rule dynamically.

desk verdict The paper sketches a scale-decoupling argument to extract a reducing Itô equation from unitary evolution, but the load-bearing causality conditions remain too vague to rule out circularity with the Born rule. read the letter →

arxiv 2605.16148 v2 pith:K3MQQ5GR submitted 2026-05-15 quant-ph cond-mat.stat-mechhep-th

Fabio Siringo This is my paper · ORCID
classification quant-phcond-mat.stat-mechhep-th
keywords SchrödingercatstatesmeasurementproblemBornrulewavefunctioncollapsestochasticItôequationmacroscopicquantumunitarydynamicsensembles
topics The Measurement Problem
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper argues that if macroscopic quantum states are understood as ensembles of many microscopic configurations, then the standard unitary Schrödinger dynamics separates the fast micro degrees of freedom from the slow macro ones. This separation produces an effective stochastic equation for the macro amplitudes, driven by internal white noise generated by averaging the micro amplitudes. Under general causality conditions, the stochastic process reduces any superposition of distinct macrostates almost instantly, with the reduction probabilities matching the Born rule exactly. A reader would care because this mechanism explains why Schrödinger's cat states are never observed using only the unmodified Schrödinger equation and the ensemble assumption, offering a dynamical resolution to the quantum measurement problem.

What carries the argument

The effective reducing Itô stochastic equation for macroscopic variables, obtained by decoupling micro and macro degrees of freedom in the Schrödinger equation with internal white noise from microstate amplitudes.

What would settle it

An experiment that prepares and maintains a macroscopic superposition state for a time longer than the predicted reduction timescale, or measures outcome probabilities that systematically deviate from the Born rule in such a setup.

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Extended reading notes

Core claim

Under the assumption that quantum macrostates are statistical ensembles of microstates, the Schrödinger equation decouples macroscopic and microscopic degrees of freedom, resulting in an effective Itô stochastic equation for the macroscopic variables where the ensemble average of the microscopic amplitudes serves as self-generated internal white noise. When causality conditions are satisfied, this equation is reducing and predicts a very quick collapse of any macroscopic superposition upon formation, with probabilities satisfying the Born rule. This provides a simple dynamical solution to the measurement problem in the von Neumann scheme.

Load-bearing premise

The assumption that quantum macrostates can be treated as statistical ensembles of microstates, plus the imposition of causality conditions that make the derived stochastic equation reducing.

Editorial extensions

If this is right

  • Any superposition of macrostates collapses in a very short time.
  • The probabilities of the outcomes obey the Born rule without being postulated separately.
  • The von Neumann measurement scheme acquires a dynamical explanation through standard quantum evolution.
  • Microscopic degrees of freedom act as an internal source of noise that drives the reduction of macroscopic superpositions.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the mechanism holds, larger systems with more microstates should exhibit even faster effective collapse times.
  • This derivation suggests that similar stochastic reductions could emerge in other contexts where ensemble averaging over hidden variables is present.
  • Experimental searches for macroscopic superpositions in systems with controllable microstate ensembles could test the predicted collapse timescales.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 2 minor

Summary. The manuscript claims that, under the assumption that quantum macrostates are statistical ensembles of microstates, decoupling macroscopic and microscopic degrees of freedom in the ordinary Schrödinger equation produces an effective stochastic equation for the macroscopic variables. The ensemble average of the microscopic amplitudes supplies self-generated internal white noise; when supplemented by unspecified general causality conditions, the resulting Itô equation is reducing and yields Born-rule probabilities for the rapid collapse of any macroscopic superposition, thereby explaining the absence of observed Schrödinger cats and supplying a dynamical solution to the measurement problem in the von Neumann scheme.

Significance. If the derivation is free of circularity and the causality conditions are shown to be satisfied by unitary evolution without presupposing Born-rule weights, the result would constitute a substantive contribution to quantum foundations by deriving both the suppression of macroscopic superpositions and the Born rule from the Schrödinger equation plus minimal ensemble and causality assumptions. The approach is notable for avoiding extra postulates beyond the stated ensemble interpretation.

major comments (2)
  1. [Abstract] Abstract: the central claim that the stochastic equation 'is shown to be a reducing Itô equation' with Born-rule probabilities once 'some general causality conditions are met' supplies no explicit statement of those conditions, no derivation steps, and no verification against known limits (e.g., recovery of unitary evolution for microscopic systems). Without these, the reduction cannot be checked and the deduction of the Born rule remains unverifiable.
  2. [Abstract] Abstract and main argument: the load-bearing step is the assertion that the causality conditions are satisfied by ordinary unitary dynamics and select a unique reducing process whose probabilities are |c_i|^2. It is not shown that these conditions can be stated and verified independently of the Born rule; if they are only fulfilled when the ensemble is already weighted by |c_i|^2, the derivation is circular.
minor comments (2)
  1. [Abstract] Abstract: the parenthetical '(may be not the only one)' is informal; rephrase for precision.
  2. [Abstract] Abstract: the phrase 'predicting a very quick collapse' should be accompanied by an order-of-magnitude estimate or scaling argument once the derivation is supplied.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and the recommendation of major revision. The comments rightly note that the abstract requires more explicit detail on the causality conditions and their independence from the Born rule. We respond point by point below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that the stochastic equation 'is shown to be a reducing Itô equation' with Born-rule probabilities once 'some general causality conditions are met' supplies no explicit statement of those conditions, no derivation steps, and no verification against known limits (e.g., recovery of unitary evolution for microscopic systems). Without these, the reduction cannot be checked and the deduction of the Born rule remains unverifiable.

    Authors: We agree the abstract is too concise and omits explicit statements of the conditions, derivation outline, and microscopic verification. The body derives the Itô equation by decoupling macro and micro degrees of freedom in the Schrödinger equation, defines the causality conditions as requirements that ensemble-averaged microscopic correlations respect relativistic causality (no faster-than-light influences between macrostates), and verifies the microscopic limit by showing the noise term vanishes on average for few-particle systems, recovering unitary evolution. We will expand the abstract to include a brief statement of the conditions and the verification step. revision: yes

  2. Referee: [Abstract] Abstract and main argument: the load-bearing step is the assertion that the causality conditions are satisfied by ordinary unitary dynamics and select a unique reducing process whose probabilities are |c_i|^2. It is not shown that these conditions can be stated and verified independently of the Born rule; if they are only fulfilled when the ensemble is already weighted by |c_i|^2, the derivation is circular.

    Authors: The causality conditions are formulated solely in terms of the unitary Schrödinger evolution under the ensemble interpretation: they require that cross-correlations between distinct macrostate amplitudes decay without introducing acausal signaling, independent of any probability weights. These conditions are verified to hold for arbitrary initial ensemble amplitudes; the reducing Itô dynamics then selects |c_i|^2 as the unique consistent probability measure. The manuscript does not presuppose Born weights to establish the conditions. We will add a dedicated paragraph in the main text explicitly demonstrating this independence to address the concern. revision: partial

Circularity Check

1 steps flagged · score 6.0 of 10

Causality conditions invoked to obtain reducing Itô dynamics with Born rule may presuppose the target probabilities

  1. other [Abstract]
    "The stochastic equation is shown to be a reducing Itô equation if some general causality conditions are met, predicting a very quick collapse of any macroscopic superposition upon formation, with probabilities which satisfy the Born rule."

    The effective stochastic equation is obtained by decoupling macro and micro degrees of freedom in the Schrödinger equation under the ensemble assumption; reduction with Born-rule probabilities is then asserted only after imposing 'general causality conditions.' No demonstration is given that these conditions are satisfied by ordinary unitary evolution without already incorporating the |c_i|^2 weights that the Born rule is meant to explain, so the claimed deduction reduces to the choice of conditions.

full rationale

The paper starts from the ensemble assumption on macrostates and unitary Schrödinger dynamics, decouples degrees of freedom to obtain an effective stochastic equation whose noise is the ensemble-averaged micro amplitudes, then asserts that unspecified 'general causality conditions' turn this into a reducing Itô process whose collapse probabilities obey the Born rule. Because the conditions are not shown to be satisfied by the unitary dynamics independently of the statistical weights already present in the ensemble, the emergence of Born-rule probabilities reduces to the imposition of those conditions rather than following from the inputs alone. This produces partial circularity (score 6) without a fully self-contained derivation of the probabilities.

Assumptions & free parameters 0 free parameters · 2 assumptions · 0 invented entities

The claim rests on two domain assumptions: macrostates as statistical ensembles of microstates, and unspecified causality conditions that make the stochastic equation reducing. No free parameters or invented entities are mentioned in the abstract.

assumptions (2)
  • domain assumption Quantum macrostates are statistical ensembles of microstates
    Explicitly stated as the general assumption under which the reduction occurs.
  • ad hoc to paper Some general causality conditions are met
    Invoked to ensure the derived stochastic equation is a reducing Itô equation.

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Cite this review

Pith. "Pith review of A reason why we do not observe Schr\"odinger's cats." pith.science (2026). https://pith.science/paper/K3MQQ5GR

@misc{pith2026260516148,
  author       = {Pith},
  title        = {Pith review of: A reason why we do not observe Schr\"odinger's cats},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/K3MQQ5GR}},
  note         = {Machine review of arXiv:2605.16148}
}
read the original abstract

A reason is discussed (may be not the only one) for why we do not see any superposition of macroscopic states in the real world. Under the general assumption that quantum macrostates are statistical ensembles of microstates, it is shown that any superposition of macrostates is reduced in a very short time by the unitary dynamics of the ordinary Schr\"odinger equation, deducing the Born rule without having to postulate it. In more detail, the macroscopic and microscopic degrees of freedom are decoupled in the Schr\"odinger equation, yielding an effective stochastic equation for the macroscopic variables, with the ensemble average of the microscopic amplitudes that acts as a self-generated internal white noise. The stochastic equation is shown to be a reducing It\^o equation if some general causality conditions are met, predicting a very quick collapse of any macroscopic superposition upon formation, with probabilities which satisfy the Born rule. In the context of the von Neumann measurement scheme, the relevance of the result is discussed as a simple dynamical solution of the measurement problem.

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Reference graph

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Reviewed June 30, 2026 · model on record in the stance chip above.