A reason why we do not observe Schr\"odinger's cats
Pith reviewed 2026-05-20 18:11 UTC · model grok-4.3
The pith
Any superposition of macroscopic states collapses rapidly under the unitary dynamics of the Schrödinger equation, yielding the Born rule without extra postulates.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
Under the assumption that quantum macrostates are statistical ensembles of microstates, the unitary dynamics of the Schrödinger equation reduces any superposition of macrostates in a very short time. Decoupling the macroscopic and microscopic degrees of freedom produces an effective stochastic equation for the macroscopic variables in which the ensemble average of the microscopic amplitudes functions as self-generated internal white noise. When general causality conditions are satisfied, this equation is a reducing Itô equation that predicts rapid collapse with probabilities given by the Born rule. In the von Neumann measurement scheme the same mechanism supplies a dynamical resolution ofhow
What carries the argument
The effective stochastic Itô equation obtained by decoupling macroscopic variables from the ensemble-averaged microscopic amplitudes, which then serve as internal white noise.
If this is right
- Superpositions of macrostates collapse almost immediately after they form.
- The probabilities of the resulting macrostates are exactly those given by the Born rule.
- The measurement problem is solved dynamically inside unmodified quantum mechanics once an apparatus reaches macroscopic scale.
- No external environment or additional collapse postulate is required to explain the absence of observable cats.
Where Pith is reading between the lines
- The collapse timescale should shorten as the number of microscopic degrees of freedom increases, suggesting a possible test in mesoscopic mechanical resonators.
- Systems in which macroscopic and microscopic variables remain strongly coupled might evade the reduction and exhibit observable macroscopic coherence.
- The same internal-noise mechanism could be applied to other contexts where effective stochastic equations emerge from unitary dynamics, such as in open quantum systems.
Load-bearing premise
The macroscopic and microscopic degrees of freedom can be cleanly decoupled inside the Schrödinger equation so that the microscopic amplitudes generate white noise for the macroscopic variables.
What would settle it
An experiment that maintains a coherent superposition of two macroscopically distinguishable states (for example, two distinct positions of a large object) for a time longer than the predicted collapse timescale, or that measures outcome probabilities that deviate from the Born rule in such a system.
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.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper claims that macroscopic quantum states can be treated as statistical ensembles of microstates. Under this assumption, the unitary Schrödinger equation on the joint system, after decoupling macroscopic and microscopic degrees of freedom, produces an effective stochastic equation for the macroscopic variables in which the ensemble-averaged microscopic amplitudes act as self-generated internal white noise. When general causality conditions are satisfied, this stochastic equation becomes a reducing Itô process that collapses any macroscopic superposition on short timescales while yielding Born-rule probabilities, thereby providing a dynamical solution to the measurement problem within the von Neumann scheme without additional postulates.
Significance. If the central derivation can be made rigorous and non-circular, the result would constitute a significant contribution to the foundations of quantum mechanics by deriving both state reduction and the Born rule directly from unitary dynamics plus ensemble averaging and causality, without introducing new free parameters, collapse operators, or ad-hoc entities. The approach is notable for attempting to obtain an exact reducing dynamics rather than mere decoherence from standard quantum evolution.
major comments (2)
- [Abstract] Abstract and derivation sketch: The transition from the deterministic linear Schrödinger equation on the full Hilbert space to an effective reducing Itô stochastic equation for macroscopic variables is asserted via macro-micro decoupling and ensemble averaging of microscopic amplitudes, but no explicit steps, intermediate equations, or verification are supplied showing that this averaging produces genuine reduction (as opposed to decoherence) for a single pure state rather than a pre-mixed ensemble. This step is load-bearing for the central claim that unitary dynamics alone suffices.
- [Abstract] Abstract: The statement that the resulting stochastic equation yields Born-rule probabilities under general causality conditions is not accompanied by an independent derivation or check that the probabilities emerge from the noise term rather than being presupposed by the choice of ensemble averaging; without this, the deduction of the Born rule risks circularity.
minor comments (1)
- [Abstract] The abstract phrasing 'may be not the only one' is informal; a more precise statement of the scope and assumptions would improve clarity.
Simulated Author's Rebuttal
We thank the referee for the careful reading and for recognizing the potential significance of deriving both reduction and the Born rule from unitary dynamics. We address the two major comments point by point below.
read point-by-point responses
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Referee: [Abstract] Abstract and derivation sketch: The transition from the deterministic linear Schrödinger equation on the full Hilbert space to an effective reducing Itô stochastic equation for macroscopic variables is asserted via macro-micro decoupling and ensemble averaging of microscopic amplitudes, but no explicit steps, intermediate equations, or verification are supplied showing that this averaging produces genuine reduction (as opposed to decoherence) for a single pure state rather than a pre-mixed ensemble. This step is load-bearing for the central claim that unitary dynamics alone suffices.
Authors: We agree that the abstract is highly condensed and that the derivation sketch would benefit from more explicit intermediate equations to clarify the transition. The full manuscript (Sections II–IV) derives the decoupling of macroscopic and microscopic degrees of freedom and shows how the ensemble average of microscopic amplitudes generates the white-noise term. To address the concern directly, we will add a new subsection with the key intermediate steps, explicitly demonstrating that the procedure applies to a single pure-state superposition (not a pre-mixed ensemble) and produces genuine reduction via the Itô dynamics rather than decoherence alone. A simple two-macrostate verification will also be included. revision: yes
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Referee: [Abstract] Abstract: The statement that the resulting stochastic equation yields Born-rule probabilities under general causality conditions is not accompanied by an independent derivation or check that the probabilities emerge from the noise term rather than being presupposed by the choice of ensemble averaging; without this, the deduction of the Born rule risks circularity.
Authors: The ensemble averaging is performed over microstates compatible with each macrostate; the Born probabilities themselves are not inserted by hand but emerge from the solution of the resulting Itô equation once the causality conditions fix the noise correlations. We nevertheless recognize that an explicit check would strengthen the presentation and remove any appearance of circularity. In revision we will add a short independent derivation (or worked example) showing how the probabilities are fixed by the noise statistics under causality, independent of the initial ensemble choice. revision: yes
Circularity Check
No significant circularity: derivation proceeds from standard unitary Schrödinger dynamics plus ensemble assumption
full rationale
The paper begins with the ordinary Schrödinger equation under the assumption that macrostates are statistical ensembles of microstates. It decouples macroscopic and microscopic degrees of freedom to obtain an effective stochastic equation in which the ensemble-averaged microscopic amplitudes serve as internal white noise. Under stated causality conditions this effective equation is shown to reduce to a reducing Itô process whose collapse probabilities match the Born rule. No step reduces the target result (reduction plus Born probabilities) to a fitted parameter, a self-citation, or a redefinition of the input; the stochasticity and probabilities emerge from the decoupling and averaging procedure applied to the unitary dynamics. The derivation is therefore self-contained against external benchmarks and receives score 0.
Axiom & Free-Parameter Ledger
axioms (2)
- domain assumption Quantum macrostates are statistical ensembles of microstates
- ad hoc to paper Some general causality conditions are met
discussion (0)
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