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arxiv: 2604.11814 · v1 · submitted 2026-04-10 · 🪐 quant-ph · cond-mat.mtrl-sci· physics.chem-ph· physics.comp-ph

After 100 Years of Quantum Mechanics: Toward a Constructive Observation-Centered Perspective

Timothy Stroschein , Markus Reiher This is my paper

Pith reviewed 2026-05-10 17:22 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.mtrl-sciphysics.chem-phphysics.comp-ph
keywords quantum mechanicsobservation-centered perspectivesignalsconstructive theoryspectral equationeffective descriptionswave functionsfinite observation time
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The pith

Quantum mechanics should treat observed signals as primary, with wave functions and Hamiltonians reconstructed as auxiliary structures from the data.

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

The paper argues that the traditional Hilbertian formalization of quantum mechanics does not align well with practical limits of finite-dimensional computations and finite accuracy, calling for a new constructive mathematical program focused on effective descriptions. It proposes an observation-centered perspective that makes signals the main objects of analysis rather than starting from abstract wave functions. From a signal-based spectral equation that recasts frequency analysis as an operator problem, the approach reconstructs wave functions and Hamiltonians only as needed to explain the observations. This integrates approximation directly into the foundations and highlights how necessary observation time relates to effective spectral density for accurate resolution. A sympathetic reader would care because it aims to identify essential degrees of freedom for describing complex quantum systems without circular reliance on the full formalism.

Core claim

The central claim is that quantum mechanics can be placed on a constructive footing by adopting an observation-centered viewpoint in which signals are primary, a signal-based spectral equation reformulates frequency analysis as an operator problem, and wave functions together with Hamiltonians are derived as auxiliary structures to rationalize the observed data, thereby incorporating finite accuracy and approximation as fundamental features from the outset.

What carries the argument

The signal-based spectral equation, which reformulates frequency analysis as an operator problem to enable reconstruction of auxiliary structures from observed signals.

If this is right

  • Wave functions and Hamiltonians function only as rationalizing tools rather than starting points.
  • A sharp accuracy transition appears that ties required observation time to the signal's effective spectral density.
  • Approximation enters the foundations of quantum mechanics directly instead of as an afterthought.
  • The framework supports effective descriptions for complex systems such as those in the molecular sciences.

Where Pith is reading between the lines

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

  • Simulations could focus computational effort on finite-time signal extraction rather than full state spaces.
  • Direct data-driven identification of minimal degrees of freedom might become possible across quantum chemistry applications.
  • Short-time quantum simulation techniques could gain systematic accuracy bounds from the observation-time transition.

Load-bearing premise

A signal-based spectral equation can be developed into a rigorous constructive theory that identifies essential degrees of freedom without circular dependence on the wave-function formalism it aims to subordinate.

What would settle it

A concrete calculation or experiment in which signal analysis under finite observation time fails to accurately reconstruct the spectrum or dynamics of a known quantum system without falling back on standard wave-function methods.

read the original abstract

Quantum mechanics owes much of its extraordinary success to a Hilbertian program of mathematical formalization. Yet, the formalism remains poorly aligned with the practical limitations of computations in finite dimensions and under finite accuracy. In this perspective, we argue that this mismatch points to the need for a new mathematical program: a rigorous constructive theory for effective descriptions to identify essential degrees of freedom. We propose an observation-centered point of view in which signals are treated as the primary objects of analysis, while wave functions and Hamiltonians are reconstructed as auxiliary structures to rationalize the observed data. Our starting point is a signal-based spectral equation that reformulates frequency analysis as an operator problem. We connect this point of view to results on prolate Fourier theory, spectral analysis with finite observation time, and short-time quantum simulation. We highlight a sharp accuracy transition relating necessary observation time to the effective spectral density of a signal for achieving accurate resolution. The resulting framework integrates approximation as a fundamental necessity more directly into the foundations of quantum mechanics and points toward a broader program for the effective description of complex quantum systems, such as those found in the molecular sciences.

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 is a perspective article critiquing the mismatch between the Hilbert-space formalism of quantum mechanics and practical constraints of finite-dimensional computations with finite accuracy. It proposes a new constructive mathematical program based on an observation-centered perspective, in which signals are the primary objects of analysis and wave functions and Hamiltonians are reconstructed as auxiliary structures. The proposal begins with a signal-based spectral equation reformulating frequency analysis as an operator problem, connects this to prolate Fourier theory, finite-observation-time spectral analysis, and short-time quantum simulation, and highlights a sharp accuracy transition relating necessary observation time to effective spectral density, with the goal of integrating approximation into the foundations for effective descriptions of complex quantum systems such as those in molecular sciences.

Significance. If the outlined program can be developed into a rigorous constructive theory, it would be significant for embedding finite-resource and approximation considerations directly into quantum foundations, offering a route to identify essential degrees of freedom without presupposing the full Hilbert-space structure. The explicit links to established results on prolate spheroidal functions and short-time simulation provide a credible mathematical anchor. However, the manuscript advances only a high-level conceptual outline without derivations, examples, or validations, so any significance remains prospective and contingent on future work.

major comments (2)
  1. Abstract: The signal-based spectral equation is introduced as the starting point for the observation-centered framework but is never formulated, derived, or illustrated. This equation is load-bearing for the central claim that signals can be treated as primary objects while subordinating wave functions, and its absence prevents evaluation of whether the approach can be made rigorous and non-circular.
  2. Abstract: The 'sharp accuracy transition' relating observation time to spectral density is presented as a key highlight demonstrating that approximation is fundamental, yet no quantitative characterization, derivation, or concrete example is supplied. Without this, the argument that the new perspective integrates approximation more directly than standard QM remains unsupported.
minor comments (1)
  1. The abstract invokes 'prolate Fourier theory' and 'short-time quantum simulation' without specific citations or indications of which results are being referenced, which would help readers trace the connections.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading, positive assessment of the program's potential significance, and constructive identification of areas needing clarification. As a perspective article, the manuscript intentionally remains at a high conceptual level while pointing to established mathematical anchors; however, we agree that explicit formulations and characterizations will strengthen the presentation. We address each major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [—] Abstract: The signal-based spectral equation is introduced as the starting point for the observation-centered framework but is never formulated, derived, or illustrated. This equation is load-bearing for the central claim that signals can be treated as primary objects while subordinating wave functions, and its absence prevents evaluation of whether the approach can be made rigorous and non-circular.

    Authors: We acknowledge the referee's point that the signal-based spectral equation requires more explicit treatment to support the central claim. Although the manuscript links it to prolate Fourier theory and finite-observation-time analysis, we agree an explicit statement is needed for evaluation. In revision we will add a short subsection that states the equation (reformulating frequency analysis as an operator eigenvalue problem on finite-time signals), sketches its derivation from observable data, and provides a simple illustrative example. This addition will demonstrate grounding in signals without presupposing the full Hilbert space, while preserving the perspective character of the article. revision: yes

  2. Referee: [—] Abstract: The 'sharp accuracy transition' relating observation time to spectral density is presented as a key highlight demonstrating that approximation is fundamental, yet no quantitative characterization, derivation, or concrete example is supplied. Without this, the argument that the new perspective integrates approximation more directly than standard QM remains unsupported.

    Authors: We accept that the sharp accuracy transition is highlighted without sufficient quantitative support in the current text. The transition arises from the spectral properties of the prolate spheroidal operator under finite observation time, but we agree a concrete characterization is required to substantiate the claim that approximation enters more directly than in standard QM. In the revised manuscript we will insert a quantitative description (relating necessary observation time T to the effective number of significant eigenvalues) together with a brief numerical example for a model signal, drawing directly on known results in prolate Fourier theory. A full general derivation for arbitrary quantum systems will remain part of the future constructive program. revision: partial

Circularity Check

0 steps flagged

No significant circularity in this perspective proposal

full rationale

The paper is a high-level conceptual perspective advocating an observation-centered framework with signals as primary objects. No mathematical derivations, theorems, or quantitative predictions are advanced in the provided text. The signal-based spectral equation is introduced as a starting point but not developed into any closed-form construction or fitted result that reduces to its own inputs. References to prolate Fourier theory and related results are external connections rather than self-citations carrying the central claim. The manuscript explicitly frames itself as a program proposal rather than a completed formal theory, so no load-bearing steps exist that could be circular by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper introduces no new free parameters or invented entities. It relies on the domain assumption that quantum mechanics admits a constructive reformulation centered on finite observations.

axioms (1)
  • domain assumption Quantum mechanics admits a rigorous constructive theory built from signals as primary objects
    This is the central proposal; no independent justification is supplied in the abstract.

pith-pipeline@v0.9.0 · 5504 in / 1237 out tokens · 45976 ms · 2026-05-10T17:22:47.497838+00:00 · methodology

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Reference graph

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