After 100 Years of Quantum Mechanics: Toward a Constructive Observation-Centered Perspective
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Quantum Physics arXiv:2604.11814 (quant-ph) [Submitted on 10 Apr 2026] Title:After 100 Years of Quantum Mechanics: Toward a Constructive Observation-Centered Perspective Authors:Timothy Stroschein, Markus Reiher View a PDF of the paper titled After 100 Years of Quantum Mechanics: Toward a Constructive Observation-Centered Perspective, by Timothy Stroschein and Markus Reiher View PDF HTML (experimental) 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. Comments: Subjects: Quantum Physics (quant-ph); Materials Science (cond-mat.mtrl-sci); Chemical Physics (physics.chem-ph); Computational Physics (physics.comp-ph) Cite as: arXiv:2604.11814 [quant-ph] (or arXiv:2604.11814v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.11814 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Markus Reiher [view email] [v1] Fri, 10 Apr 2026 14:18:47 UTC (13 KB) Full-text links: Access Paper: View a PDF of the paper titled After 100 Years of Quantum Mechanics: Toward a Constructive Observation-Centered Perspective, by Timothy Stroschein and Markus ReiherView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 Change to browse by: cond-mat cond-mat.mtrl-sci physics physics.chem-ph physics.comp-ph References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)