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

Quantum Physics [Submitted on 10 Apr 2026] After 100 Years of Quantum Mechanics: Toward a Constructive Observation-Centered Perspective Timothy Stroschein, Markus Reiher 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: 18 pages 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 Submission history From: Markus Reiher [view email] [v1] Fri, 10 Apr 2026 14:18:47 UTC (13 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > 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 ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)