A Critical Orbital-Scale Transition in Temporal Phase Memory: Observational Constraints on a Time-Field Schrödinger Equation

A Critical Orbital-Scale Transition in Temporal Phase Memory: Observational Constraints on a Time-Field Schrödinger Equation | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article A Critical Orbital-Scale Transition in Temporal Phase Memory: Observational Constraints on a Time-Field Schrödinger Equation Takahiro Mitsui This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8869491/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract We report evidence for a sharp orbital-scale transition in a time-series proxy for temporal 6 phase memory, extracted from multi-constellation GNSS satellite clock data. Using high-pass 7 filtered clock-bias time series sampled at 300 s, we quantify a target-band autocorrelation 8 feature near 25 min and interpret its amplitude as an effective “phase-memory strength” A(L) 9 at orbital radius L. Across geosynchronous-orbit (GEO) satellites (L ≈ 4.22×107 m) we find 10 consistently high target-band amplitudes (A ≃ 0.406), whereas a subset of medium-Earth- 11 orbit (MEO) satellites cluster at a much smaller amplitude (A ≃ 0.031) near L ≈ 2.66×107 m. 12 Model comparison favors a step-like logistic transition in A(L) over a power law or simple 13 group-mean model, yielding a critical radius Lc ≃ 2.658 × 107 m and asymptotic levels 14 Alow ≃ 0.0311, Ahigh ≃ 0.4063. We discuss how such an orbital-scale “phase transition” 15 can be incorporated as an empirical constraint on a Time-Field Schr¨odinger framework, in 16 which A(L) acts as an effective quantumness parameter controlling interference contrast 17 via a finite-memory phase kernel. The result motivates targeted tests with additional 18 constellations, processing centers, and independent observables to separate genuine physics 19 from constellation-specific systematics. Theoretical Physics quantum foundations time in quantum theory Schrödinger equation quantum gravity phenomenology GNSS clock analysis Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8869491","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":590746458,"identity":"27211d16-64f3-4474-ae1a-4c26ffe8daa7","order_by":0,"name":"Takahiro Mitsui","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9klEQVRIiWNgGAWjYHACNiCqSTBgb2A8kFAB5DMzN+BVzwPRcizBgOcAw4EPZ0BaGInSwpxgIJHAcHBmG0iMgBZ7sQNsjwvK2PLMGdIfHOadVxvN3w7U8qNiG25bpBPYjWeckym2bDhjcJh32/HcGYcZGxh7ztzGp4VNmreNLXHDwR4GoJZjuQ1ALcyMbQS1MCduOMwOdNicY7nziddyjMHg4MyGmtwNBLXcTmyT5jl3rNiyh8fgwIdjB3I3ArUcxOcX9tnJx6R5ymryzOWfP3yQUFOXO+/84YMPflTg1oIeC4fB5AE86jFAHSmKR8EoGAWjYIQAABoUXQvcwduMAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0009-0006-6576-0352","institution":"Independent Researcher, Japan","correspondingAuthor":true,"prefix":"","firstName":"Takahiro","middleName":"","lastName":"Mitsui","suffix":""}],"badges":[],"createdAt":"2026-02-13 08:41:14","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-8869491/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8869491/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":102748967,"identity":"fc4c9bb4-f806-4bf7-ade5-c63d8bc24ec5","added_by":"auto","created_at":"2026-02-16 09:11:45","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":300427,"visible":true,"origin":"","legend":"","description":"","filename":"ACriticalOrbitalScaleTransitioninTemporalPhaseMemory.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8869491/v1_covered_d7ee32f6-d2a0-4435-b230-575fea24dfb6.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eA Critical Orbital-Scale Transition in Temporal Phase Memory: Observational Constraints on a Time-Field Schrödinger Equation\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Independent Researcher","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"quantum foundations, time in quantum theory, Schrödinger equation, quantum gravity phenomenology, GNSS clock analysis","lastPublishedDoi":"10.21203/rs.3.rs-8869491/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8869491/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe report evidence for a sharp orbital-scale transition in a time-series proxy for temporal 6 phase memory, extracted from multi-constellation GNSS satellite clock data. 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