The Golden Ratio Reveals Universal Quantum DiscretizationAcross All Scalesă

The Golden Ratio Reveals Universal Quantum DiscretizationAcross All Scalesă | 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 Article The Golden Ratio Reveals Universal Quantum DiscretizationAcross All Scalesă chen Chen xuehong This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7878229/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 Quantum discretization phenomena exist across microscale (neutrinos) to cosmic scale(black holes), but a universal critical scale and predictive law unifying these fragmented observations have long been missing. Notably, in the discrete state (α < 1), energy level ratiosof all systems strictly converge to the golden ratio (0.618ś0.01), supported by 7 types ofcross-scale experiments (error < 5%, combined P 1,continuous spectrum), APS ice crystal phonons (α ≈ 1, ratio 0.618ś0.005), and Chandra blackhole X-rays (α < 1, ratio 1:0.618:0.382). This scale-dependent law connects with quantumgravity theories (e.g., AdS/CFT duality) and provides a unified framework for discretizationorigin. It also offers quantitative guidance for controllable nuclear fusion (extending confinement time) and quantum bit stability, while opening a low-energy window for quantumgravity verification. Physical sciences/Physics/Quantum physics/Quantum mechanics Physical sciences/Mathematics and computing/Applied mathematics Full Text Additional Declarations There is NO Competing Interest. 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-7878229","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":530672933,"identity":"1234cad4-0566-4255-b38b-c5afa2653db9","order_by":0,"name":"chen Chen xuehong","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1ElEQVRIiWNgGAWjYFACHsYHHwz+yfGzNzY+/ECkFmbDGRUHjCV7DjcbSxCphU2Y58yBxA030tsEeIjRwD8j9xgzb9sdxpkzH7YxSDDYyek2ENAiceZc2sO5bc+Y+aUT2x4UMCQbmx0goMWAvcfc4G0bM5vk7MR2AwmGA4nbCGph5jGT4G1j5jG4ebBNgocoLew9ZpI8Zw5LGNxgJFKLxJkzxsBATjOQ7EkEBrIBEX7hn5FjCIxKm/p+9uMPH36osJMjqAXdnaQpHwWjYBSMglGAAwAAAGtE8MLw9FsAAAAASUVORK5CYII=","orcid":"https://orcid.org/0009-0004-6568-878X","institution":"Donghua University of Technology","correspondingAuthor":true,"prefix":"","firstName":"chen","middleName":"Chen","lastName":"xuehong","suffix":""}],"badges":[],"createdAt":"2025-10-16 13:25:50","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-7878229/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7878229/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":94003138,"identity":"cc74435e-97a1-4c03-a3ae-e0974ae2ccd9","added_by":"auto","created_at":"2025-10-21 08:40:08","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1759906,"visible":true,"origin":"","legend":"Article File","description":"","filename":"10templateArticle.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7878229/v1_covered_500596d3-a8c6-47bd-a476-3b8a0ca22101.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"The Golden Ratio Reveals Universal Quantum DiscretizationAcross All Scalesă","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"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":"","lastPublishedDoi":"10.21203/rs.3.rs-7878229/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7878229/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Quantum discretization phenomena exist across microscale (neutrinos) to cosmic scale(black holes), but a universal critical scale and predictive law unifying these fragmented ob\u0002servations have long been missing. Notably, in the discrete state (α \u003c 1), energy level ratiosof all systems strictly converge to the golden ratio (0.618ś0.01), supported by 7 types ofcross-scale experiments (error \u003c 5%, combined P \u003c 10−15) including IceCube neutrinos (α \u003e 1,continuous spectrum), APS ice crystal phonons (α ≈ 1, ratio 0.618ś0.005), and Chandra blackhole X-rays (α \u003c 1, ratio 1:0.618:0.382). This scale-dependent law connects with quantumgravity theories (e.g., AdS/CFT duality) and provides a unified framework for discretizationorigin. 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