Complete and incomplete entanglements energy examination due to energy analysis of nonlocal lattice vibration

Complete and incomplete entanglements energy examination due to energy analysis of nonlocal lattice vibration | 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 Complete and incomplete entanglements energy examination due to energy analysis of nonlocal lattice vibration Michiaki KOBAYASHI This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7217591/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 Regarding with nonlocal causality, the author proposed nonlocality mechanism introduced by the share of the phase information between entangled particles and/or fields based on the nonlocal phenomenon physically caused by the optical mode of lattice vibration under wave number k = 0. At wave number k = 0 under which both the phase velocity and the wavelength of the optical mode are infinity, the phase information is transferred instantaneously far away and then the entanglement of optical mode of lattice vibration examined by violating CHSH inequality S is established completely (complete entanglement) due to instantaneously simultaneous synchronization. However, incomplete entanglement between moving particles with mass is dependent on locations, distance/space and time due to delayed synchronization under the finite phase velocity and the finite wavelength. In this paper, complete and incomplete entanglements energy are examined based on energy analysis of nonlocal lattice vibration. The proposed nonlocality mechanism and entanglement energy examination supports and contributes to the holographic principle and suggests that clocks of every place are connected and synchronized by the complete entanglement under wave number k = 0 caused by the phase transformation due to the cosmic inflation and Big Bang. The Minkowski space-time suggests that the cosmic space is expanded by the entangled and synchronized time. Theoretical Physics Nonlocality mechanism Complete entanglement Incomplete entanglement Entanglement energy Holographic principle Full Text Additional Declarations The authors declare no competing interests. Supplementary Files Supplementarymaterials.docx 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. 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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-7217591","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":491075162,"identity":"4a9dc879-964f-4ae9-9b81-fd01d9a841a6","order_by":0,"name":"Michiaki KOBAYASHI","email":"data:image/png;base64,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","orcid":"","institution":"Kitami Institute of Technology","correspondingAuthor":true,"prefix":"","firstName":"Michiaki","middleName":"","lastName":"KOBAYASHI","suffix":""}],"badges":[],"createdAt":"2025-07-25 23:51:59","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-7217591/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7217591/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":87817173,"identity":"bfdcfef2-c305-4335-979c-a013102a9b71","added_by":"auto","created_at":"2025-07-29 10:22:18","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1520526,"visible":true,"origin":"","legend":"","description":"","filename":"Submittedmanuscriptnonlocalenergyupdated.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7217591/v1_covered_8b466d45-5f4d-43b1-983b-2baf629c9c99.pdf"},{"id":87815324,"identity":"1ead33c3-a52f-492e-ae2c-9f3a33e20ce7","added_by":"auto","created_at":"2025-07-29 09:58:13","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":11771968,"visible":true,"origin":"","legend":"","description":"","filename":"Supplementarymaterials.docx","url":"https://assets-eu.researchsquare.com/files/rs-7217591/v1/24fda28dc88ff66dd77aff6d.docx"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eComplete and incomplete entanglements energy examination due to energy analysis of nonlocal lattice vibration\u003c/strong\u003e\u003c/p\u003e","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":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":"Nonlocality mechanism, Complete entanglement, Incomplete entanglement, Entanglement energy, Holographic principle","lastPublishedDoi":"10.21203/rs.3.rs-7217591/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7217591/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eRegarding with nonlocal causality, the author proposed nonlocality mechanism introduced by the share of the phase information between entangled particles and/or fields based on the nonlocal phenomenon physically caused by the optical mode of lattice vibration under wave number k\u0026thinsp;=\u0026thinsp;0. At wave number k\u0026thinsp;=\u0026thinsp;0 under which both the phase velocity and the wavelength of the optical mode are infinity, the phase information is transferred instantaneously far away and then the entanglement of optical mode of lattice vibration examined by violating CHSH inequality S is established completely (complete entanglement) due to instantaneously simultaneous synchronization. However, incomplete entanglement between moving particles with mass is dependent on locations, distance/space and time due to delayed synchronization under the finite phase velocity and the finite wavelength. In this paper, complete and incomplete entanglements energy are examined based on energy analysis of nonlocal lattice vibration. The proposed nonlocality mechanism and entanglement energy examination supports and contributes to the holographic principle and suggests that clocks of every place are connected and synchronized by the complete entanglement under wave number k\u0026thinsp;=\u0026thinsp;0 caused by the phase transformation due to the cosmic inflation and Big Bang. 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