Quaternion algebra on 4D superfluid quantum spacetime: the Lorentz gauge is a gate to the invisible world of dark matter and dark energy

Quaternion algebra on 4D superfluid quantum spacetime: the Lorentz gauge is a gate to the invisible world of dark matter and dark energy | 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 Quaternion algebra on 4D superfluid quantum spacetime: the Lorentz gauge is a gate to the invisible world of dark matter and dark energy Valeriy Sbitnev This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3934133/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 Quaternion algebra is used for the description of the motion of material objects in 4D space-time. In the same quaternion basis, the energy-momentum density tensor is also written, accurate to arbitrary scalar fields. Quaternionic generating operators defined in this space being applied repeatedly to the energy-momentum density tensor lead to the gravitomagnetic equations that are parent equations for the series of physical equations ranging from the wave equations up to the quantum mechanical ones. Before finally deducing the gravitomagnetic equations, it is necessary to use the Lorentz gauge at a certain stage to cut off the arbitrary scalar fields. We declare that these superfluous scalar fields, inaccessible to direct observation, represent dark matter and dark energy. Dark matter manifesting through the Bose-Einstein condensate looks like a time crystal composed of particle-antiparticle pairs. We show in what way the dark matter can provide a flat profile of the orbital speed of the galaxy's arm rotations. time crystel Navier-Stokes equation Helmholtz decomposition theorem toroidal vortex toroidal bubble helicoidal ring irrotational velocity solenoidal velocity Full Text Additional Declarations No competing interests reported. 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-3934133","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":271516401,"identity":"f141848f-5b10-4954-9db9-568536164592","order_by":0,"name":"Valeriy Sbitnev","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABAUlEQVRIiWNgGAWjYFAC5gYwZcAMpmyAmLHxAH4tjDAtYD1pYBEitTCAtRwGc/BqMTh+sPFxZRuDvTk7/7EHH9vO261tPwy0pcYmGqeWM4nNhmfbGBJ3NjOzG85su5287UwiUMuxtNwGHFokGxLbJBvbGBIMDjOzSfOcuZ1sdgCohbHhMG4t/Q/bfwK12IO1/DlzLtns/EP8WvglEtsYgVoYN4C0MFQcsDO7QcAWfomHzZIN5yRAfjGT7KlITjC7AbQlAY9f2PiTD35sKLOxN+c/+Ezih4Gdvdn59IcPPtTY4NQCBoxsEnB2IlhlAj7lYPAHwbQnqHgUjIJRMApGHAAAWXNfc8kyn9gAAAAASUVORK5CYII=","orcid":"","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Valeriy","middleName":"","lastName":"Sbitnev","suffix":""}],"badges":[],"createdAt":"2024-02-06 14:14:43","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3934133/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3934133/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":52893478,"identity":"fa0fa95c-c17e-42a6-ae8e-2a4436c154c4","added_by":"auto","created_at":"2024-03-18 12:16:21","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1575042,"visible":true,"origin":"","legend":"","description":"","filename":"InvisibleworlddarkmatterdarkenergyFoundPhys.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3934133/v1_covered_977b0d43-6d70-444c-b5d0-d04d69c9c113.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Quaternion algebra on 4D superfluid quantum spacetime: the Lorentz gauge is a gate to the invisible world of dark matter and dark energy","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"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":"time crystel, Navier-Stokes equation, Helmholtz decomposition theorem, toroidal vortex, toroidal bubble, helicoidal ring, irrotational velocity, solenoidal velocity","lastPublishedDoi":"10.21203/rs.3.rs-3934133/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3934133/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Quaternion algebra is used for the description of the motion of material objects in 4D space-time. In the same quaternion basis, the energy-momentum density tensor is also written, accurate to arbitrary scalar fields. Quaternionic generating operators defined in this space being applied repeatedly to the energy-momentum density tensor lead to the gravitomagnetic equations that are parent equations for the series of physical equations ranging from the wave equations up to the quantum mechanical ones. Before finally deducing the gravitomagnetic equations, it is necessary to use the Lorentz gauge at a certain stage to cut off the arbitrary scalar fields. We declare that these superfluous scalar fields, inaccessible to direct observation, represent dark matter and dark energy.\nDark matter manifesting through the Bose-Einstein condensate looks like a time crystal composed of particle-antiparticle pairs.\nWe show in what way the dark matter can provide a flat profile of the orbital speed of the galaxy's arm rotations.","manuscriptTitle":"Quaternion algebra on 4D superfluid quantum spacetime: the Lorentz gauge is a gate to the invisible world of dark matter and dark energy","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-02-08 10:48:32","doi":"10.21203/rs.3.rs-3934133/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"d61aeffd-6ed7-4f28-b777-03cf767d5dcc","owner":[],"postedDate":"February 8th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-03-18T12:08:12+00:00","versionOfRecord":[],"versionCreatedAt":"2024-02-08 10:48:32","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3934133","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3934133","identity":"rs-3934133","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}