Causal Quantum Relativity: Deriving Quantum Mechanics, General Relativity, and Standard Model Gauge Structure from Discrete Causality

Causal Quantum Relativity: Deriving Quantum Mechanics, General Relativity, and Standard Model Gauge Structure from Discrete Causality | 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 Causal Quantum Relativity: Deriving Quantum Mechanics, General Relativity, and Standard Model Gauge Structure from Discrete Causality M. Freeman This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8857825/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 present Causal Quantum Relativity (CQR), a framework that unifies quantum mechanics, general relativity, and the Standard Model gauge group SU(3),x,SU(2),x,U(1) from two axioms: (1) spacetime is a locally finite partial order (causal set), and (2) the Planck length is dynamic, increasing with local energy density. Quantum mechanics emerges from the path sum over causal histories, with interference forced by the combinatorics of discrete causality. General relativity is recovered via the Benincasa--Dowker--Glaser action in the continuum limit. The gauge group is derived through two independent mechanisms: branchial fiber bundles (building on Gorard's framework) and noncommutative geometry (building on Connes' spectral triples), both yielding SU(3) from three spatial dimensions. Black hole singularities are resolved by finite causal depth and unitarity is preserved via an explicit S-matrix through the causal bottleneck. We derive the observed CMB amplitude from Poisson statistics of causal set growth, and show that the spectral index is achievable through chaotic amplification and causal knot formation. Crucially, CQR makes specific falsifiable predictions that distinguish it from competing quantum gravity approaches: gravitational wave echoes at approximately 10,ms delay (testable with current LIGO/Virgo sensitivity), modified Hawking spectra with Planck-scale UV suppression, vanishing linear Lorentz violation with quadratic corrections, and density-dependent QED radiative corrections in extreme astrophysical environments. The combination of vanishing linear Lorentz violation with GW echoes uniquely identifies CQR among quantum gravity approaches. All results follow from the two axioms without additional postulates. Open problems include the fermion mass hierarchy and cosmological constant, which are shared challenges across all approaches to quantum gravity. quantum gravity causal set theory gauge symmetry emergence noncommutative geometry discrete spacetime Standard Model 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-8857825","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":591357151,"identity":"68ea4c1b-7b10-4f5f-9407-19f1f5b197ab","order_by":0,"name":"M. 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Quantum mechanics emerges \nfrom the path sum over causal histories, with interference forced by the \ncombinatorics of discrete causality. General relativity is recovered via \nthe Benincasa--Dowker--Glaser action in the continuum limit. The gauge \ngroup is derived through two independent mechanisms: branchial fiber \nbundles (building on Gorard's framework) and noncommutative geometry \n(building on Connes' spectral triples), both yielding SU(3) from three \nspatial dimensions. Black hole singularities are resolved by finite \ncausal depth and unitarity is preserved via an explicit S-matrix through \nthe causal bottleneck. We derive the observed CMB amplitude from Poisson \nstatistics of causal set growth, and show that the spectral index is \nachievable through chaotic amplification and causal knot formation. \nCrucially, CQR makes specific falsifiable predictions that distinguish it \nfrom competing quantum gravity approaches: gravitational wave echoes at \napproximately 10\\,ms delay (testable with current LIGO/Virgo sensitivity), \nmodified Hawking spectra with Planck-scale UV suppression, vanishing \nlinear Lorentz violation with quadratic corrections, and density-dependent \nQED radiative corrections in extreme astrophysical environments. The \ncombination of vanishing linear Lorentz violation with GW echoes uniquely \nidentifies CQR among quantum gravity approaches. All results follow from \nthe two axioms without additional postulates. Open problems include the \nfermion mass hierarchy and cosmological constant, which are shared \nchallenges across all approaches to quantum gravity.","manuscriptTitle":"Causal Quantum Relativity: Deriving Quantum Mechanics, General Relativity, and Standard Model Gauge Structure from Discrete Causality","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-05 03:00:07","doi":"10.21203/rs.3.rs-8857825/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":"62c674d0-db04-4af2-a6a3-feb7c488c7db","owner":[],"postedDate":"March 5th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-03-10T09:57:02+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-05 03:00:07","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8857825","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8857825","identity":"rs-8857825","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}