God Does Not Play Dice: Quantum Determinism in the MMA-DMF Framework

God Does Not Play Dice: Quantum Determinism in the MMA-DMF Framework | 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Article God Does Not Play Dice: Quantum Determinism in the MMA-DMF Framework Paulo Adriano This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8622287/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 a deterministic, superdeterministic completion of quantum theory inside a cosmological scalar–tensor framework called MMA-DMF. A single scalar degree of freedom with fundamental scale M ≃ 100 TeV regularises the Big Bang into a non-singular Big Bounce, replaces particle dark matter and dark energy, and acts as a global hidden variable whose phase correlates all measurement settings and outcomes through common initial conditions. This article consolidates and reorganises six monographic technical reports, plus the associated Python codes and CSV files, into a single submission-ready paper. The programme proceeds in four layers. First, we establish that the scalar dynamics are chaotic and ergodic (Tests T1–T2), so coarse-grained observables appear stochastic even though the microscopic evolution is unique. Second, we construct contextual hidden-variable models for Bell and GHZ experiments (Tests B1–B3, GHZ-1) in which the local outcome is a deterministic function of the scalar phase λ and the measurement setting, but the distribution ρ(λ|a, b) is fixed by the global scalar geometry and therefore violates statistical independence. The model reproduces CHSH violations up to S ≃ 2.82 and GHZ parity constraints while remaining consistent with relativistic causality and operational no-signalling. A detailed no-signalling analysis and dedicated numerical tests show that marginal probabilities at each wing are independent of the distant setting. Third, we derive the Born rule and explicit deterministic collapse dynamics (Tests P1–P3). The scalar field defines an ergodic flow in phase space with an invariant measure that pushes forward to a density proportional to |ψ| 2 for the effective wavefunction, and detection rates are proportional to the squared amplitude of the classical scalar field. Monte Carlo simulations of detection events match the Born prediction for a variety of effective wavefunctions. Fourth, we embed more demanding foundational experiments (KS-1, W-1, W-2, QFT-1) in the same framework. Kochen–Specker contextuality arises from the dependence of ρ(λ|C) on the full commuting set C, Wheeler delayed choice is mapped to a causal spacetime diagram anchored at the bounce, Wigner’s friend / Frauchiger–Renner paradoxes are resolved by recognising the wavefunction as a partial encoding of the underlying scalar configuration, and a deterministic reinterpretation of the path integral reproduces tree-level scattering amplitudes to within a few ×10 −4 . On the cosmological side, the same scalar sector aims to address and can alleviate a series of anomalies of the standard ΛCDM picture. The ancillary file espectro_geometrico_vali dacao_global.csv shows that MMA-DMF predicts M = 100 TeV, an Early-X component with fpeak = 0.362 (Thermodynamic Test T-Thermo), a BBN Yukawa shift ζBBN = −0.009 (Baryogenesis Test T-Zeta), a Hubble constant H0 ≃ 72.1 km s −1 Mpc −1 , a late-time clustering amplitude S8 ≃ 0.772, a lithium abundance 7 Li/H ≃ 2.8 × 10− 10 consistent with the Spite plateau, and a gravitational-wave echo delay ∆t ≃ 32 ms for compact objects. A companion CSV, setup_TDT_consolidated_parameters.csv, summarises a “Total Determinism Test” (TDT) in which all key macroscopic parameters — including fpeak and ζBBN — are derived from M, geometric flavour charges q f and the scalar dynamics, rather than fitted. Within this framework, quantum probabilities, Bell and GHZ correlations, cosmological tensions and flavour hierarchies all emerge from a single deterministic scalar–geometric dynamics anchored at the Big Bounce. Within this effective MMA–DMF description, no additional fundamental randomness is required at the macroscopic level: once the hidden scalar background and its boundary conditions are fixed, the apparent stochasticity of quantum measurements arises from ignorance about the scalar configuration, so that—in this restricted sense—the Universe does not “play dice”. Theoretical Physics quantum foundations determinism superdeterminism hidden variables Bell inequality GHZ Born rule scalar–tensor cosmology Big Bounce Full Text Additional Declarations The authors declare no competing interests. Supplementary Files files.zip 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-8622287","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":575838023,"identity":"8ebbb2af-b9f4-4c31-a263-b71d486cc65f","order_by":0,"name":"Paulo Adriano","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAuklEQVRIiWNgGAWjYBACAxDxgeEAD2laGGeAtLBBBCSI0sLMw3CAgXgt5uzdiY9tau7ImMs3H/zAuMOmjqAWy56zm41zjj3jsWxjS5ZgPJNGhMNu5G6Tzm04zGNwjMeMgbHtMFFatv+2BGvh/wbU8p84W5gZIbawAbUcIELLmbObJXuOHQb6Jc1YIrEtWbKBoJbjvRs//Kg5bG/OfPjhh49tdvwEbUHoBREJxKuHaRkFo2AUjIJRgA0AAAQWO13tMX01AAAAAElFTkSuQmCC","orcid":"https://orcid.org/0009-0008-4646-4616","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Paulo","middleName":"","lastName":"Adriano","suffix":""}],"badges":[],"createdAt":"2026-01-16 21:47:59","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-8622287/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8622287/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":100596077,"identity":"48e9b1c2-5fa1-47d2-bcf9-a3f7264a3504","added_by":"auto","created_at":"2026-01-19 13:50:46","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":8304420,"visible":true,"origin":"","legend":"","description":"","filename":"GodDoesNotPlayDiceQuantumDeterminism.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8622287/v1_covered_3828ee06-e7b8-4904-bab4-85e56d038420.pdf"},{"id":100568295,"identity":"f04c18cf-96d2-4b23-b4c1-3cccf52beb7d","added_by":"auto","created_at":"2026-01-19 09:17:56","extension":"zip","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":20734377,"visible":true,"origin":"","legend":"","description":"","filename":"files.zip","url":"https://assets-eu.researchsquare.com/files/rs-8622287/v1/1d5d086f85eb67179de731f1.zip"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eGod Does Not Play Dice: Quantum Determinism in the MMA-DMF Framework\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":"quantum foundations, determinism, superdeterminism, hidden variables, Bell inequality, GHZ, Born rule, scalar–tensor cosmology, Big Bounce","lastPublishedDoi":"10.21203/rs.3.rs-8622287/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8622287/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe present a deterministic, superdeterministic completion of quantum theory inside a cosmological scalar–tensor framework called MMA-DMF. A single scalar degree of freedom with fundamental scale M ≃ 100 TeV regularises the Big Bang into a non-singular Big Bounce, replaces particle dark matter and dark energy, and acts as a global hidden variable whose phase correlates all measurement settings and outcomes through common initial conditions.\u003c/p\u003e\n\u003cp\u003eThis article consolidates and reorganises six monographic technical reports, plus the associated Python codes and CSV files, into a single submission-ready paper. The programme proceeds in four layers. First, we establish that the scalar dynamics are chaotic and ergodic (Tests T1–T2), so coarse-grained observables appear stochastic even though the microscopic evolution is unique. Second, we construct contextual hidden-variable models for Bell and GHZ experiments (Tests B1–B3, GHZ-1) in which the local outcome is a deterministic function of the scalar phase λ and the measurement setting, but the distribution ρ(λ|a, b) is fixed by the global scalar geometry and therefore violates statistical independence. The model reproduces CHSH violations up to S ≃ 2.82 and GHZ parity constraints while remaining consistent with relativistic causality and operational no-signalling. A detailed no-signalling analysis and dedicated numerical tests show that marginal probabilities at each wing are independent of the distant setting.\u003c/p\u003e\n\u003cp\u003eThird, we derive the Born rule and explicit deterministic collapse dynamics (Tests P1–P3). The scalar field defines an ergodic flow in phase space with an invariant measure that pushes forward to a density proportional to |ψ|\u003csup\u003e2\u003c/sup\u003e for the effective wavefunction, and detection rates are proportional to the squared amplitude of the classical scalar field. Monte Carlo simulations of detection events match the Born prediction for a variety of effective wavefunctions. Fourth, we embed more demanding foundational experiments (KS-1, W-1, W-2, QFT-1) in the same framework. Kochen–Specker contextuality arises from the dependence of ρ(λ|C) on the full commuting set C, Wheeler delayed choice is mapped to a causal spacetime diagram anchored at the bounce, Wigner’s friend / Frauchiger–Renner paradoxes are resolved by recognising the wavefunction as a partial encoding of the underlying scalar configuration, and a deterministic reinterpretation of the path integral reproduces tree-level scattering amplitudes to within a few ×10\u003csup\u003e−4\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eOn the cosmological side, the same scalar sector aims to address and can alleviate a series of anomalies of the standard ΛCDM picture. The ancillary file espectro_geometrico_vali dacao_global.csv shows that MMA-DMF predicts M = 100 TeV, an Early-X component with fpeak = 0.362 (Thermodynamic Test T-Thermo), a BBN Yukawa shift ζBBN = −0.009 (Baryogenesis Test T-Zeta), a Hubble constant H0 ≃ 72.1 km s\u003csup\u003e−1\u003c/sup\u003e\u0026nbsp;Mpc\u003csup\u003e−1\u003c/sup\u003e, a late-time clustering amplitude S8 ≃ 0.772, a lithium abundance\u0026nbsp;\u003csup\u003e7\u003c/sup\u003eLi/H\u0026nbsp;≃\u0026nbsp;2.8\u0026nbsp;×\u0026nbsp;10−\u003csup\u003e10\u003c/sup\u003e\u0026nbsp;consistent with the Spite plateau, and a gravitational-wave echo delay ∆t ≃ 32 ms for compact objects. A companion CSV, setup_TDT_consolidated_parameters.csv, summarises a “Total Determinism Test” (TDT) in which all key macroscopic parameters — including\u0026nbsp;\u003csub\u003efpeak\u003c/sub\u003e\u003csup\u003e\u0026nbsp;and\u003c/sup\u003e\u0026nbsp;ζBBN — are derived from M, geometric flavour charges q\u003cem\u003ef\u0026nbsp;\u003c/em\u003eand the scalar dynamics, rather than fitted.\u003c/p\u003e\n\u003cp\u003eWithin this framework, quantum probabilities, Bell and GHZ correlations, cosmological tensions and flavour hierarchies all emerge from a single deterministic scalar–geometric dynamics anchored at the Big Bounce. 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