This paper demonstrates that quantization arises naturally in NUVO space from the geometric coherence of the scalar fieldλ,without invoking probabilistic or wave—mechanical postulates.By enforcing closure of the sca...This paper demonstrates that quantization arises naturally in NUVO space from the geometric coherence of the scalar fieldλ,without invoking probabilistic or wave—mechanical postulates.By enforcing closure of the scalar—weighted arc element on the conformal manifold(M,g)with g=λ^(2)η,discrete action levels are obtained.The coherence condition leads to a universal action constant,empirically identified withhwhen calibrated to the ground—state energy of hydrogen.This result establishes quantization as a geometric property of NUVO space itself,forming the bridge between scalar conformal geometry and microscopic physical structure.展开更多
This paper develops the second stage of quantization in the NUVO scalarconformal framework,extending the arc-closure geometry of Quantization I to include loop structures and circulation.A two-substrate ontology is es...This paper develops the second stage of quantization in the NUVO scalarconformal framework,extending the arc-closure geometry of Quantization I to include loop structures and circulation.A two-substrate ontology is established:a continuous under-substrate sinertia field flowing at speed c,and an above-substrate geometry g=λ^(2)η whose scalar modulation λ(x)encodes observable curvature.Elementary particles are represented as inseparable bundles B=(C,O),where the closed loop C(mass coupling)sustains conservative circulation with impedance and the open loop O(charge coupling)provides the sole path for exchange.The resulting formalism yields continuity and transport laws bounded by c,a classification of closed,open,and geometric-alignment kinematic states,and a description of dynamic loops(photons)as substrate-detached,coherence-gated excitations propagating at c.The framework models inertia,mass,charge,and photon behavior as geometric expressions of a single scalar field,uniting them within one self-consistent scalar-modulated space and establishing the basis for future work on depletion and power connections.展开更多
We derive the gravitational field equation on NUVO space(M,g),where g=λ^(2)η with η flat and λ>0 smooth.Starting from the scalar curvature functional and theλ-weighted calculus developed in NUVO Space I-II,we ...We derive the gravitational field equation on NUVO space(M,g),where g=λ^(2)η with η flat and λ>0 smooth.Starting from the scalar curvature functional and theλ-weighted calculus developed in NUVO Space I-II,we perform a constrained conformal variation to obtain the dynamical equation forλand its coupling to matter via the trace of the energy-momentum tensor.We show that diffeomorphism invariance implies energy-momentum conservation ∇_(g)⋅T=0 and recover a λ-weighted continuity relation for the sinertia current Jμ=λρu^(μ).In the weak-field limit the field equation reduces to a Poisson-type equation for λ,yielding the Newtonian regime and setting the stage for a post-Newtonian(PPN)analysis in subsequent work.展开更多
We construct the differential-geometric foundation of NUVO space as a conformally flat manifold(M,g)endowed with a scalar unit constraint.Starting from a flat background formηand scalarλ>0,we derive the associate...We construct the differential-geometric foundation of NUVO space as a conformally flat manifold(M,g)endowed with a scalar unit constraint.Starting from a flat background formηand scalarλ>0,we derive the associated frame-bundle reduction,induced metric g=λ^(2)η,and Levi-Civita connection.Existence,uniqueness,and regularity of the induced connection are proved,defining the canonical calculus objects required for subsequent curvature and variational analyses.展开更多
We develop the analytic,geometric,and variational framework on NUVO space,the conformally flat manifold(M,g)with g=λ^(2)η introduced in Part I.Weighted divergence and Stokes theorems,curvature identities,and the Lap...We develop the analytic,geometric,and variational framework on NUVO space,the conformally flat manifold(M,g)with g=λ^(2)η introduced in Part I.Weighted divergence and Stokes theorems,curvature identities,and the Laplace-Beltrami operator are derived in full detail.We construct the variational principles governing geodesic motion and scalar currents and prove the existence and regularity of solutions to representative nonlinear scalar field equations.Together with Part I,this paper provides the mathematical foundation required for subsequent applications to gravitation and field dynamics.展开更多
We develop the strong-field and higher-order expansion framework for the NUVO scalar geometry.Starting from the nonlinear field equation R_(g)=-c^(4)/8πGT obtained in a previous work,we perform systematic perturbativ...We develop the strong-field and higher-order expansion framework for the NUVO scalar geometry.Starting from the nonlinear field equation R_(g)=-c^(4)/8πGT obtained in a previous work,we perform systematic perturbative expansions of λ and the metric g_(μv)=λ^(2)η_(μv) to second and third order in the post-Newtonian hierarchy.The resulting expressions establish the analytic structure required to compute the post-Newtonian parameters(β,γ,δ,…)in the forthcoming flagship study.展开更多
文摘This paper demonstrates that quantization arises naturally in NUVO space from the geometric coherence of the scalar fieldλ,without invoking probabilistic or wave—mechanical postulates.By enforcing closure of the scalar—weighted arc element on the conformal manifold(M,g)with g=λ^(2)η,discrete action levels are obtained.The coherence condition leads to a universal action constant,empirically identified withhwhen calibrated to the ground—state energy of hydrogen.This result establishes quantization as a geometric property of NUVO space itself,forming the bridge between scalar conformal geometry and microscopic physical structure.
文摘This paper develops the second stage of quantization in the NUVO scalarconformal framework,extending the arc-closure geometry of Quantization I to include loop structures and circulation.A two-substrate ontology is established:a continuous under-substrate sinertia field flowing at speed c,and an above-substrate geometry g=λ^(2)η whose scalar modulation λ(x)encodes observable curvature.Elementary particles are represented as inseparable bundles B=(C,O),where the closed loop C(mass coupling)sustains conservative circulation with impedance and the open loop O(charge coupling)provides the sole path for exchange.The resulting formalism yields continuity and transport laws bounded by c,a classification of closed,open,and geometric-alignment kinematic states,and a description of dynamic loops(photons)as substrate-detached,coherence-gated excitations propagating at c.The framework models inertia,mass,charge,and photon behavior as geometric expressions of a single scalar field,uniting them within one self-consistent scalar-modulated space and establishing the basis for future work on depletion and power connections.
文摘We derive the gravitational field equation on NUVO space(M,g),where g=λ^(2)η with η flat and λ>0 smooth.Starting from the scalar curvature functional and theλ-weighted calculus developed in NUVO Space I-II,we perform a constrained conformal variation to obtain the dynamical equation forλand its coupling to matter via the trace of the energy-momentum tensor.We show that diffeomorphism invariance implies energy-momentum conservation ∇_(g)⋅T=0 and recover a λ-weighted continuity relation for the sinertia current Jμ=λρu^(μ).In the weak-field limit the field equation reduces to a Poisson-type equation for λ,yielding the Newtonian regime and setting the stage for a post-Newtonian(PPN)analysis in subsequent work.
文摘We construct the differential-geometric foundation of NUVO space as a conformally flat manifold(M,g)endowed with a scalar unit constraint.Starting from a flat background formηand scalarλ>0,we derive the associated frame-bundle reduction,induced metric g=λ^(2)η,and Levi-Civita connection.Existence,uniqueness,and regularity of the induced connection are proved,defining the canonical calculus objects required for subsequent curvature and variational analyses.
文摘We develop the analytic,geometric,and variational framework on NUVO space,the conformally flat manifold(M,g)with g=λ^(2)η introduced in Part I.Weighted divergence and Stokes theorems,curvature identities,and the Laplace-Beltrami operator are derived in full detail.We construct the variational principles governing geodesic motion and scalar currents and prove the existence and regularity of solutions to representative nonlinear scalar field equations.Together with Part I,this paper provides the mathematical foundation required for subsequent applications to gravitation and field dynamics.
文摘We develop the strong-field and higher-order expansion framework for the NUVO scalar geometry.Starting from the nonlinear field equation R_(g)=-c^(4)/8πGT obtained in a previous work,we perform systematic perturbative expansions of λ and the metric g_(μv)=λ^(2)η_(μv) to second and third order in the post-Newtonian hierarchy.The resulting expressions establish the analytic structure required to compute the post-Newtonian parameters(β,γ,δ,…)in the forthcoming flagship study.
