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Universal Entanglement from the Unity of the Continuous Field in UD Theory

Dan Zhu

Published Jun 23, 2026• 0 citations
Publisher

Abstract

We derive universal quantum entanglement from the unity of the continuous field in UD theory. Matter formation converts the $U$ attribute in space ($U_u$) into the $U$ attribute in matter ($D_u$) via the vertex $\lambda U_u D_d$; all $D_u$ excitations are perturbations of the same underlying $U_u$ field. The correlation function of these perturbations inherits the connectedness of space. Because the physical observable $\langle\hat S_A\hat S_B\rangle\propto e^{-m_{\rm eff}r}$, this background correlation does not yield observable Bell violation; a conditionally normalized $E=\cos\Delta\theta$ is a formal construct. When two (or more) particles originate from the same matter formation event, their $D_u$ excitations share the same $U_u$ source, and momentum conservation $\sum\mathbf{k}_a=0$ elevates the weak background correlation to strong, distance-independent multi-particle entanglement, with $\langle\mathcal{B}\rangle=2\sqrt{2}$. The measurement process is the unitary coupling of $D_u$ to $D_d$ via $\hat H_{\rm meas}=(m_0^2/8)\int d^3x\,\hat\varphi_{D_u}\hat\varphi_{D_d}$; the Born rule follows from the reduced density matrix. All results are derived from first principles without collapse postulates or adjustable parameters.

DOI
10.5281/zenodo.20809229

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Universal Entanglement from the Unity of the Continuous Field in UD Theory

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We derive universal quantum entanglement from the unity of the continuous field in UD theory. Matter formation converts the UUU attribute in space (UuU_uUu​) into the UUU attribute in matter (DuD_uDu​) via the vertex λUuDd\lambda U_u D_dλUu​Dd​; all DuD_uDu​ excitations are perturbations of the same underlying UuU_uUu​ field. The correlation function of these perturbations inherits the connectedness of space. Because the physical observable ⟨S^AS^B⟩∝e−meffr\langle\hat S_A\hat S_B\rangle\propto e^{-m_{\rm eff}r}⟨S^A​S^B​⟩∝e−meff​r, this background correlation does not yield observable Bell violation; a conditionally normalized E=cos⁡ΔθE=\cos\Delta\thetaE=cosΔθ is a formal construct. When two (or more) particles originate from the same matter formation event, their DuD_uDu​ excitations share the same UuU_uUu​ source, and momentum conservation ∑ka=0\sum\mathbf{k}_a=0∑ka​=0 elevates the weak background correlation to strong, distance-independent multi-particle entanglement, with ⟨B⟩=22\langle\mathcal{B}\rangle=2\sqrt{2}⟨B⟩=22​. The measurement process is the unitary coupling of DuD_uDu​ to DdD_dDd​ via H^meas=(m02/8)∫d3x φ^Duφ^Dd\hat H_{\rm meas}=(m_0^2/8)\int d^3x\,\hat\varphi_{D_u}\hat\varphi_{D_d}H^meas​=(m02​/8)∫d3xφ^​Du​​φ^​Dd​​; the Born rule follows from the reduced density matrix. All results are derived from first principles without collapse postulates or adjustable parameters.
We derive universal quantum entanglement from the unity of the continuous field in UD theory. Matter formation converts the U attribute in space (UU) into the U attribute in matter (DU) via the vertex λUUDD; all DU excitations are perturbations of the same underlying UU field. The correlation function of these perturbations inherits the connectedness of space. Because the physical observable ⟨ŜAŜB⟩ ∝ e^(-meff r), this background correlation does not yield observable Bell violation; a conditionally normalized E = cos Δθ is a formal construct. When two (or more) particles originate from the same matter formation event, their DU excitations share the same UU source, and momentum conservation ∑ka = 0 elevates the weak background correlation to strong, distance-independent multi-particle entanglement, with ⟨B⟩ = 2√2. The measurement process is the unitary coupling of DU to DD via Ĥmeas = (m0²/4) ∫d³x φ̂DU φ̂DD; the Born rule follows from the reduced density matrix. All results are derived from first principles without collapse postulates or adjustable parameters.
We derive the foundational postulates of quantum mechanics from the UD axioms. Starting from the four-aspect field structure, we construct the spinor projection ψ=(Uu+iUd,  Dd+iDu)T\psi = (U_u + iU_d,\; D_d + iD_u)^{\mathsf{T}}ψ=(Uu​+iUd​,Dd​+iDu​)T. The U(1)U(1)U(1) Noether current from the Dirac action gives the conserved probability density, and the global normalization axiom yields the Born rule. The DuD_uDu​ field (U in matter) is continuous and linear, explaining wave-like phenomena such as interference. The DdD_dDd​ field (D in matter) is localized and determinate, explaining particle-like behavior and the absence of macroscopic superpositions. The measurement process is described by a coupling Hamiltonian derived from the UD interaction, which entangles the DuD_uDu​ field with a macroscopic DdD_dDd​ apparatus, leading to dissipation of DuD_uDu​ coherence and the Born rule without collapse. The U↔DU\leftrightarrow DU↔D duality implies the existence of antiparticles with opposite phase. All derivations are self-contained and logically inevitable.
ABSTRACT Quantum entanglement is one of the most mysterious phenomena in quantum mechanics. Based on the fundamental axioms of UD theory, this paper demonstrates that quantum entanglement is the coherent structure of D_U in the continuous space U. In UD theory, space is the U attribute itself—continuous and non-local by nature. The D_U field is inherently indefinite; the D_D field is inherently definite. Superposition is a category mistake—D_U simply has no definite state until it couples to D_D. Two particles become entangled when their D_U fields form a single coherent structure in U. The coherence length is ξ = 2πe^π ℓ_P ≈ 2.3×10^{-33} m, derived from UD constants. No wavefunction collapse occurs; no superluminal signaling is possible. The mystery of quantum entanglement is unveiled. KEY FINDINGS 1. D_U is inherently indefinite; D_D is inherently definite. Superposition is a category mistake—D_U simply has no definite state. 2. Quantum entanglement is a single coherent structure of D_U in the continuous space U—no action at a distance. 3. Coherence length is exactly ξ = 2πe^π ℓ_P ≈ 2.3×10^{-33} m, derived from UD constants. 4. No wavefunction collapse exists—measurement is indefinite D_U coupling to definite D_D. 5. Apparent randomness is epistemic—it arises from ignorance of initial phases, not from ontic indeterminism. 6. No superluminal signaling is possible—the correlation is a static property of the extended coherent structure. ELIMINATED ASSUMPTIONS - Action at a distance → Continuity of U (space itself)- Wavefunction collapse → Continuous D_U evolution- Superposition of states → D_U is inherently indefinite- Ontic randomness → Epistemic probability- Abstract quantum states → Physical D_U field Keywords: quantum entanglement, Bell inequality, non-locality, continuous space, UD theory
In the Cosmology of the Quarkbase, quantum particles and photons are interpreted as excitations of an etheric plasma represented by the scalar or vector field Ψ(x,t). An experiment that, in standard quantum theory, produces an entangled pair instead generates in this framework a single non-local field excitation: a coherent combination of Ψ-modes correlated through conservation of momentum, spin, and polarization, as well as through the coupling topology between local sources (quarkbases). Local measurement acts as a projection on this extended excitation, producing the experimentally observed strong correlations without any exchange of causal signals between detectors. The Quarkbase formalism introduces explicit medium parameters —density ρp, compressibility K, and effective mass mΨ— that define physical scales such as the screening length λ = 1/mΨ. These quantities determine the spatial decay of entanglement visibility according to V(r) ∝ e⁻ʳ/λ / r, and the effective CHSH parameter becomes Seff = C(r) 2√2. Therefore, if the vacuum possesses a finite λ, Bell-type correlations should attenuate exponentially with distance, providing a falsifiable signature of a massive or screened etheric field. Mathematically, the framework reproduces the predictions of quantum field theory —Bell states, coincidence probabilities, CHSH violation— while offering an ontological interpretation in which entanglement arises from the geometry and coherence of the Ψ-field rather than from instantaneous nonlocal action. The theory therefore unifies microscopic quantum behavior with macroscopic medium dynamics, transforming questions about “collapse” and “nonlocality” into experimentally testable properties of the underlying ether-plasma.
This paper is Part II of the UD theory foundational series. Part I derives general relativity from the scalar projection (doi: 10.5281/zenodo.19494052). Abstract: This paper derives quantum mechanics from the spinor projection of UD theory. The four-aspect structure (U_U, U_D, D_D, D_U) naturally forms an SU(2) doublet ψ = (U_U + iU_D, D_D + iD_U)^T. Using the equilibrium background values and the mass scale from Part I, we derive the coupled field equations and prove their equivalence to the Dirac equation. In the non-relativistic limit, the Pauli equation follows, reducing to the Schrödinger equation for spinless particles. The SU(2) symmetry is intrinsic, and the U(1) subgroup gives the conserved probability current. Quantum phenomena such as interference are explained directly in UD terms: the D_U field is continuous and interferes; "particles" are discrete coupling events between D_U and D_D. The standard quantum mechanical notions of superposition and collapse are not fundamental—they are artifacts of describing a continuous field in particle language. The UD theory is a metatheoretical framework. It does not replace existing theories but reveals their origins. This paper demonstrates that quantum mechanics is the spinor projection of UD theory—the natural mathematical consequence of extracting a two-component spinor from the four-aspect structure.
This paper extends the stochastic electrodynamic framework of Paper 1 [3] to multiparticle systems, providing a physical derivation of quantum entanglement. When a highenergy gamma ray creates an electron-positron pair, both particles emerge from the same spacetime point and share a common electromagnetic quantum field. We propose that the electromagnetic vacuum retains a cross-correlation component S(12)E (x1, x2, ω) in their joint electromagnetic quantum field, arising from the common creation event. The spatial dependence of this cross-correlation—a sinc(ωr12/c) factor—is derived from the known two-point vacuum correlation function of the electromagnetic field, not postulated. This cross-correlation is identified as the physical carrier of quantum entanglement. The two particles undergo correlated Brownian motion in six-dimensional configuration space, each with diffusion coefficient D = ℏ/2m derived in [3]. Nelson’s stochastic mechanics in configuration space gives the two-particle Schrödinger equation. The foundational ergodicity assumption underlying Papers 1 and 2—that the coupled electron-vacuum system admits a unique stationary ergodic measure—is proved in the companion Paper 3 [5] via the Caldeira–Leggett model and the Ford–Kac–Mazur theorem. The EPR paradox is resolved: the instantaneous correlation upon measurement is a consequence of conditional probability applied to a joint stochastic process, not a physical signal. Bell inequality violations are derived explicitly: the cross-correlation is nonlocal in configuration space, bypassing Bell’s locality assumption while satisfying the no-signalling theorem. Decoherence arises naturally as disruption of S(12)E by environmental electromagnetic noise. Fermi and Bose statistics emerge as boundary conditions on the joint stochastic process in configuration space.