This work establishes a quantitative entanglement model built upon the vacuum quantum medium hypothesis. Instead of postulating instantaneous wave‑function collapse and intrinsic randomness, entanglement is interpreted as long‑range synchronized coupling among particles mediated by vacuum medium units. Based on geometric shell‑layer packing constraints of medium units, this model derives a finite critical distance for stable entanglement coupling. Entanglement completeness decays in piecewise fashion with particle separation, and environmental disturbances including geomagnetic field, thermal noise and ionospheric effects are introduced as multiplicative correction coefficients. Corresponding deterministic spin‑synchronization geometric formulas replace the stochastic probability framework of Bell‑inequality statistics. Extensions to multi‑particle GHZ‑type network entanglement are also provided. Calculated results show reasonable order‑of‑magnitude consistency with existing experimental observations including the Micius satellite‑ground entanglement test. A falsifiable prediction is put forward: under near‑Earth ionospheric‑geomagnetic conditions, entanglement synchronization signals will exhibit a steep cliff‑style drop within the 1400–1490 km distance interval. Light‑weight engineering formulas are supplied for rapid practical estimation. This model offers an alternative deterministic geometric description for quantum entanglement phenomena.
This work establishes a quantitative entanglement model built upon the vacuum quantum medium hypothesis. Instead of postulating instantaneous wave‑function collapse and intrinsic randomness, entanglement is interpreted as long‑range synchronized coupling among particles mediated by vacuum medium units. Based on geometric shell‑layer packing constraints of medium units, this model derives a finite critical distance for stable entanglement coupling. Entanglement completeness decays in piecewise fashion with particle separation, and environmental disturbances including geomagnetic field, thermal noise and ionospheric effects are introduced as multiplicative correction coefficients. Corresponding deterministic spin‑synchronization geometric formulas replace the stochastic probability framework of Bell‑inequality statistics. Extensions to multi‑particle GHZ‑type network entanglement are also provided. Calculated results show reasonable order‑of‑magnitude consistency with existing experimental observations including the Micius satellite‑ground entanglement test. A falsifiable prediction is put forward: under near‑Earth ionospheric‑geomagnetic conditions, entanglement synchronization signals will exhibit a steep cliff‑style drop within the 1400–1490 km distance interval. Light‑weight engineering formulas are supplied for rapid practical estimation. This model offers an alternative deterministic geometric description for quantum entanglement phenomena.
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.
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 introduces the 'Information-Union' framework, a novel model for quantum entanglement derived from the foundational principle of Information-Processing Invariance, expressed as 𝑐²= 𝑣 ⋅ 𝐿. This principle posits a universal 'vacuum bandwidth' that governs the trade-off between a system's temporal update rate (𝑣) and its spatial expression (𝐿). We model entanglement as a physical phase transition termed the 'Information Union,' where constituent particles surrender local spatial metrics to a global, photonic mediator. Applying Landauer's principle and Vopson's mass-energy-information equivalence, we demonstrate that the establishment of this union requires quantifiable 'merger work' (𝑾𝚽) against the vacuum's inherent resistance. The mediator acts as a hardware channel coupling the system to the universe's minimal update rate, 𝜖, which we show correlates exactly with the Hubble constant (𝐻o). The framework culminates in a falsifiable prediction: entanglement maintained over cosmological distances must exhibit a distance-dependent degradation in synchronicity – a 'coincidence jitter' – proportional to √𝐿. This intrinsic decoherence, independent of environmental noise, provides a direct experimental test of the coupling between quantum nonlocality and cosmic expansion.
Abstract For ultra-long-distance free-space quantum communication such as satellite-to-ground quantum key distribution, decoherence is conventionally described by an exponential decay model. Such exponential environmental decoherence theory works well for short and medium propagation distances, yet its validity over thousands of kilometers of vacuum transmission remains open to discussion. This work proposes a phenomenological model of intrinsic vacuum coherence leakage for freely propagating entangled photons. Different from traditional exponential decoherence, the model predicts sub-exponential decay of entanglement fidelity with propagation distance. Numerical comparison indicates that the two models yield nearly identical predictions at short distances, while obvious deviations gradually emerge for ultra-long transmission. We further derive the modified secure key rate under the sub-exponential dissipation model. The theoretical prediction is testable using existing space-ground quantum experimental platforms. This preprint provides a new candidate framework to describe quantum channel behavior for deep-space and ultra-long-range quantum communication. This manuscript is released as a preprint for open discussion and academic archiving. No references are attached in the initial version; supplementary citations will be added for subsequent formal journal submission.
Attention: This version is preliminary and contains errors that will be corrected in subsequent publications. Standard quantum mechanics postulates the existence of entangled states and instantaneous correlations between distant particles, yet offers no physical mechanism explaining how these correlations arise. This paper proposes an explanation within FKGP 4.0: quantum entanglement is the projection of a single informational state of the chi-channel — a layer of reality decoupled from the spacetime metric and hidden from the observer by the 'light cloak'. The properties of the chi-channel (globality, absence of causal constraints, finite information-processing speed Veff >> c) naturally give rise to all known entanglement phenomena without superluminal energy transfer. An upper bound on maximal entanglement is derived via the generalised Bekenstein–Hawking holographic entropy, yielding the verifiable scaling S ~ R 2.46. A planetary-scale Bell test (Earth–Mars) is proposed as a falsifying experiment.
Quantum entanglement is a central resource of quantum information science, yet its correlations are ordinarily treated as properties of the quantum state rather than as the outcome of an underlying physical process. Here we explore the hypothesis that these correlations are mediated dynamically by a field propagating locally at finite velocity through an extension of ordinary spacetime. The model embeds physical (3,1)-dimensional spacetime in a warped five-dimensional geometry containing an additional timelike coordinate. Within the adopted geometric ansatz, the form of the extended spacetime metric is determined by the five-dimensional vacuum Einstein equations. A massless field propagating through the resulting five-dimensional bulk can mediate correlations whose projection onto observable four-dimensional spacetime connects arbitrarily distant locations at equal laboratory time, while preserving operational no-signaling. Coupling this field to a Bohm--Bub-inspired collapse scheme provides a possible dynamical realization of entanglement correlations and, under a stated statistical consistency condition, reproduces Born statistics. The framework leads to a concrete experimental test. Two nominally independent Bell pairs are predicted to develop a weak, distance-dependent contextual correlation between particles belonging to different pairs, as a consequence of bulk-field mediation. This cross-pair correlation is absent in standard quantum mechanics for independently prepared systems and is predicted to decrease as the inverse square of their separation. It could therefore be tested by varying the distance between two simultaneous Bell experiments using existing photonic technology. Observation of such a signal would support a dynamical spacetime account of quantum entanglement and could have implications for quantum networks employing multiple independent entangled resources.