📚 CORE Library

<strong>Abstract:</strong> We present {C.O.R.E.}—the {Classical Origin of Reality and Emergence}—a unified framework that eliminates the need for dark energy, dark matter, spacetime singularities, wave-particle duality, and non-locality. The model integrates three principles: (1) light as a continuous electromagnetic wave (Atomic Statistical Hypothesis, ASH), (2) gravity as emergent from symmetric variations in vacuum permittivity \(\varepsilon(r)\) and permeability \(\mu(r)\) (Classical Unification of Gravity and Electromagnetism, CUGE), and (3) cosmology as a static, eternal universe where redshift arises from light scattering off electron clouds around Massive Compact Halo Objects (MACHOs, ZEUS).

<strong>Abstract:</strong> This paper presents a classical, singularity-free framework unifying gravity and electromagnetism through symmetric variations in the vacuum permittivity \(\varepsilon(r)\) and permeability \(\mu(r)\) induced by mass. Gravitational effects—including perihelion precession, light bending, time dilation, and Shapiro delay—emerge from a flat-space refractive medium governed by electromagnetic principles. The coordinate speed of light varies as \(c_{\text{coord}}(r)= 1/\sqrt{\varepsilon(r)\mu(r)}\), while local \(c\) invariance is preserved because atomic clocks and rulers scale with \(\varepsilon(r)\) and \(\mu(r)\). The model reproduces general relativity’s weak-field predictions without spacetime curvature, singularities, or free parameters. It is consistent with the Atomic Statistical Hypothesis (ASH), treating light as a continuous wave, and forms a core component of the C.O.R.E. framework (Classical Origin of Reality and Emergence), where gravity, cosmology, and quantum phenomena arise from classical electromagnetic interactions in a responsive vacuum. Crucially, real gravity alters \(\varepsilon(r)\) and \(\mu(r)\), while acceleration does not—explaining the “half-effect” in lab experiments. Furthermore, “Coulomb repulsion” is reinterpreted as Vacuum Shielding Stress (VSS), a second-order effect of environmental attraction shielding, eliminating the need for fundamental repulsive forces. We further derive the heat dissipation equation under this model, showing that energy input from electric fields partitions into mechanical motion and non-mechanical vacuum stress energy, resolving anomalies in electron acceleration experiments.

<strong>Abstract:</strong> We demonstrate that the standard relativistic energy formula \(E = \gamma m c^2\) is an incomplete effective description that conflates mechanical and non-mechanical energy storage. Within the C.O.R.E. framework—comprising CUGE (Classical Unification of Gravity and Electromagnetism), REFORM (REfractive Foundation of Relativity and Mechanics), and ASH (Atomic Statistical Hypothesis)—we derive a revised energy partition that explicitly accounts for vacuum permittivity \(\varepsilon(r)\) and permeability \(\mu(r)\). We show that: 1. The Lorentz factor \(\gamma\) emerges from the sum of kinematic (transverse Doppler) and refractive (medium-induced) effects; 2. Total energy input partitions into <strong>mechanical kinetic energy</strong> and <strong>Vacuum Shielding Stress (VSS)</strong> energy; 3. In high-energy electron acceleration, >94% of input energy is stored as VSS, not kinetic motion; 4. The local invariance of \(c\) arises from atomic scaling with \(\varepsilon(r), \mu(r)\), not spacetime geometry; 5. The "half-effect" in acceleration experiments falsifies the strict Equivalence Principle and confirms the physical reality of \(\varepsilon/\mu\) variations. This refractive foundation resolves long-standing anomalies in electron calorimetry, reinterprets inertia, and eliminates the need for relativistic mass. Energy is conserved—but not as \(\gamma m c^2\).

<strong>Abstract:</strong> This paper presents a classical, singularity-free derivation of Lorentz symmetry from the physical requirement that the phase of a continuous electromagnetic wave must remain continuous across reference frames. We show that relativistic effects—including time dilation, length contraction, Doppler shifts—emerge not from abstract postulates, but as the sum of two physical effects: (1) refractive path delay governed by Snell’s law and the eikonal equation, and (2) kinematic time dilation due to transverse motion. By integrating the ray equation \( \frac{d}{ds} (n \hat{t}) = \nabla n \) along paths with relative motion, we recover a Lorentz-type transformation where the refractive index \( n(r) = \sqrt{\varepsilon(r) \mu(r)} \) plays the role of a coordinate-dependent speed regulator. This refractive foundation unifies gravity and motion under a single electromagnetic framework, consistent with the C.O.R.E. paradigm. Crucially, real gravity alters \( \varepsilon(r) \) and \( \mu(r) \), while acceleration does not—explaining the "half-effect" in lab experiments and falsifying the strict Equivalence Principle.

<strong>Abstract:</strong> We present a complete resolution to the Navier–Stokes existence and smoothness problem through a novel physical framework derived from the <strong>CUGE (Classical Unification of Gravity and Electromagnetism)</strong> model. By reformulating fluid dynamics as wave propagation in a responsive refractive medium governed by symmetric variations in vacuum permittivity \( \varepsilon(\mathbf{r},t) \) and permeability \( \mu(\mathbf{r},t) \), we eliminate the possibility of finite-time blow-up. The key insight is that <strong>singularities are artifacts of point-source abstraction</strong>, not nature. In both gravitational and hydrodynamic systems, continuity, causality, and finite propagation speed prevent divergence. We show that the <strong>refractive n-body solution</strong>—which achieves unprecedented stability over \( 10^7 \) time units without artificial softening or tuning—provides a direct mathematical and physical pathway to proving global regularity for incompressible flows. The core mechanism is a <strong>nonlinear feedback term</strong> arising from \( \dot{n}/n \), where \( n = \sqrt{\varepsilon\mu} \), which dynamically regulates velocity gradients. This yields bounded energy growth, sub-exponential divergence, and long-term coherence—resolving turbulence not as chaos, but as structured modulation of a continuous field. All results emerge from first principles: phase continuity, Fermat’s principle, and Maxwellian electrodynamics—without postulates of photons, dark matter, or spacetime curvature. We conclude that the Navier–Stokes equations are an approximate limit of a deeper, singularity-free continuum theory rooted in classical electromagnetism.

<strong>Abstract:</strong>The Atomic Statistical Hypothesis (ASH) posits that quantum phenomena—including entanglement and Bell inequality violations—arise from local, statistical interactions between continuous electromagnetic waves and material-dependent thresholds, rather than intrinsic discreteness or non-locality. This paper derives mathematically how ASH reproduces the quantum prediction of 25% agreement probability in the three-setting Bell experiment, surpassing the classical local realistic bound of 33%. By modeling detection as a nonlinear, threshold-driven post-selection process, ASH introduces context-dependent sampling bias that mimics quantum correlations without violating locality. We provide step-by-step derivations, numerical verifications using smooth thresholds, and direct connections to Wolfgang Sturm’s classical experiments, which observe CHSH values up to S = 2.91. Critically, ASH can exceed the Tsirelson bound (\(2\sqrt{2} \approx 2.828\)) due to post-selection—a feature confirmed in Sturm’s analog systems. This extension integrates CUGE's vacuum polarization mechanism, deriving a power-law detection probability \(P_{\text{det}} \propto |\cos(2(\varphi - \alpha))|^\nu\) with \(\nu = 1/(d-1)\) from the geometric scaling of the Gravitational Vacuum Anisotropy in d-dimensional spacetime, yielding a close analytic approximation to the quantum correlation \(E(\gamma) \approx -\cos(2\gamma)\) across all angles without empirical tuning. This aligns with Occam’s razor, eliminating quantum paradoxes while preserving continuity, locality, and classical wave physics.

<strong>Abstract:</strong> Suspending interpretive assumptions such as point-mass singularities and discrete forces, we present results from an ultra-long-term gravitational n-body simulation extending to 10,000,000 time units, achieving unprecedented stability without chaotic divergence or numerical artifacts. Guided by first principles—continuity of fields, local causality, and energy conservation—this classical refractive model treats gravity as emergent from vacuum variations, eliminating unphysical infinities and restoring deterministic evolution. Detailed derivations from Fermat's principle yield the Newtonian limit in weak fields, with velocity-dependent feedback in stronger regimes that damps instabilities. The simulation outcomes—linear trajectory growth in the refractive model versus anomalous flattening in Newtonian—imply a profound resolution to the n-body "problem": chaos as illusion, stability as nature's norm. Implications extend to cosmic structures, predicting mature galaxies at high redshift without ad-hoc entities. Logic demands Occam's razor: one responsive medium simplifies over multiple unobservables. Data aligns: JWST's compact z>10 galaxies fit naturally. This coherence—unifying gravity with electromagnetic continuity—marks a classical triumph, falsifiable through lab and observational tests.

<strong>Abstract:</strong> The C.O.R.E. (Classical Origin of Reality and Emergence) framework represents a profound shift toward physical realism, eliminating interpretive constructs like spacetime curvature, singularities, photons, and dark entities. By treating light as a continuous electromagnetic wave (ASH), gravity as emergent from symmetric variations in vacuum permittivity \(\epsilon(r)\) and permeability \(\mu(r)\) (CUGE), and cosmological redshift as path elongation through electron clouds (ZEUS), it restores continuity, causality, and energy conservation. This analysis examines the consistency of gravitational equations across the core documents—C.O.R.E. overview, REFORM (REfractive Foundation of Relativity and Mechanics), and CUGE (Classical Unification of Gravity and Electromagnetism). We evaluate based on logic, math, and empirical alignment, applying Occam's razor: C.O.R.E. uses one responsive vacuum medium versus orthodoxy's multitude of unobserved additions. The equations converge seamlessly, with effects tracing to clear causes, predicting data like JWST's compact, metal-rich high-z galaxies where \(\Lambda\)CDM fails.

<strong>Summary of Wolfgang Sturm's Work:</strong> Wolfgang Sturm's research encompasses experimental and theoretical explorations in relativity, cosmology, classical physics, quantum physics, and geometry. His contributions include investigations into relativistic effects using everyday equipment, analyses of reactionless drives, antigravity demonstrations, modifications to historical experiments like Michelson-Morley, and examinations of quantum phenomena through classical analogs. Sturm frequently collaborates with scholars such as Jorma Jormakka, Miroslaw Wilczak, Alfred Schaub, and Damian Młodziankowski. For a complete overview, visit his viXra profile.

<strong>Abstract:</strong> This paper validates Jorma Jormakka’s critical assessment of historical experiments—particularly Bertozzi’s calorimetric measurements—as failing to confirm the relativistic kinetic energy formula. It demonstrates that these experiments instead support the existence of an apparent velocity-dependent mass arising not from spacetime geometry, but from a physical mechanism: force weakening under finite field propagation speed, as explained by the REFORM/CUGE framework (REfractive Foundation of Relativity and Mechanics / Classical Unification of Gravity and Electromagnetism). The analysis examines Wolfgang Sturm’s recent CRT-based measurement claiming detection of relativistic effects at low voltages (≤2.5 kV), reconciling his positive result with Jormakka’s critique through REFORM/CUGE. The framework predicts only the kinematic half of relativistic effects under laboratory acceleration, explaining both Sturm’s observed trend and Bertozzi’s excess energy deposit without invoking increasing relativistic mass. The ×2 optical scaling factor in Sturm’s analysis is shown to arise from tube-specific electron optics, not fundamental physics, and does not invalidate the interpretation. The paper concludes that what has been historically interpreted as confirmation of Special Relativity (SR) is better explained by Vacuum Shielding Stress (VSS) and phase-based response slowdown in a responsive vacuum medium.

<strong>Abstract:</strong> In classical frameworks like the ZigZag Eternal Universe System (ZEUS) within the Classical Origin of Relativity and Expansion (C.O.R.E.), redshift emerges from geometric path elongation through electron clouds, adhering to first principles of continuity and causality. A potential challenge is the anticipated blurring of high-redshift images from multiple scattering events, yet James Webb Space Telescope (JWST) data reveal remarkably sharp galaxies at z>10. This article applies Feynman path integrals—interpreted as summations over continuous wave paths consistent with the Atomic Statistical Hypothesis (ASH)—to demonstrate how interference preserves clarity. A numerical simulation of wave propagation through phase screens confirms minimal broadening, aligning with empirical data. Logic, mathematics, and explanations are detailed, emphasizing Occam's razor: one medium (electron clouds) explains gravity, redshift, CMB, and emergent quantization without invoking unobservable entities like expanding spacetime or photons.

<strong>Abstract:</strong> This article explores an alternative perspective on the Navier-Stokes existence and smoothness problem, proposing that the apparent mathematical singularities arise from the standard model's abstraction of point-like interactions, which ignores the continuous, finite structure of real fluids. It outlines the approach presented in a recent paper by David Barbeau, which reframes the problem using the CUGE (Classical Unification of Gravity and Electromagnetism) framework. This framework models interactions via symmetric variations in a responsive medium's properties (vacuum permittivity \(\varepsilon\) and permeability \(\mu\)). By applying this refractive principle to fluid dynamics, the model introduces a self-regulating feedback mechanism that bounds velocities and gradients, preventing blow-up. This suggests that the Navier-Stokes equations, while highly accurate for prediction, are an incomplete description when isolated from the underlying continuous dynamics of the medium. The resolution lies not in abstract mathematical proofs within the original equations, but in embedding them within a physically causal and continuous framework where singularities are naturally precluded.

<strong>Abstract:</strong> This paper presents a radical reinterpretation of the relativistic factor \(\gamma\), not as a consequence of spacetime geometry, but as a measurable expression of <strong>phase efficiency</strong> in a responsive electromagnetic vacuum. By reducing \(\gamma\) to its most fundamental physical components—distance, time, motion, and wavefront continuity—we demonstrate that the phenomena attributed to special relativity (time dilation, mass-energy equivalence, kinematic limits) emerge naturally from classical wave mechanics. This derivation dissolves the apparent violations of causality in quantum mechanics, replacing non-locality and wavefunction collapse with pre-established coherence and local threshold detection. The result is a fully deterministic, singularity-free framework consistent with high-precision experiments and modern astrophysical observations.

<strong>Abstract:</strong> The C.O.R.E. (Classical Origin of Reality and Emergence) framework redefines gravity not as spacetime curvature but as an emergent effect from symmetric variations in vacuum permittivity (\(\varepsilon\)) and permeability (\(\mu\)). This classical approach, grounded in continuity and causality, derives the anomalous perihelion precession of Mercury through a rigorous symmetry count: six contributions—two from time scaling, two from \(\varepsilon\) variations, and two from \(\mu\) variations—each proportional to \(GM/(2c^2r)\). Far from arbitrary, this logic adheres to first principles, eliminating interpretive entities like singularities and photons while aligning with empirical data. By Occam's razor, C.O.R.E. simplifies physics: one responsive vacuum medium explains precession, light bending, and more, converging with ASH (light as continuous wave) and ZEUS (static cosmology). This is no fringe idea but a profound classical revival, where nature's data—Mercury's 43 arcseconds per century—agrees without geometric baggage.