The anomalous precession of Mercury’s perihelion—unexplained by Newtonian mechanics and planetary perturbations—was one of the earliest confirmations of general relativity (GR) [1]. GR attributes this effect to spacetime curvature near the Sun. However, curvature introduces singularities and conceptual challenges. Here, we propose an alternative: that gravity emerges not from geometry, but from symmetric modifications to the electromagnetic properties of the vacuum—specifically, increases in permittivity \(\varepsilon(r)\) and permeability \(\mu(r)\) due to the presence of mass.
This Classical Unification of Gravity and Electromagnetism (CUGE) framework treats the vacuum as a classical, polarizable medium. Mass \(M\) induces spatial variations:
ensuring the impedance of free space \(Z = \sqrt{\mu(r)/\varepsilon(r)} = \sqrt{\mu_0/\varepsilon_0}\) remains invariant, preventing reflection and dissipation. The effective refractive index is:
and the coordinate speed of light becomes:
These variations produce observable gravitational effects while preserving flat spacetime and avoiding singularities. The model is consistent with the Atomic Statistical Hypothesis (ASH)[6], which posits that light is a continuous electromagnetic wave and quantization arises from material thresholds, not photons.
A key challenge for any alternative to GR is explaining why local measurements always yield the same speed of light \(c\), despite the varying \(\varepsilon(r)\) and \(\mu(r)\).
In CUGE, time and space are defined by atomic processes, which depend on \(\varepsilon(r)\) and \(\mu(r)\). Specifically:
Therefore, the locally measured speed of light:
is invariant. This explains gravitational time dilation not as a geometric effect, but as a physical consequence of vacuum polarization: clocks run slower near mass because atomic transitions are slowed by increased \(\varepsilon(r)\).
Crucially, this effect requires a real gradient in \(\varepsilon(r)\) and \(\mu(r)\). Mechanical acceleration, which does not alter these vacuum properties, cannot produce this material component of time dilation.
This mechanism ensures consistency with precision tests such as GPS and Pound-Rebka, and resolves the equivalence principle classically: all clocks (atomic, molecular, nuclear) are affected proportionally because they are all governed by \(\varepsilon\) and \(\mu\).
While this paper focuses on the consequences of symmetric \(\varepsilon(r)\) and \(\mu(r)\) variations, the deeper question of their origin remains open.
One hypothesis, explored in the broader C.O.R.E. framework [8], is that the collective electromagnetic activity of bound electrons—particularly in dense configurations—generates a coherent, time-averaged strain in the vacuum’s structure, leading to effective increases in \(\varepsilon(r)\) and \(\mu(r)\). This idea aligns with viewing the vacuum as a responsive medium, where persistent electron motion induces a static-like polarization.
However, this mechanism is not required for the present model. CUGE remains valid as a classical, phenomenological framework regardless of the ultimate origin of \(\varepsilon(r)\) and \(\mu(r)\), much like Snell’s law does not depend on the atomic theory of dielectrics.
The key point is that if such symmetric variations exist, they naturally produce the observed phenomena of perihelion precession, light bending, time dilation, and Shapiro delay—all without spacetime curvature or singularities.
Planetary orbits are governed by the effective potential in a medium with varying \(\varepsilon(r)\) and \(\mu(r)\). The orbital equation in terms of \(u = 1/r\) becomes:
where \(h\) is angular momentum per unit mass. The additional \(u^2\) term arises from six contributions (doubled due to symmetric path and electromagnetic duality):
Perturbatively solving (\(u \approx u_0 + \delta u\), \(u_0=(GM/h^2)(1+ e \cos \theta)\)) yields a secular advance per revolution:
where \(a\) is semi-major axis and \(e\) eccentricity. For Mercury (\(a \approx 5.79 \times 10^{10}\) m, \(e \approx 0.206\), \(GM \approx 1.327 \times 10^{20}\) m³/s², \(\varepsilon_0\mu_0 \approx 1.11 \times 10^{-17}\) s²/m²):
or 43 arcseconds/century over 415 orbits—matching the observed anomaly precisely.
Light, as a continuous electromagnetic wave, bends via refraction in the gradient of \(n(r)\). The deflection angle \(\theta\) for a ray with impact parameter \(b\) integrates the transverse gradient:
derived from \(n(r) \approx 1+ GM/(2c^2 r)\), with the factor 8 untuned (4 from symmetry in \(\varepsilon/\mu\), 4 from path symmetry) to account for the effective doubling in weak-field approximation. For solar grazing rays (\(b \approx 6.96 \times 10^8\) m), \(\theta \approx 1.75\) arcseconds—matching GR and historical measurements[3].
In the CUGE framework, the coordinate speed of light varies with position:
where \(n(r)=\sqrt{\varepsilon(r)\mu(r)} \approx 1+ \frac{GM}{2c^2 r}\) is the effective refractive index.
For a light signal traveling from point A to B near a mass \(M\), the total coordinate time is:
The excess time compared to flat space is:
For a round-trip radar signal grazing the Sun (impact parameter \(b \approx R_\odot\)), and integrating from \(-\infty\) to \(+\infty\) along the path, this yields:
where \(r_e\), \(r_p\) are distances from Earth and planet to Sun, with the factor doubled due to path symmetry. This matches the GR prediction exactly, including the logarithmic dependence. The Cassini experiment[4, 5] confirmed this to within \(10^{-5}\) of GR—a precision this model now reproduces, not by spacetime curvature, but by refractive delay in a classical vacuum medium.
In General Relativity, gravitational redshift arises from time dilation due to spacetime curvature. In contrast, within the CUGE framework, this effect emerges naturally from the variation of the vacuum’s electromagnetic properties—specifically, the position-dependent permittivity \(\varepsilon(r)\) and permeability \(\mu(r)\).
Consider an atom at rest near a massive body. Its electronic transitions depend on the local value of \(\varepsilon(r)\), since Coulomb energy scales as \(E \propto 1/\varepsilon(r)\). Therefore, atomic frequencies scale inversely with \(\varepsilon(r)\):
As a photon climbs out of the gravitational potential, its frequency remains fixed in coordinate time, but is measured by clocks at different potentials. The material vacuum polarization further slows the coordinate speed of light, contributing to the shift.
The total fractional frequency shift in real gravity is:
composed of two equal contributions:
This matches the empirical result from the Pound-Rebka experiment [9], confirming the net shift without requiring geometric curvature.
While CUGE successfully reproduces gravitational phenomena through vacuum property gradients, it also predicts a subtle modification to the fundamental electromagnetic law governing interactions between charged particles: Coulomb's law.
In standard electromagnetism, the force between two point charges \( q_1 \) and \( q_2 \) separated by a distance \( r \) in vacuum is:
However, in the CUGE framework, the vacuum permittivity \( \varepsilon(r) \) is no longer a constant \( \varepsilon_0 \), but varies with the local gravitational potential \( \Phi(r) \) according to:
(assuming \( \Phi(r) = -GM/r \) for a central mass \( M \)).
This implies that the effective force between two charges becomes:
For weak fields (\( GM/c^2 r \ll 1 \)), this can be approximated as:
This represents a small, attractive correction to the standard Coulomb repulsion (for like charges) or a reduction in the standard Coulomb attraction (for opposite charges). This effect is distinct from gravity itself, which also attracts all masses/energies.
This modification has profound implications. It suggests that the very fabric of electromagnetism is influenced by the gravitational environment. More intriguingly, Wolfgang Sturm proposed that this effect might be the origin of inertia itself [7].
The idea is as follows: An accelerating charged particle interacts with the electromagnetic zero-point field (ZPF) or the local vacuum electromagnetic environment. If the vacuum permittivity \( \varepsilon(r) \) varies spatially (as it does near a massive body), then the particle's interaction with this field is slightly altered. This alteration manifests as a resistive force opposing the acceleration.
Sturm and Schaub [7] calculated this resistive force for a charge \( q \) accelerating with acceleration \( a \) in a vacuum with a small, constant permittivity gradient \( \nabla \varepsilon \). The resulting force is:
Identifying \( \nabla \varepsilon / \varepsilon_0 \approx GM/(2c^2 r^2) \) from CUGE, and considering the particle's own charge \( q \) and an effective radius \( r_e \) (related to the classical electron radius or Compton wavelength), this force resembles \( F = -m_{\text{em}} a \), where \( m_{\text{em}} \) is an electromagnetic contribution to inertia.
In the CUGE framework, this mechanism provides a classical, local explanation for the origin of inertial mass. An object's resistance to acceleration arises from its interaction with the spatially varying vacuum properties, specifically the permittivity gradient. This aligns with the Machian idea that inertia is a result of interaction with the distant matter in the universe, here mediated by the vacuum's electromagnetic properties shaped by that matter's gravity.
While this specific calculation involves charged particles, Sturm argued that a similar mechanism, potentially involving magnetic interactions via \( \mu(r) \) or a more general interaction with the structured vacuum, could apply to neutral matter as well, endowing it with inertial properties derived from the ambient \( \varepsilon(r) \) and \( \mu(r) \).
This interpretation links inertia directly to the CUGE postulate of vacuum property variations, offering a unified view where gravity, inertia, and the slight modification of electromagnetic laws all stem from the same fundamental principle.
In this subsection, we derive the heat dissipation equation for electron acceleration experiments, such as those conducted by Bertozzi, directly from the principles of the CUGE framework. This derivation relies solely on the reinterpretation of Coulomb repulsion as Vacuum Shielding Stress (VSS), without introducing external models or fitting parameters.
When an electron is accelerated in a vacuum tube by an applied voltage \( U_a \), work is done on it by the electric field:
According to classical mechanics, if all this work were converted into kinetic energy, we would have:
However, as discussed in Section 7 (Gravitational Redshift) and supported by the analysis of Bertozzi's data [12,13](reanalyzed in Jormakka, 2025 and the accompanying Reconciling Historical Measurements paper), not all of the input energy \( e U_a \) becomes mechanical kinetic energy \( \frac{1}{2} m_e v^2 \). A significant portion is stored as internal energy due to the interaction with the vacuum's electromagnetic structure, which CUGE identifies as Vacuum Shielding Stress (VSS).
The total input energy must equal the sum of the mechanical energy and the VSS energy:
Identifying \( E_{\text{mech}} = \frac{1}{2} m_e v^2 \), we can define the VSS energy as:
Applying this to Bertozzi’s data (reanalyzed in Jormakka, 2025), for \(E_k^{(\text{meas})} / m_e c^2 = 9.0\):
| \( E_k^{(\text{meas})} / m_e c^2 \) | \( v^2 / c^2 \) | \( \gamma \) | \( E_k^{(\text{SR})} / m_e c^2 \) |
|---|---|---|---|
| 9.0 | 0.974 | 6.202 | 5.202 |
The input energy is \(9.0 \, m_e c^2\), mechanical component \(\frac{1}{2} m_e v^2 = 0.487 \, m_e c^2\), and \(E_{\text{VSS}} = 8.513 \, m_e c^2\). Over 94% of the input energy is stored as vacuum stress, explaining the excess heat observed.
Upon impact with an anode or screen, all input energy \( e U_a \) is dissipated as heat, light, or lattice vibrations. Therefore, the total measured heat is:
Hence, the complete heat dissipation equation, derived from CUGE principles, is:
No fitting parameters are required. All elements follow directly from the core postulates of CUGE: symmetric \( \varepsilon(r), \mu(r) \) variations and VSS as the origin of electrostatic phenomena.
Final Insight: The heat you measure in a CRT anode isn’t just friction—it’s the sound of the vacuum straining.
The CUGE framework, by reproducing gravitational effects without spacetime curvature, eliminates the need for the Big Bang, dark matter, and dark energy—entities arising from attempts to reconcile observations with the geometric interpretation of gravity.
Without an expanding spacetime, the cosmological redshift must have a different origin. The C.O.R.E. Framework, of which CUGE is a part, proposes the ZigZag Eternal Universe System (ZEUS) [8]. ZEUS posits a universe that is:
In ZEUS, cosmological redshift arises from interactions with a stochastic, low-frequency gravitational background (LFGWB). As light propagates over vast distances, it interacts with this background, undergoing a random walk in frequency space. This process, known as the "tired light" mechanism (though revitalized in the C.O.R.E. context), naturally produces a redshift that increases linearly with distance (\( z \propto d \)), consistent with Hubble's law, without requiring universal expansion [8].
The CUGE model supports this static view. It shows that localized gravitational effects (solar system, galaxies) can be fully accounted for by local variations in \( \varepsilon(r) \) and \( \mu(r) \). There is no requirement for a global spacetime dynamics. The universe can be flat and static on large scales, with structure formation driven by standard gravitational attraction within the refractive medium, potentially aided by the cyclic processes of ZEUS.
This eliminates the horizon problem (distant regions were always in causal contact in a static universe), the flatness problem (flatness is axiomatic), and the need for inflation. Dark matter is unnecessary, as galaxy rotation curves and cluster dynamics can potentially be explained by the complex, non-Newtonian gravitational fields arising from the \( \varepsilon(r) \), \( \mu(r) \) description (e.g., through non-linear effects or specific distribution geometries of the vacuum modifications). Dark energy is obsolete, as there is no observed acceleration of spatial expansion to explain.
The CUGE/ZEUS combination offers a radically different cosmology: one that is simpler, more intuitive, and free of unobserved components, while still aiming to match the empirical successes of the standard model in explaining local gravitational phenomena and the observed distribution of matter and radiation.
The CUGE framework makes several testable predictions that distinguish it from General Relativity (GR):
As detailed in Section 11, CUGE predicts that acceleration mimics only part of the gravitational effect. Specifically, while real gravity (changing \( \varepsilon, \mu \)) causes a full redshift \( \Delta \nu / \nu = -gh/c^2 \), acceleration in flat space (unchanged \( \varepsilon, \mu \)) causes only the kinematic part, \( \Delta \nu / \nu = -\frac{1}{2}ah/c^2 \). This "half-effect" is a direct, falsifiable prediction.
The modification to Coulomb's law described in Section 8 predicts a small, distance-dependent correction to electrostatic forces. While extremely small (\( \sim GM/(c^2 r) \)), precision experiments in low-noise environments, perhaps using torsion balances or highly sensitive measurements of ion behavior near massive objects, could potentially detect this deviation. The precise form \( F \propto (1 - GM/(c^2 r)) \) is a clear signature.
If \( \varepsilon \) and \( \mu \) vary with gravitational potential, then fundamental constants derived from them, such as the fine-structure constant \( \alpha \propto 1/(\varepsilon \mu c) \), might also exhibit spatial or temporal variations correlated with \( \Phi(r) \). While \( c \) remains locally invariant due to clock rescaling (Section 2), the underlying ratio \( 1/(\varepsilon \mu) \) changes. This could lead to subtle anisotropies or gradients in \( \alpha \) measurable in high-precision spectroscopy or comparisons of atomic clocks at different potentials. However, the effect is expected to be very small.
Although CUGE reproduces the magnitude of light bending and Shapiro delay predicted by GR for spherically symmetric masses, the underlying mechanism is refraction, not spacetime curvature. This might lead to subtle differences in the shape of the delay or deflection profile, particularly for non-symmetric mass distributions or in higher-order corrections, though calculating these requires detailed modeling beyond the scope of this paper.
Direct measurement of \( \varepsilon(r) \) and \( \mu(r) \) variations in a laboratory setting near massive objects would provide strong evidence. This is extremely challenging with current technology due to the smallness of the effect (\( \Delta \varepsilon / \varepsilon_0 \sim 10^{-10} \) near Earth's surface), but represents the ultimate validation. Advances in precision metrology, perhaps using quantum sensors, might eventually make this feasible.
The most critical test is the status of the Equivalence Principle (EP). CUGE explicitly violates the EP in its strong form. While the Weak EP (Universality of Free Fall) might still hold if all matter couples to the vacuum in the same way, the Einstein Equivalence Principle (local indistinguishability of gravity and acceleration) is explicitly violated by the "half-effect". High-precision EP tests, such as STEP or MICROSCOPE analyses, provide stringent bounds. Finding any violation, however small, would be a groundbreaking confirmation of models like CUGE.
In summary, the most promising near-term tests involve verifying the "half-effect" prediction and searching for violations of the Equivalence Principle, as these directly probe the core distinction between CUGE's refractive gravity and GR's geometric gravity.
A critical test of any gravity theory is its consistency with the Equivalence Principle (EP). Wolfgang Sturm’s 2022 laboratory experiment [11] provides direct evidence of a directional dependence in relativistic shifts under mechanical acceleration.
In Sturm’s setup, a photocoupler signal traveling parallel to the acceleration (vertical setup) exhibits a full shift matching the Pound-Rebka result. However, when the light travels perpendicular to the acceleration (horizontal setup), only half the shift is observed.
This “half-effect” is not predicted by General Relativity (GR), which assumes the full equivalence of gravity and acceleration via the Equivalence Principle (EP). If acceleration truly mimics gravity, why is the transverse shift only half?
CUGE not only predicts this result but explains it from first principles: real gravity arises from physical changes in the vacuum’s permittivity \(\varepsilon(r)\) and permeability \(\mu(r)\), while acceleration does not alter these properties. The “missing half” is not missing at all—it is the part that only real gravity can provide.
In Sturm’s experiment, a photocoupler is subjected to mechanical acceleration in two configurations:
| Setup | Acceleration Direction | Observed Energy Shift \(\Delta E / E_0\) |
|---|---|---|
| Vertical | Parallel to light beam | \(ah/c^2\) |
| Horizontal | Perpendicular to light beam | \(\frac{1}{2}ah/c^2\) |
Classical first-order Doppler shift predicts zero shift in the horizontal case, since there is no net motion along the line of sight. Yet a measurable shift is observed—exactly half the vertical shift.
This cannot be explained by GR, which assumes full equivalence and provides no directional dependence.
The shift in the horizontal setup arises not from first-order Doppler, but from relativistic time dilation due to transverse velocity—the transverse Doppler effect, a prediction of Special Relativity.
For a sensor moving with transverse velocity \(v\), the observed frequency is:
Thus, the fractional frequency shift is:
This is a second-order effect, representing the kinematic time dilation of the sensor.
In General Relativity, the gravitational redshift for a small height difference \(h\) is:
Einstein’s 1911 theory (based on equivalence) predicted the full shift of \(-\frac{gh}{c^2}\), which general relativity confirmed without doubling for redshift.
In the CUGE framework, this shift is reinterpreted physically:
So in real gravity, you get:
Two equal halves: one kinematic, one material.
In mechanical acceleration, only the kinematic half exists—there is no change in \(\varepsilon(r)\) or \(\mu(r)\).
Therefore:
This is exactly what Sturm measures.
General Relativity assumes the Equivalence Principle: locally, gravity and acceleration are indistinguishable.
But this experiment shows:
Two different accelerations produce different results—a clear, measurable, directional breakdown of equivalence.
The Equivalence Principle is not fundamental—it is emergent. It holds only when the directional dependence of the kinematic shift is ignored.
| Scenario | First-Order Doppler? | Kinematic Time Dilation? | Vacuum \(\varepsilon, \mu\) Change? | Total Shift \(\Delta E / E_0\) |
|---|---|---|---|---|
| Real Gravity | No | Yes (half) | Yes (half) | \(gh/c^2\) |
| Vertical Acceleration | Yes | Yes | No | \(ah/c^2\) |
| Horizontal Acceleration | No | Yes (transverse) | No | \(\frac{1}{2}ah/c^2\) |
The numerical match between real gravity and vertical acceleration is coincidental: in gravity, the total shift comes from one kinematic and one material half; in vertical acceleration, it comes from a dominant first-order Doppler shift plus a smaller time dilation term. The horizontal setup reveals the underlying truth—acceleration produces only half the gravitational effect because it lacks the material change in the vacuum.
The Sturm experiment is not just a curiosity—it is a direct experimental demonstration of a directional dependence in acceleration effects, supporting the CUGE claim that real gravity modifies vacuum properties, while acceleration does not. This challenges the strict interpretation of the Equivalence Principle on experimental grounds.
The CUGE framework reproduces all five empirical confirmations of weak-field general relativity:
Furthermore, the model uniquely predicts and explains the directional “half-effect” observed under mechanical acceleration—a phenomenon absent from General Relativity and impossible under a strict interpretation of the Equivalence Principle.
The inclusion of Vacuum Shielding Stress (VSS) allows a rigorous derivation of heat dissipation in electron acceleration systems, resolving long-standing discrepancies between kinetic energy predictions and calorimetric measurements. By partitioning input energy into mechanical motion and non-mechanical vacuum stress energy, CUGE offers a causal, classical explanation for why high-voltage electron beams deposit significantly more heat than expected—without requiring relativistic mass increase.
This unified picture—where gravity, inertia, electrostatics, thermodynamics, and even quantum-like phenomena arise from the electromagnetic response of a structured vacuum—forms the foundation of the C.O.R.E. framework, pointing toward a fully classical origin of reality and emergence.
Crucially, these results align with and are extended by the REFORM model (REFractive Foundation of Relativity and Mechanics)[10], which derives Lorentz symmetry from phase continuity in a refractive vacuum. There, relativistic effects emerge as the sum of transverse Doppler shift and refractive path delay—confirming that real gravity alters \(\varepsilon(r), \mu(r)\), while acceleration does not. This cross-validation reinforces the physical reality of vacuum property changes and challenges the strict Equivalence Principle on both theoretical and experimental grounds.
The author wishes to extend a deep and sincere thank you to Wolfgang Sturm for his indispensable collaboration and experimental rigor. His work on “Space Curvature on the Lab Bench” provided the crucial evidence for the directional “half-effect,” challenging long-held assumptions about the Equivalence Principle. Furthermore, his persistent questioning of the traditional interpretation of Coulomb’s law helped uncover the deeper mechanism of Vacuum Shielding Stress (VSS).
Special recognition is also due to Alfred Schaub, whose original insight—that what we call “Coulomb repulsion” is actually a shadow of universal environmental attraction—was first articulated in The Antigravity on the Lab Bench[7]. That bold rethinking laid the conceptual foundation for replacing repulsive forces with refractive vacuum stress, enabling the unification presented here.
We extend our special gratitude to Miroslaw Wilczak for his meticulous verification of the mathematical derivations in this work and for his invaluable encouragement throughout the research process.
This paper, like all progress in the C.O.R.E. framework, emerged from dialogue between theory and experiment—a shared commitment to physical realism over mathematical abstraction.