Preliminary Paper

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The μ–ε continuum represents the dynamic electromagnetic fabric of the universe.
Rather than treating μ (magnetic permeability) and ε (electric permittivity) as fixed constants, this model regards them as spatially and temporally responsive variables that encode the capacity of the ether to store and transmit energy.
Every region of space is characterized by its local pair (μ, ε), defining a unique propagation speed c = 1/sqrt{με}​ and impedance Z = sqrt{μ/ε}​.

This establishes a three-dimensional field space (μ, ε, c), where the c-axis represents the velocity dimension derived from the product μ·ε. Within this space:

• Planes of constant c define regions of equal wave speed.
   
• Surfaces of constant Z represent equal impedance between electric and magnetic energy densities.
   
• The energy-equilibrium condition, μ = ε/c^2, forms a curved sheet separating electric-dominant and magnetic-dominant domains.
   

Together, these surfaces form a nested lattice of field states through which electromagnetic waves, particles, and even matter itself evolve.
The continuum therefore acts as a unified geometry of electromagnetic motion, where both light and mass represent different trajectories through μ–ε–c space.

In this 3D field space, the curvature of the μ–ε surface corresponds to energy density gradients.
Regions of high curvature—where μ and ε vary rapidly with position—act as energy traps or potential wells, confining wave energy and giving rise to mass-like behavior.
Conversely, flatter regions permit nearly uniform propagation, corresponding to free radiation.

This structure parallels the geometry of spacetime curvature in general relativity but derives from impedance gradients rather than metric distortion.
Thus, gravitational effects emerge naturally as manifestations of electromagnetic curvature:

∇(με) ≠ 0 ⇒  energy localization, time dilation, and gravitational potential.

The curvature in μ–ε space is therefore equivalent to the presence of mass-energy, unifying electromagnetic and gravitational dynamics without additional postulates.

Because the μ–ε–c field space is curved and dynamically rotating, charged particles experience Coriolis-like transverse forces as they move through it.
These forces arise from the changing impedance vector and produce spiral trajectories reminiscent of those observed in charged-particle detectors such as bubble chambers.

The direction of rotation—clockwise or counterclockwise—depends on the charge polarity and the local gradient of μ and ε.
A positively charged particle spirals one way; a negative particle, the opposite.
This correspondence provides a natural geometric explanation for charge duality and spin quantization.

The Coriolis analogy further implies that the ether possesses rotational inertia: when energy moves through it, a residual rotational motion remains, generating curl energy that persists after wave passage.
This rotational memory is the source of potential energy storage and inertia within the medium.
In effect, the ether acts as both the origin of motion and the record of its passage.

Within this 3D field geometry, certain μ–ε–c configurations are energetically stable, forming quantized “layers” in the continuum.
These discrete states correspond to resonance points where oscillations in μ and ε synchronize, producing standing-wave impedance nodes.
At these nodes, energy oscillates without net propagation, similar to orbital electron states in atomic structure.

Thus, atomic quantization emerges from field impedance resonance, not from arbitrary quantized energy postulates.
Matter becomes the stable expression of electromagnetic equilibrium conditions within the μ–ε continuum, linking subatomic structure to cosmological field organization.

This geometric–resonant model implies that the same fundamental laws governing vacuum impedance also dictate atomic orbitals, molecular bonds, and large-scale energy balance.
It suggests that quantum structure and cosmic structure are manifestations of the same underlying electromagnetic field geometry.