AXIOM: The Conservation of Resonance

Abstract

Energy moving through a non-uniform Charge Continuum must maintain its fundamental resonance relative to the local substrate. As the density of the medium changes, the energy does not "lose" or "gain" itself; rather, it adapts its frequency and velocity to match the local Admittance.

The Ice Skater Effect

Much like an ice skater changing their rotational rate (RPM) by moving their arms to conserve angular momentum, a photon moving through a density gradient changes its frequency to conserve its energy state relative to the local lattice.

If the local permittivity \(\epsilon\) and permeability \(\mu\) increase due to the proximity of mass (the Lumpy Dielectric), the medium becomes "thicker." To maintain the same energy without a mismatch in impedance, the frequency must shift.

Invariance of Impedance

While speed \(v\) and frequency \(\nu\) are variables of the local density, the Characteristic Impedance \(Z_0\) remains the universal "Handshake" of the continuum:

The shift in frequency observed in the Pound-Rebka experiment is the physical manifestation of this conservation. The energy is "tucking its arms in" as it enters the denser substrate near the Earth.

The Mechanical Conclusion

Frequency shift is not a "stretching of space" but a mechanical adaptation. The energy remains identical; its "rotational rate" through the lattice is simply modified by the local loading of the substrate.