Evidence For the Need For Constant \( Z_0 \)
Abstract
To maintain the 90-degree phase coherence required for electromagnetic propagation at variable speeds, the ratio of \(\mu_0\) to \(\varepsilon_0\) must remain constant. This is a Physical Proof that Impedance (\(Z_0\)), rather than the speed of light (\(c\)), is the governing constant of the universe.
The Propagation Constraint
The wave speed ($c$) depends on the product of electromagnetic parameters, while the impedance ($Z_0$) depends on their ratio:
\[ Z_0 = \sqrt{\frac{\mu_0}{\varepsilon_0}} \approx 376.73 \,\Omega \] \[ c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} \]If the local speed of light varies due to gravitational gradients, the individual values of \(\mu_0\) and \(\varepsilon_0\) must change. However, if their ratio did not remain locked, the wave would lose its 90-degree phase alignment, leading to total decoherence.
The Impedance Match Requirement
In any transmission medium, a change in impedance causes a reflection. If \(Z_0\) varied alongside the speed of light, every gravitational gradient would act as a partial mirror. The high-fidelity images of distant quasars prove that the lattice maintains a Perfect Impedance Match across all gradients, allowing energy to transit without reflection.
Mechanical Necessity: The Phase-Lock
For a traveling wave to exist in the RR, the electric (potential) and magnetic (kinetic) components must remain in perfect quadrature. This 90-degree offset is a mechanical limit switch. If the impedance were not constant, the "timing" of the energy exchange between the lattice's stretch (\(\varepsilon\)) and its flow (\(\mu\)) would slip, causing the wave to collapse.
Conclusion
The universe does not just "have" a speed of light; it has a Standard of Coherence. The fixed impedance reveals a universe that is a precision-tuned architecture designed to preserve information across billions of light-years without phase-drift.
If the impedance weren't constant, the universe would be blind.