Cross-Prediction Web
The ether framework has one free parameter (me) and three observational constraints, so measuring any single quantity determines all others. The inverse constraint chain (Eq 9.33) shows that a sub-millimetre gravity measurement of ξ uniquely fixes me — and with it, every prediction in the framework.
Viable window: 6–10 μm (me = 0.3–4 eV)
All Derived Quantities from ξ = 8.7 μm
- m_e (Eq 9.33)
- 1.015 eV
- \u03BC\u0302 (Eq 9.14)
- 0.253 meV
- c_s (Eq 4.109)
- 4.74 × 10⁶ m/s
- c_s/c
- 0.0158
- n\u2080 (Eq 9.19)
- 1.23 × 10⁹ m⁻³
- a_s (Eq 9.22)
- 0.428 m
- \u03C3_c (\u03B4=80)
- 490 km/s
me ∝ ξ−5: A 10% change in ξ produces a 50% change in me. Sub-millimetre gravity is the most sensitive single probe of the entire ether framework.
Table 9.1: Standard me Values
| m_e (eV) | ξ (μm) | \u03BC\u0302 (meV) | c_s (10\u2076 m/s) | \u03C3_c (km/s) | a_s (m) |
|---|---|---|---|---|---|
| 0.3 | 11.1 | 0.527 | 12.56 | 2487 | 0.078 |
| 0.5 | 10.0 | 0.388 | 8.35 | 1258 | 0.159 |
| 1.0 | 8.7 | 0.256 | 4.79 | 499 | 0.419 |
| 2.0 | 7.6 | 0.169 | 2.75 | 198 | 1.11 |
| 3.0 | 7.0 | 0.132 | 1.99 | 115 | 1.95 |
Table 9.2: If ξ Is Measured
| ξ (μm) | m_e (eV) | \u03BC\u0302 (meV) | c_s (10\u2076 m/s) | \u03C3_c (km/s) | a_s (m) |
|---|---|---|---|---|---|
| 6 | 6.51 | 0.083 | 1.07 | 41 | 5.76 |
| 8 | 1.54 | 0.197 | 3.39 | 280 | 0.769 |
| 10 | 0.51 | 0.385 | 8.27 | 1239 | 0.161 |
| 12 | 0.20 | 0.665 | 17.15 | 4178 | 0.045 |
| 15 | 0.07 | 1.299 | 41.87 | 18496 | 0.009 |
Verification
ξ = 8.7 μm at m_e = 1.0 eV (Table 9.1)
c_s = 4.80 × 10⁶ m/s at m_e = 1.0 eV
σ_c ≈ 499 km/s at m_e = 1.0 eV, δ=80
Round-trip: m_e(ξ(1.0 eV)) ≈ 1.0 eV (self-consistency)
m_e ∝ ξ⁻⁵ scaling: ratio at ξ=6 vs ξ=12
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