CORE SIZE ESTIMATES
The numbers on this site (15.8 m, up to 48.3 m, and 0.63 m) are not contradictory. They answer different questions.
The two estimates
| Estimate A (energy matching) | Estimate B (from density) | |
|---|---|---|
| Where it appears | Revision III (heuristic scale RE), slides “Anatomy of a 2.8 M☉ Quantum Core” | “Mechanical squeezing” paper |
| Formula | RE = G·M·mN / E | r = (3M / 4πρ)1/3, with ρ = ρEW |
| Condition it expresses | the radius at which the gravitational energy per nucleon equals an energy scale E (W, Z, Higgs, electroweak crossover, or the Higgs field value 246 GeV) | the radius that holds the mass M at the energy density of a Standard-Model plasma at TEW = 159.5 GeV (ρEW ≈ 5.27×1030 kg/m3) |
| Result for 2.8 M☉ | 15.8 m (E = 246 GeV) up to 48.3 m (E = 80.4 GeV) | 0.63 m |
| Scales with mass as | M (linear) | M1/3 |
| Status | diagnostic scale only; Revision III: a thermalised sphere of this size would hold 4×104 to 106 M☉, so these are not real shells | assumed density; no mechanism that halts collapse is derived |
Why they differ by a factor of about 25
Estimate A fixes the energy per particle. Estimate B fixes the energy density. These are different conditions, so they give different radii: 15.8 m / 0.63 m ≈ 25 (and 48.3 m / 0.63 m ≈ 76 for the W-boson scale).
The two also scale differently with mass. A grows linearly with M, B only as M1/3. They would agree at a single mass (about 0.02 M☉ for E = 246 GeV) and move apart for heavier objects, so for a stellar-mass object the gap is large.
Small differences inside estimate A
Values for the same scale can differ in the second decimal place between documents. For example, the Higgs zone is 31.02 m in Revision III and 31.06 m on the slides, because the Higgs mass is rounded differently (125.25 vs 125.10 GeV). W and Z values differ only by rounding (48.33 vs 48.35 m, 42.60 vs 42.62 m).
What this means
These sizes are scale estimates from stated assumptions, not predictions of a verified structure. Revision III states that a regular finite core supported by Standard-Model matter has not been demonstrated, and the singularity theorems of classical general relativity still apply. Which estimate, if any, corresponds to physical reality is an open question.
Two sizes, two assumptions: A asks “where does the energy per particle match?”, B asks “how small must the volume be for this density?”