How Big, How Small: The Measured Working Range of Push-Gravity
July 2026
Every physical model has a range where it actually works. Newton’s own gravity is a clean example — extraordinarily accurate for apples to orbits, and it needed a real replacement (general relativity) once measurements got precise enough to catch it failing near the Sun and at high speed. Having a bounded range isn’t a failure of a model. Not knowing where that boundary is, is.
This site’s shadowing mechanism — a body partially blocking the ambient particle flux described in Paper 1, producing a directional deficit that reads as gravitational attraction — has now been tested at both ends: pushed down toward atomic and nuclear scale, and pushed up toward galactic and collapsed-object scale. In short: it holds in the classical weak-field middle, and fails in both directions by many orders of magnitude — not a gentle slope, a bounded island with two hard edges.
Where it holds: the classical middle
Before testing any scaling behavior, the underlying calculation was checked against the one case where the answer is already known beyond dispute: two ordinary masses, at ordinary separation, in the weak-field limit. The computed force matched exact Newtonian $-GM/R^2$ gravity to within 0.01% — necessary, but not yet evidence for anything PBT claims beyond Newton. The real question is what happens outside this window, in the two directions PBT claims to do something Newton and General Relativity don’t.
The large end: two different failures
Galaxies. PBT’s published papers invoke a scale-dependent effective coupling — an effective $G$ that changes with distance, $G_{eff}(l)$ — specifically to explain flat galactic rotation curves without dark matter. Testing this directly, by modeling a galaxy’s mass distribution and computing the actual shadow-deficit a star at a given radius would experience — same mass model, same published formula, no retuning — the mechanism doesn’t reshape the rotation curve. It rescales the whole thing uniformly: Paper 1’s flagship number for predicted orbital velocity comes out roughly 32 times too high — the same declining curve shape as plain Newtonian gravity, just multiplied up. The reason is structural: past a few galactic scale-radii, the galaxy’s mass already fully occults the inward line of sight, so moving further out doesn’t deepen the shadow. A saturating attenuation can only rescale a curve, never reshape it — a generic property of any simple isotropic shadowing model on a realistic mass distribution, not an artifact of one profile or parameter choice.
Collapsed matter. Separately, Paper 1 claims gravitational collapse stabilizes near the Planck scale ($\sim10^{-35}$ m) instead of forming a true singularity. Solving the stated equilibrium condition for a solar-mass collapse gives a stabilization radius larger than the observable universe itself — 66 to 123 orders of magnitude above the Planck scale, depending on which exponent the formula allows ($\gamma=2$ to $4$). Already noted on the paper (2026-07-21): the honest state of this claim right now is that it’s wrong, not merely unverified.
Both large-end claims fail, for different reasons. Galaxies: the mechanism structurally can’t reshape a curve once shadowing saturates — no retuning fixes that. Collapse: a plain mismatch between the claimed answer and what the equation actually gives when solved.
The small end: a different kind of gap, moving inward
PBT has one published formula relating ambient energy density to length scale — $\varepsilon(l) = \varepsilon_0(l_0/l)^\gamma$, energy density rising as length shrinks — calibrated only at galactic scale. Tested anyway against real pressures at scales it was never fit to: 7 to 36.5 orders of magnitude too small at the Bohr radius, 18 to 38.2 orders too small at the roughly-one-femtometer nuclear scale, for every exponent the formula allows. A separate, more direct check computing nuclear binding energy specifically agrees — 18 to 30-plus orders too small, by two independent methods (an analytic self-consistency check and a numeric fit).
Unlike the large end, this isn’t a proven dead end — nobody has shown it’s structurally unfixable by a different functional form, only that this one, unmodified, misses badly everywhere it’s been tested outside its fitted window. Large end: mechanism can’t reshape (structural). Small end: this scaling undershoots (fit, not yet ruled out).
What this doesn’t mean
None of this shows the underlying idea — that gravity might be an emergent, mechanical effect of a real ambient medium — is wrong. It shows something narrower: the specific, currently-published formula connecting that idea to different length scales doesn’t work outside the classical, everyday-object regime it was never actually tested against until now. That’s different from either “confirmed” or “falsified,” and it’s the claim the numbers actually support.
One more thing deliberately left out: a single invented confidence percentage per scale. These are deterministic calculations checked against real, measured targets, not a statistical sample — “73% likely accurate” for a nuclear-scale prediction off by twenty orders of magnitude would manufacture a precision nothing here has. Not “5% off at galaxy scale, 20% off at nuclear” — right in the middle, wrong by factors of $10^n$ everywhere else.
Where this leaves the theory
The theory should state an explicit working range. It doesn’t yet — gaps.md, this site’s own running account of what’s unsolved, describes how $G_{eff}(l)$ operates but never says where it stops applying. A model that’s honest about a bounded, validated middle, one structurally closed large-end extreme, and one small-end extreme that’s failing but not yet proven unfixable, is a stronger, more checkable claim than one that gestures at working across all scales without ever having been tested that way.
“It works” isn’t the same as “we know how”
None of the theories standing in for PBT at these same extremes has actually solved them either. Dark matter fits real rotation curves well, but its density profile is calibrated to the data it explains, and no particle has ever been directly detected — a working fit, not a demonstrated mechanism. General Relativity’s own equations predict a genuine singularity at a black hole’s center, not a stabilized alternative — a real, acknowledged breakdown, unresolved without a quantum theory of gravity that doesn’t yet exist.
The pattern worth naming: a great deal of real, working physics is validated by prediction without being explained by mechanism. Newton’s gravity predicted orbits to extraordinary precision for two centuries while Newton himself declined to say what gravity actually was. A working physicist says the same, on camera, about a more basic case still open today: why gravity only pulls while Coulomb’s law, identical in form, can push or pull. The equation works. The reason is still open.
That’s the actual target here — not matching more numbers regime by regime the way dark matter fits galaxies without explaining nuclei, but one mechanism doing all of it for a stated reason. The real open question this article leaves: whether a genuinely different scaling relation — not a re-fit of the same power law, but something derived from different first principles — could close either gap, or whether the classical middle is simply this theory’s actual domain, the way Newtonian gravity’s is.