Every electric force in nature is — in this theory — a sliver of one enormous background pressure. The size of that sliver is a single number, ƒ = 2.123×10⁻¹⁷. This page derives it from scratch, pushes it to its limits, and then tries its hardest to break it.
↓ scroll · drag the sliders · every number here is live
Spatial Displacement Theory (SDT) starts with one picture. Space is a lattice of tiny cells called spations, each one Planck-length wide (ℓ_P = 1.616×10⁻³⁵ m). Movement relays from spation to spation, nearest-neighbour, one Planck tick at a time.
Here is the crucial property, and it is easy to get wrong: an empty spation is perfectly transparent. Whatever movement arrives at its boundary passes directly through to the spation on the opposite side — undisturbed, unstored, nothing piling up. The lattice does not accumulate. It relays.
Because the relay is lossless, every point in space sits exactly one tick from every boundary condition at once. Not a staggered sum of signals that set out long ago and arrive at different times — every spation is simultaneously one-tick-coupled to all the boundaries of the causal volume around it. That is why the throughput is identical everywhere. This is the “shell cancellation” of Law I: transparency is what keeps it the same at every point.
We can read this colossal throughput as a “pressure,” but notice you never feel it — because in empty space it passes straight through you-that-isn’t-there. The machinery is completely invisible. It only becomes relevant against matter — and that is the whole next act.
Matter is the one thing a spation cannot pass straight through. Where there is an exclusion volume, the one-tick relay is interrupted — and the interrupted throughput, the part that no longer makes it to the far side, is what we call force. Nothing attracts; matter simply fails to be transparent, and the surrounding throughput imbalance does the rest.
So when two charges push on each other they are not inventing a new force — each one occludes a sliver of the convergence throughput the other would otherwise have passed through cleanly. Each particle casts a shadow; the shadow is the force.
But a charge is unimaginably small compared to the cosmos. It cannot tap the whole ocean — only the fraction that reaches across its own tiny cross-section. SDT writes the electromagnetic force as the universal occlusion law:
Here P_eff is the effective pressure a single interaction actually feels, and the transfer function ƒ is simply how much of the full ocean that is:
So the whole question of EMC01 is one sentence: is ƒ a number we derived, or a number we fitted to make the answer come out right? Hold that question — the honest answer is the most interesting part of this page.
The first move is exact and beautiful. The strength of the electric force, written with Coulomb’s constant and the electron charge, is identical to the fine-structure constant times the quantum of action:
proof EMC01-1a · PASS · err 0.0000% This isn’t SDT — it’s standard physics, the very definition of α. But it lets us erase the human-chosen units of charge and write everything in nature’s own coupling constant. Substituting into P_eff:
proof EMC01-1b · PASS · err 0.0000%
Replace P_conv by its lattice definition (shells × whisper), and the ratio ƒ expands into a single closed expression in measured constants:
proof EMC01-1d · PASS · err 0.0000% Read it like a sentence: the EM coupling α, scaled by the lattice cell as a fraction of the causal depth (ℓ_P/R_CMB), divided by the two-body cross-section and the energy density of the medium. Local spark over global ocean.
This recomputes ƒ live from the exact constants in laws.hpp. Sliders move in log-space around each measured value. The green target is the value the C++ engine printed: 2.123360×10⁻¹⁷.
If ƒ is real, the same P_eff should also build Coulomb at atomic range, the strong force at the femtometre, and — through a different geometry — gravity. Here is what the engine actually computed when we ran it. Honest scoreboard:
| Proof | What it tests | Result | Error |
|---|---|---|---|
| 1a | αℏc = k_e e² | PASS | 0.0000% |
| 1b | P_eff from α | PASS | 0.0000% |
| 1c | ƒ = P_eff/P_conv | PASS | 0.0000% |
| 1d | full closed form of ƒ | PASS | 0.0000% |
| 2a | Coulomb at 1 Å | PASS | 0.0000% |
| 2b | Gravity G via shell cancellation | FAIL | 99.88% |
| 2d | Nuclear > Coulomb at fm | PASS | 0.0000% |
6 / 7 PASS The program returns exit code 1 on purpose — it refuses to call itself finished while gravity is off. That honesty is the point.
Why is electricity ~10³⁹ times stronger than gravity between a proton and an electron? The engine measured it directly:
In SDT this giant number is not a fitted coupling — it is pure geometry: the charge cross-section versus the displacement cross-section. Same ocean, different shadows.
Run the naïve gravitational coupling straight from the ocean and you get a catastrophe — the same 10¹²² that wrecks the standard “vacuum energy” calculation:
SDT’s proposed cure is shell cancellation: convergence arrives from S = 4πN² ≈ 4.37×10¹²⁴ source cells on the Clearing and almost all of it cancels. Divide it out and the monster shrinks by 122 orders of magnitude — but it doesn’t quite land. The closest test overshoots by ~5×:
This is where we turn hostile, because a fair theory should survive its harshest reader. The SDT audit spine gives every quantity two independent labels:
Run ƒ through it. The expansion in Step 2 looks like a derivation from fundamentals. But trace the path: P_eff was defined by forcing the occlusion law to reproduce the measured Coulomb force at hydrogen scale. The “fundamental” formula and P_eff/P_conv are therefore the same equation written twice. They cannot disagree — so their agreement (proof 1d, err 0.0000%) confirms algebra, not physics.
In laws.hpp the engine labels its own constant honestly: P_eff and f_transfer are class E — calibrated. The hydrogen Coulomb force fixes their scale. ƒ’s magnitude is inherited, not derived.
So what survives? The structure does. The 1/r² occlusion law itself — that force is a shadow of a pressure — is provenance SDT-first, correspondence known-match: class C. The shape is a genuine SDT result that converges on Coulomb/Newton/strong-force; only the overall coefficient is borrowed from measurement. Honest headline: SDT derives the geometry of the force hierarchy; the single pressure coefficient is still a calibration waiting to be derived.
The operational test, which you can feel in the next two widgets: delete the correspondence check from a real derivation and the number is unchanged; delete it from a calibration and the number vanishes. ƒ’s magnitude vanishes. Its 1/r² shape does not.
If ƒ truly carries α, then mis-setting α must break the Coulomb prediction by exactly the same factor — no hidden parameter can absorb it. Drag α away from its measured value and watch the SDT Coulomb force walk off the real one. There is nowhere to hide.
What you should see: the two bars lock together only at α/α=1. Any drift and they split — because α is genuinely load-bearing here. This part is real physics. (Provenance of the α-dependence: passes.)
Now the uncomfortable one. The claim “ƒ is derived from R_p and r_e” predicts that changing the proton/electron radii should change ƒ and leave Coulomb untouched (since Coulomb is “independent”). Try it. Watch what actually happens to the match between SDT-Coulomb and real-Coulomb as you move R_p.
SDT proposes G = G_naive / (4πN^p) with the cancellation exponent p = 2 fixed by geometry (the Clearing is a 2-sphere). If that exponent were a free knob, someone could just dial it to hit G exactly — and the theory would explain nothing. Test the rigidity: sweep p and see that no integer-clean value nails G; the honest result sits ~5× off at the geometrically-mandated p=2.
F = (π/4)P·R²R²/r² — that every force is occluded convergence — is SDT-first and converges on Coulomb, Newton and the strong force. This is a real result. Survives.
The 10³⁹ EM/gravity ratio is geometric, and α’s role is load-bearing (falsifier #1). Survives.
ƒ = 2.123×10⁻¹⁷ is calibrated to hydrogen, not derived. Its “fundamental” form is the same equation written twice (falsifier #2). Honest open problem.
Shell cancellation kills 122 orders of magnitude but misses by ~5× (falsifier #3). Not yet derived.
That is the shape of an honest theory: a genuine structural insight (forces are shadows), one beautiful exact identity it borrows (αℏc=k_e e²), one coefficient it still has to fit, and one famous number it gets within a factor of five and refuses to fudge. EMC01 is not “f is universal, done.” It is “the geometry is SDT’s; the scale is still on loan.”