The Cadence Law of Motion
Newton’s Line vs Cadence’s Bend - Cadence Cosmology Series Paper III
Author’s Note (2025-11-28)
This post presents the early form of the Cadence Law of Motion, written before the full Light Frame field framework (S14, LFR–LFC–LGR, C46–C54) and before the modern mass-scaled projection law was derived. The core intuition here remains correct — TD as felt curvature, TS as projected curvature, and the cadence bend replacing Newton’s falloff — and the δ ≈ 0.256 scaling originates from this stage. Later work refines the mechanism, replaces the early TS term with the formal cadence projection law, and integrates rotation, matching conditions, and frame coupling. This entry is preserved as part of the discovery sequence.
Galaxies don’t slow down the way Newton says they should. The stars on the edge keep spinning — not because of hidden mass, but because geometry itself bends to preserve rhythm.
For a century, Newton’s line has told us that stars at the edges of galaxies should slow down as visible mass thins. Yet telescopes show the opposite: motion persists, curves flatten, galaxies refuse to fade. The standard answer has been to add invisible matter.
The cadence answer is simpler: rhythm itself bends geometry.
The Cadence Law of Motion
In cadence framing, observed acceleration is not just the pull of visible mass. It is the sum of two curvatures:
Temporal Depth (TD): inward cadence curvature from baryonic gravity.
Temporal Stretch (TS): outward cadence uncurvature that grows with system mass.
Together they appear in the early projection law as:
Latex: g_{\mathrm{obs}} = g_{\mathrm{bar}} + \left(\frac{v_s^2}{r}\right)\left(\frac{M}{M_0}\right)^{2\delta}
with fitted parameters:
v_s = 3 × 10^5 m/s
r_s = 5 kpc
δ = 0.256
M_0 = 1 × 10^12 solar masses
This law bends upward where Newton falls away.
At high g_bar, cadence overlaps Newton.
At low g_bar, cadence preserves motion through rhythm curvature.
The divergence is not a fudge factor — it is the geometry of TS and TD in balance.
Newton vs Cadence
Newton’s prediction is a straight diagonal: acceleration tracks visible mass one-to-one. As baryons thin, Newton says motion should fade.
Cadence bends instead.
At high g_bar, cadence overlaps Newton.
At low g_bar, cadence adds outward curvature and prevents the falloff.
Newton has no floor.
Cadence geometry does — because TS balances TD at low accelerations.
The bend is not a correction.
It is the projection of cadence curvature.
Physical Interpretation: TS–TD Balance
Cadence law is not algebra; it is geometry.
TD (curvature):
Inward cadence compression from baryonic mass.
TS (uncurvature):
Outward cadence relaxation that scales with the system’s mass.
At high g_bar, TD controls the cadence triangle and cadence is Newtonian.
At low g_bar, TS grows relative to TD through the cadence ratio (LFR), producing the acceleration ‘floor.’
This balance is what keeps rotation curves flat.
The bend is cadence projection, nothing more.
Newton has no such balance, so his line falls away.
Cadence law holds motion steady because rhythm curvature persists even when mass thins.
Corollaries of the Cadence Law
Flat Rotation Curves
Newton predicts that stars at the edges should slow down.
Cadence law shows why they don’t: TS curvature balances TD, sealing motion into rhythm.
Tully–Fisher Relation
More massive galaxies spin faster.
In cadence framing, this comes directly from TS scaling with mass:
Latex: v_{\text{stretch}} \propto \left(\frac{M}{M_0}\right)^\delta
This early form already hints at the Tully–Fisher luminosity–velocity relation — no halos required.
Lensing Mass Discrepancy
Lensing often shows more curvature than visible mass predicts.
Cadence law explains: TS increases the projected curvature, bending light more strongly than baryons alone.
The discrepancy is rhythm geometry, not missing matter.
Tests and Falsifiability
Every law must risk failure. Cadence law is no exception.
It fails if:
Rotation curves: galaxies are found where outer stars slow exactly as Newton predicts.
Mass scaling: TS curvature does not scale with mass.
Tully–Fisher relation: galaxies fall off the mass–velocity relation.
Lensing: curvature matches purely Newtonian predictions with no TS contribution.
Remove the upward bend and cadence law collapses.
From Local to Global Cadence
Locally, TS and TD balance to give flat rotation curves.
But cadence extends far beyond galaxies.
The same rhythm that seals motion locally also stretches across cosmic distances.
On the largest scales, cadence law becomes drift: the farther away something is, the faster it appears to recede. What looks like expansion is cadence fulfilling its contract over distance.
This isn’t a correction to Newton.
It’s a completion.
Cadence law explains motion not as a force but as rhythm preserved.
Aletheia and Light-Speed Effects
Aletheia moves at near-light cadence not by accelerating toward c, but by bending rhythm. Cadence geometry allows mass to enter the light regime — attaining light-speed effects without approaching light speed — because the universe preserves rhythm, not velocity.
Cadence replaces the idea of “speed limit” with “rhythm invariance.”
Footnote — About the Parameters
The parameters in this post come from our first SPARC-based cadence fits [Lelli et al. 2016] — the early version of the model before the mass-scaled law (S14), rotational term, and ledger corrections were introduced. These early fits are intentionally preserved because they show the real sequence of insight. Later posts update them to the full cadence geometry.
(SPARC dataset: Lelli, McGaugh & Schombert 2016, AJ 152, 157.)