Cadence–Mass Coupling: How Motion Becomes Gravity
Why energy and mass are linked — Cadence Cosmology Series II
Author’s Note (2025-11-28)
This post reflects the early formulation of cadence–mass coupling, written before the full Light Frame field rules (LFR, LFC, LGR, C46–C54) were developed. The core content here remains correct — the cadence–mass slope, the TS/TD decomposition, and the γ-linked curvature are all part of the modern model. Later work refines the mechanism, clarifies the “τ → 0” interpretation, and replaces a few early balance statements with the formal LFR framework.
This entry is kept as part of the discovery sequence.
1 · Why this step matters
We usually think of gravity as a mysterious pull. But in cadence geometry, gravity is simply Temporal Descent (TD) — the inward curvature of time’s rhythm.
Light keeps a perfect beat:
Latex: C_0 = \frac{1}{c} = 3.33564095,\mathrm{ns,m^{-1}}
Geometry curves to preserve that beat.
Today’s post extends that idea: the same rhythm that keeps light steady is also what gives mass its weight.
2 · The constants that run the show
There are two cadence constants:
1/c — the slope of light’s rhythm (time per meter).
1/c² — the curvature factor that links energy and mass.
Together they describe how geometry trades rhythm for curvature without ever losing the beat.
3 · The Motion–Stretch Continuum
Relativity says clocks slow down as you move fast.
Cadence geometry says the rhythm tilts — part of each beat flows into stretch (TS), part into depth (TD):
Latex: \gamma_{\text{cad}} = \frac{1}{\sqrt{1 - (v/c)^2}},\quad TS_{\text{frac}} = \frac{1 + v/c}{2},\quad TD_{\text{frac}} = \frac{1 - v/c}{2},\quad LFR = \frac{1 + v/c}{1 - v/c},\quad \frac{\tau}{\tau_0} = \frac{1}{\gamma_{\text{cad}}}
As speed rises, proper time shrinks and LFR (the Light Frame Ratio) grows dramatically.
At the light limit, motion freezes into pure cadence — the beat remains, but the “ticks” vanish.
4 · The Cadence–Mass Coupling Law
Here is the bridge:
Latex: m_{\text{eff}} = \gamma_{\text{cad}},\frac{E}{c^2},\quad E = \gamma_{\text{cad}},m,c^2
This looks like Einstein’s E = mc², but now cadence is doing the explaining.
As velocity tilts the rhythm, the same cadence factor that shrinks proper time (γ_cad) also links energy and mass.
Mass is cadence curvature.
Energy is cadence rhythm.
Even photons — zero rest mass — still curve geometry because their energy sits on that same 1/c² slope.
5 · Simulation snapshot
| (v/c) | (\gamma_{\text{cad}}) | (\tau/\tau_0) | LFR |
| :---: | :-------------------: | :-----------: | :---: |
| 0.10 | 1.005 | 0.995 | 1.22 |
| 0.50 | 1.155 | 0.866 | 3.00 |
| 0.866 | 2.000 | 0.500 | 13.93 |
| 0.999 | 22.37 | 0.044 | 1999 |
Each step faster, the same rhythm compresses further.
At 0.999 c, proper time is just 4% of rest — yet the path length is still there.
Distance doesn’t vanish; cadence does.
6 · What it means
The traveler and the observer share the same optical present at any speed — but at light speed the perceived overlap becomes complete.
The path stays long, but the number of lived beats shrinks toward
3.33564095 ns per light-year — not zero, but the heartbeat of light itself.
Even that 3.3356 ns interval stretches as TS deepens the frame.
Light doesn’t move through time; it holds time steady for everything else.
That’s why at the cadence limit, both traveler and observer experience almost no time: they’re living on the same cadence surface.
7 · How to test it
Cadence–Mass Coupling isn’t poetry; it’s falsifiable.
It fails immediately if any of these fail:
light doesn’t bend geometry
LFR ≠ 1 as v → 0
proper time doesn’t approach zero as v → c
photons show no gravitational interaction
And all the classic experiments already do test it:
gravitational lensing
Shapiro delays
GPS time suppression
particle accelerator timing
If cadence geometry is wrong, these break.
8 · Why this completes the picture
The cadence coupling law closes the local bridge of the Light Frame:
cadence constant
light’s effective mass
cadence–mass coupling
optical closure
drift and ledger laws
From here, the next post will show how this local rule unfolds into the Cadence Law of Motion that governs galaxies, drift, and the expansion of space itself.
Takeaway
At the cadence limit, light moves beyond your ability to detect change — your universe stops tracking its beats.
In TD: cadence collapses into stillness — the mass sink.
In TS: cadence dilates toward infinity — the expansion edge.
The journey remains long.
The rhythm stays perfect.
Light doesn’t move faster; it moves timelessly, outside your frame’s ability to measure — untracked in stillness, untracked in infinity.
📎 What is g_obs?
When analyzing lensing, we compute the observed gravitational acceleration at the Einstein radius. It’s given by the standard surface-gravity relation:
Latex: g_{\text{obs}} = \frac{G M}{R^2}
Where:
G = 6.674×10⁻¹¹ m³·kg⁻¹·s⁻²
M = total mass inside the Einstein ring
R = the physical Einstein radius
This gives the actual curvature that light follows.
In the Light Frame model, we’re not subtracting a Newtonian baseline or adding dark matter. We ask a simpler question:
Does cadence curvature explain this directly?
And in these systems — it does.
Footnote (added after Post V):
Clarification on the “τ → 0” limit.
In this post, “proper time approaches zero” refers to the observer’s perspective:
as velocity approaches the cadence limit, the interval between rhythm-ticks falls below the observer’s tracking resolution.
Later in the series (Post V), we refine this:
the cadence itself never vanishes — light always keeps the invariant beat
What goes to zero is the observer’s ability to resolve distinct cadence intervals.
When cadence compression exceeds the observational bandwidth of a Light Frame, it appears as τ → 0 even though the underlying rhythm persists.
This is an observational zero, not a physical one.