The Two Faces of Time — Temporal Stretch and Temporal Depth
c = 299,792,458 m/s — the constant rhythm beneath motion.
In the last post we showed that two observers moving past each other never truly disagree about time. Each sees the other’s clock slowed by light’s travel delay, but when they meet again, the difference vanishes.
That reversibility is the hallmark of Temporal Stretch — time distortion that belongs purely to geometry.
The reversible side of motion
A straight-line trip, even near light speed, only stretches the light-cone between the two observers. Go out, come back, and the clocks re-align.
Nothing was lost; the universe simply bent the path of light and then un-bent it.
Stretch is reversible because geometry itself is reversible.
The bend that never cancels
Now imagine a different motion. A ship flies in a circle at steady speed. The crew feel pressed into their seats even though the speed stays constant.
That pressure is continuous acceleration — each moment the direction of motion changes, bending the path a little more. The ship’s clock now runs slightly slower than a clock resting at the center of the circle, and every lap adds to the difference.
Unlike the straight trip, this time lag never cancels; every orbit repeats the same curvature.
Circular motion behaves like a small, constant gravity field. It slows the local rhythm of time and makes weight appear where there is no planet.
This is motion pretending to be gravity.
From simulated gravity to real gravity
What the ship feels as a push, a planet produces naturally. Stand on Earth and you are inside that same curvature: time here ticks a bit slower than it does higher up, and the push you feel underfoot is the resistance to that inward curve.
This deeper, continuous slowing is what the Light-Frame view calls Temporal Depth.
Kinds of Motion
Straight, constant motion produces Temporal Stretch—a reversible, geometric effect that feels like pure drift.
Curved or continuous motion produces Temporal Depth—a persistent, gravitational slowing that feels like weight or acceleration
Between them lies the steady state we call rest.
Seen this way, gravity isn’t a mysterious pull at all. It’s the same geometric effect as motion — just one that never straightens out. Time slows near mass for the same reason it slows on the circling ship: the path is bent and keeps bending.
That bend is Temporal Depth.
The geometry Behind the rhythm
When you’re near mass, time slows down. That compression of time keeps falling objects at a steady local distance: their own clocks and rulers adjust so that motion still looks smooth.
Far from mass, the opposite happens. To keep light’s overall rhythm 1/c unchanged, space stretches so that distant clocks keep pace with the slowed ones near mass.
Formally, the geometry does this automatically.
In general relativity the time and space factors of the metric balance each other:
g_{tt}\,g_{rr} \approx -1
When the time part gtt shrinks near mass, the spatial part grr expands so that light still measures the same cadence.
In Light-Frame terms:
Temporal Depth (TD) — local compression of cadence around mass.
Temporal Stretch (TS) — reciprocal widening farther out that preserves light’s slope.
Together they keep the invariant rhythm
C_0 = \frac{1}{c}
intact across every frame.