nishi code wiki / research / world physics regimes

Physics as a per-world regime: what transforms with gravity, what does not, and what must refuse

Published 2026-08-03 · lineage: forks off the soft-tissue dynamics brief, whose every cited band turned out to carry an undeclared assumption — that it was measured at one gravity · context: worlds that must differ physically while remaining physically correct, with Earth as the benchmark

The framing that makes this tractable. A world is not a gravity number, it is a regime, and a band measured on Earth may travel to another world only through a declared transform. There are exactly three useful answers per quantity and the third is the one nobody builds: a quantity may be invariant, it may scale by a stated law, or it may refuse to transform at all because the underlying behaviour changes kind rather than degree. Treating the third class as if it were the second produces numbers that look physical, pass every arithmetic check, and are wrong by 65%.

1. The benchmark is itself a band

Earth's g = 9.80665 m/s² is a defined conventional value adopted by the 3rd CGPM in 1901, not a measurement. Real surface gravity spans 9.7639 to 9.8337 m/s² — a 0.7% range. Anyone calibrating against "Earth" is calibrating against a ±3.5 per-mille band, and no downstream tolerance can honestly be tighter than the benchmark it is measured against.

2. Three evidence classes, and a validity floor at 0.4 g

Dimensional analysis is cheap and produces a scaling law for almost anything. Whether that law survives contact with a real body under real reduced gravity is a separate question, and the answer is frequently no. The distinction is load-bearing enough that our profile table carries an evidence column on every row: MEASURED, DERIVED, or DISPUTED.

The single most important number in this brief: √g scaling of gait is valid only down to about 0.4 g. Dynamic similarity predicts the walk–run transition at a constant Froude number near 0.5, and reduced-gravity treadmill work confirms it holds from 1 g down to 0.4 g. Below that it breaks: at 0.1 g the measured transition Froude number rises to 1.1–1.4, so a √g extrapolation underpredicts the transition speed by roughly 1.65×. The Moon sits at 0.166 g, deep inside the region where the convenient law is wrong. Worse, running kinematics at matched Froude number are not dynamically similar at all (n = 10) — for running there is no valid transform to find.

Baseline theory: Alexander & Jayes, J. Zool. 201:135–152 (1983). Transition sharpness also changes: abrupt at 1 g, gradual below ~0.2 g.

3. The sign flip: geometry decides, not tissue

The intuition that low gravity makes everything floatier is correct for one geometry and inverted for the other. Effective stiffness carries a gravitational term whose sign depends on whether the mass hangs below its attachment or balances above it. Pendant tissue — breast, belly, jowl — behaves as K + mgL and therefore gets softer as gravity falls. An inverted segment balanced above a joint behaves as K − mgh and gets stiffer as gravity falls (inverted-pendulum balance analysis, which also finds standing becomes passively stable below about 0.91 g). A single global "low gravity" multiplier is guaranteed to have the wrong sign for one of the two.

Tissue composition matters independently of geometry, and it is measured. Across pre-strain from 5% to 20%, elastic moduli of breast tissue types behave differently: fat is effectively invariant (18→20 kPa, n = 40), while glandular tissue stiffens 1.71× (n = 31) and fibrous tissue 2.27× (n = 21). Since self-weight pre-strain scales with gravity, a fatty breast keeps its stiffness on the Moon while a fibrous one softens — the composition parameter we already carry becomes a physics parameter, not only an appearance one.

Whole-body corroboration under real altered gravity exists but is small: trunk apparent stiffness rises about 48% going from 0.75 g to 0.25 g (n = 6, parabolic flight), and lumbar stiffness shifts +4.1% at 0 g and −5.9% at 1.8 g (n = 8, parabolic flight).

4. Gait is a category, not a speed

The most consequential finding for a game is that reduced gravity does not slow walking down — it changes which gait a human chooses. Preferred locomotion goes walking at 1 g, running at Mars gravity, and skipping, loping and hopping on the Moon, which is what the Apollo surface record actually shows and why lunar footage looks the way it does. Metabolic cost of transport is non-monotonic in more than half of subjects, with the ranking between gaits reordering.

Therefore: retiming an Earth walk cycle cannot produce a lope. Playing an animation back at √r is kinematically correct for ballistic motion and wrong for locomotion, because the limb coordination pattern itself is different. A low-gravity world needs its own clips. This is the mechanism behind the uncanny quality of most low-gravity movement in games, and it is a content requirement, not a tuning one.

Two locomotion quantities are measured as robust: leg spring stiffness is invariant from 0.2 to 1.0 g, and peak vertical ground reaction force scales close to linearly with g (R² > 0.88 across 43 pooled studies). One is openly disputed: ground contact time is reported invariant by one group and decreasing by another, nobody has adjudicated it, and we adopt neither side.

5. What our own engine does today

Gravity is a literal in at least nine places, and Earth's g exists as four disagreeing copies. Two files carry 9.8062, one carries 9.8120 (and its own selftest asserts equality against that copy, so the divergence is self-certifying), one carries 9.810 — and none equals the defined 9.80665. The shipping game holds a bare GRAV = 9 in tick units with no recorded derivation. Not one of these constants says which body it is the gravity of, which is precisely why no world can currently differ from Earth and why no measured band can declare the gravity it was measured at. This is one root cause wearing nine masks, and it blocks the entire per-world capability before any physics question is reached.

6. The refusal rule

A quantity tagged REFUSE, DISPUTED or CATEGORY-CHANGE may not be transformed automatically. The gate reports it as untransformable for that world and names why. A validity floor of r ≥ 0.4 is enforced by construction on the locomotion transforms rather than by discipline, because the failure mode here is not a crash or an obvious artifact — it is a plausible number. Two further refusals fall out of the same rule: terminal velocity is undefined on a world with no atmosphere and must refuse rather than return infinity, and there is no sound at all on the Moon, while speed of sound is set by composition and temperature and is invariant with respect to gravity (Mars measured at 240–250 m/s against Earth's 343).

Granular terrain deserves a specific warning because it is often assumed invariant and is not: static angle of repose rises about 5° at 0.1–0.38 g while dynamic angle of repose falls about 10° with larger avalanches (33 parabolas) — again opposite signs for two quantities sharing a name. Ballistic quantities are the easy class: jump height, hang time and range all go as 1/r, and fall time as 1/√r.

UNVERIFIED / declared gaps

No measured human jump height at lunar gravity exists. The familiar "six times higher" is derived kinematics; the Apollo jump salute was never measured.
No fitted exponent for stride frequency versus gravity exists anywhere. Only the direction of change is published. The √g pendulum prediction has never been tested against a fit.
No direct measurement of pendant soft-tissue sag as a function of gravity. None — no photogrammetry, no ultrasound, no parabolic-flight body-shape study. The nearest proxy is prone-versus-supine registration (73.7 mm mean swing, n = 14), which reverses direction at fixed magnitude rather than sweeping magnitude. Our tissue transforms are therefore DERIVED from measured moduli, not measured directly, and this brief does not report them as measured.
No human gait data above about 1.5 g. Centrifuge work covers hopping and squats only.
No study separates the instantaneous elastic response to a gravity change from multi-week remodeling. Every microgravity tissue dataset is confounded by adaptation, so none of them answers "what does this body do in the first second on the Moon".
No game engine ships a per-world physics profile beyond gravity vector, drag, terminal velocity and a water flag. Unreal removed the per-volume gravity that earlier versions carried, and Unity has no per-scene gravity in classic physics. Every project needing one has built it from scratch. That means this design is ahead of shipped practice — and equally that nobody else's numbers can validate ours.
No published rule for gravity-aware animation retiming in any engine documentation, GDC talk or graphics paper. The √g result is derivable in one line and is simply never written down, so its locomotion caveat is nowhere stated either.
Several primary sources were paywalled or unreachable during the sweep, including the sample size of the foundational reduced-gravity treadmill study, and the NASA planetary fact-sheet archive was offline; Mars constants were cross-checked from mirrors rather than fetched from source.