Appendix 3. Gravity in Discrete SQ Space

Gravity in Discrete SQ Space

For Section — SER. Gravitational anomalies

Space is primary. The Universe begins with space. It is discrete and consists of fundamental Planck-scale cells (SQ).
Mass is a fundamental property of space. Mass is embedded in space and manifests as charge:
- mass charge q_m (or a part of the cell’s total charge) was emitted into substance (Matter / energy) at an early stage of the Universe’s evolution;
- spatial (metric) charge q_Λ remained in the cells;
- the amount of mass emitted as substance could have been “set” at the moment of release, depending on the space volume available at that time and the SQ dimension.

All masses in the Universe interact with each other proportionally to the magnitude of their charge and inversely proportionally to distance (to the power of SQ dimension minus 1). This includes interaction with the charge of space cells. [20]

With each other: masses act on each other directly.
With space: masses simultaneously interact with the charges of SQ cells.
SQ charges also interact with each other. Since in a region of SQ with uniform internal metric d the cell charges are equal, inter-cell interaction is effectively 0 (it acts as a background). It manifests when there is a space-cell dimension gradient (regions of SER non-uniformity).
For each gravitationally connected ensemble of masses, at every moment a local space dimension gradient corresponds and/or is established. The center of this gradient lies at the geometric center of mass (local center of mass), and the gradient magnitude is proportional to the total acting mass of the ensemble.

Note 20

There is no separate interaction carrier. A discrete cell with its charges is already a “space quantum”. Waves and effects are collective dynamics of directions, not an exchange of particles.

Dynamic homeostasis

Interactions are characterized by dynamic homeostasis. Systems “live” in continuous restructuring, adaptation, mutual tuning, and the emergence / evolution / decomposition of structures and local links.

For each gravitationally connected ensemble of masses in space, at every moment there exists a region of increased dimension. Its center coincides with the geometric center of mass, and its “height” (contrast) corresponds to the total acting mass. Substance (mass) motion in space induces space adaptation—a restructuring that follows changing conditions in gravitationally connected regions. Regions can overlap, intersect, merge, pass through each other, and split—there are no constraints on their behavior in space—substance and space remain continuously in a state of dynamic homeostasis, limited only by the propagation speed of influence.

Evolutionary origin and development

Start. Substance is nearly homogeneous and dense. Primary quantum inhomogeneities provide the seed of form—a weak dimension contrast onto which substance flows.
Growth. As the “stones assemble”, this correspondence becomes a stable rule: wherever there is a local center of mass, there is also a region of increased dimension, which is maintained and guides the distribution of substance.
Maturity. In mature systems, a balance persists: the compact central part is stable over long times, while the periphery continuously restructures in response to accretion, angular-momentum loss, tides, and external perturbations.
Dissolution. If connectedness is lost (mass leaves, the center of mass shifts), the region gradually fades back to the background on roughly the same order of causal delay with which it previously grew.

Practical implications

Without claiming full coverage:

Co-motion. Regions of increased dimension drift together with the substance “frameworks”.
Causal delay. The characteristic adjustment time for a scale R is τ ≈ R/c. This yields observable offsets between mass peaks (from lensing) and gas/light during fast events (collisions, fly-bys).
Shape: the core remains the most stable component, while the periphery smoothly restructures and catches up with a delay.
Locality of restructuring. The actual restructuring occurs at region peripheries; the interior volume changes slowly. Global profiles are stable, while the periphery is diffuse and dynamic.
Threshold and hysteresis. Local bulges are sustained only after a threshold is reached (in “effective” mass / surface density) and vanish when falling below a lower threshold.
Self-limitation. Strengthened attraction is converted into a new quasi-balance (virial balance, angular momentum, feedback), not into infinite contraction; contrast growth is limited by local face-matching constraints and causal delay.
Local emergences. In a diffuse medium, temporary bulges without a compact center are possible; they persist as long as surface density and retention time suffice, then dissolve.
Tidal limitation. In group/cluster environments, external tidal fields truncate region peripheries (tidal truncation), setting a natural outer scale.
Shape diagnostics. The shape and elongation of regions encode interaction history: elongated bridges, asymmetries, lobes ↔ recent tides/fly-bys; a more convex and symmetric shape ↔ isolated evolution.
Energy balance instead of collapse. Stronger attraction is converted into virial heating / angular-momentum redistribution (increased velocity dispersion, orbital restructuring), so the system moves to a new quasi-balance rather than collapsing.

Motion in space

Motion in space is governed not by individual transitions at the scale of a single cell, but by attraction fields formed within a connected region. These fields have two contributions:

the Matter contribution (ordinary gravity),
the Space contribution—dimension gradients ΔD maintained by dynamic homeostasis, which create an additional attraction potential.

The sum of these contributions determines the observed trajectories and effects. The ΔD contribution is scale-dependent: on stellar–planetary scales it is a subtle correction, while on galactic and cluster scales (8–10 kpc and beyond) it is comparable to, or dominant in, the total attraction.

Gravitational effects

This potential (the sum of the Newtonian contribution of baryonic mass and the additional potential from dimension gradients ΔD—an equivalent metric-mass of Space arising from relic ΔD and dynamic-homeostasis ΔD) reproduces, in a unified way, the full spectrum of gravitational phenomena.

A. Space–kinematic effects are interpreted in the “mass + ΔD” framework; the 1/r² law is preserved:

Newtonian statics and Keplerian orbits are the baseline. The bare mechanics of hot and cold rocks.
Pericenter precession: a subtle radial slope in the total source ⇒ the ellipse does not close.
Geodetic (de Sitter) precession: rotation of the inertial frame around a non-rotating source due to a weak radial slope.
Frame dragging (Lense–Thirring): rotation of the orbital plane/spin due to source rotation.
Tidal effects (geodesic deviation): second derivatives of the “mass + ΔD” potential (Roche, tidal truncation, streams).
Light deflection / gravitational lensing (weak/strong/micro): the “lensing mass” map tracks ΔD—mass maps derived from lensing effectively map the total source of gravity:
- Achromatic: the mechanism introduces no dispersion; the deflection angle does not depend on frequency; there are no “rainbows” or “prisms”.
- Image morphology (stretches/shifts) is set by the geometry of mass and ΔD distributions, not by any “optical” properties of the medium.
- No optical activity of Space: no scattering and no birefringence; a single ray does not split by polarization.

B. Temporal effects (see the Section Time)

Shapiro time delay.
Gravitational redshift / blueshift.
Gravitational time dilation.

C. Dark-matter-like effects (see Appendix 4. Relic dimension gradients).

Flat galaxy rotation curves.
Binding and velocity dispersions in clusters.
Statistical weak lensing over wide fields.

D. Gravitational waves.

A family of phenomena across different “scales”:

from the combined signal of supermassive astroscotoma pairs in galactic nuclei, slowly inspiraling over very long times,
through mergers of compact binaries: astroscotoma–astroscotoma (BBH), neutron star–neutron star (BNS), astroscotoma–neutron star (BH–NS),
and down to single events such as core collapse and supernova explosions, unstable rapidly rotating neutron stars, and strong tidal/disruptive events (disruption of a neutron star/white dwarf by an astroscotoma, highly eccentric passages—pericenter “kicks”).

These are characterized by a common set of properties:

source scale / compactness (high energy density in a small volume);
asphericity (no spherical symmetry in mass / momentum distribution);
a rapidly varying quadrupole (not quasi-static; a characteristic time ≲ the system dynamical time);
non-stationarity (mass / angular-momentum redistribution, outflows, jets, instabilities).

They trigger a sharp, aspherical ΔD restructuring via local SER dimension transitions. The restructuring propagates causally as a local-causal front (a “neighbor-to-neighbor” step). At large distances it is observed as a quadrupolar packet (sometimes with a “chirp”) and a single background step.

We are dealing with different scales of the same phenomenon—dynamic homeostasis: from local field re-basing during weak/slow processes to a long-range front (what classical language calls a gravitational wave) during fast aspherical catastrophes.

Gravity in Discrete SQ Space