Space Expansion Rule (SER)
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Space Expansion Rule (SER)
When transitioning from dimension d to (d−1), one cell SQd produces 2d new SQd−1 cells. We call this process a SER step.
This number is determined by the geometry of a d-dimensional hypercube. A hypercube of dimension d always has 2d faces of dimension (d−1). Each of these faces serves as an “exit site” for a new cell. Therefore, under degradation, SQd necessarily yields exactly 2d cells SQd−1.
Conversely, under folding: 2d neighboring quanta of dimension d−1 can merge into a single quantum of dimension d under the same caveats.
Fundamental principles
Quantization.
- Discreteness. Dimension transitions do not occur smoothly, but in jumps: SQd → 2d SQd−1. Space unfolds in “chunks”.
- Minimal interval. A single step cannot occur faster than a time quantum. This guarantees discrete evolution and makes SER “quantized” in time.
- Probabilistic character. A transition is not mandatory at every t_p. For each SQ, there exists a degradation probability that depends on its current dimension and local conditions.
Conservation laws.
- Conventional conservation laws (energy, momentum, angular momentum) apply without modification.
- In all SER events—decay, reverse assembly, emission of substance, and reverse absorption—the total charge is conserved; only its distribution and bookkeeping change (in SQ ↔ in substance).
- The inheritance of SQ geometry and topology can also be viewed as a form of conservation law (see Heredity).
Cosmological consistency
SER starts from a single high-dimension cell. On average, its action reproduces ΛCDM scaling: today’s horizon radius is ≈ 46.14 Gly, the H(z) curves match Planck 2018, and the number of cells at key epochs (Recombination, Dark Ages, Today/Now) corresponds to the radii of standard cosmology. SER does not replace ΛCDM; it provides its “mechanics”: how space actually unfolds.
The set of fundamental constants is identical to the conventional one and is used without modification. All processes and phenomena occur within the constraints imposed by these constants.
Transition rate
- Tick: over a time interval of at least one time quantum, each SQ makes one transition attempt under the SER rule.
- The decay fraction is set by the wavefunction, which specifies the full quantum state of the space cell at the current tick:
- the event component — FATE — the probability of executing a SER step on this tick. Outcomes are: a decrease in dimension (decay, “Down”), an increase in dimension (reverse, “Up”), or preserving the state (“Hold”);
- the emission component — BURDEN — the probability of emitting part of the charge into substance / absorbing substance from space back into charge.
- The large number of SQ and the homogeneity of conditions statistically ensure a constant decay fraction. At a given dimension, all SQ are described by the same wavefunction and are in the same (isotropic) conditions; at each tick they perform independent attempts of the same type. Over large ensembles, this “the same trial, many times” yields a stable mean fraction of successful decays per tick within a causally connected region. This implies a stable proportional growth in the number of SQ while conserving total charge, and on macroscales—smooth, predictable expansion of the Universe; in the Λ-dominated era, this appears as an almost constant expansion pace (the observed Hubble parameter).
Gravitational anomalies
For a more complete interpretation of gravity, see Appendix 3. Gravity in Discrete SQ Space.
The quantized nature of SER already at early stages of the Universe’s evolution provides a basis for local deviations. Rare but recurring “Hold” outcomes at early stages lock in local zones where the mean local dimensionality lags behind the mean across the whole domain (a gradient of effective dimensionality).
After the emission of substance, these local patches act as gravitational anchors: ordinary matter settles and accumulates there, forming the initial condensation centers. The subsequent uniform expansion of space carries these pockets to cosmological distances. They become nodes of the future large-scale structure.
These local zones are not static; they are characterized by dynamic homeostasis: at every location where the resultant of masses forms a center, the spatial lattice forms a corresponding local dimensionality gradient, proportional to the sum of the acting masses. Such an anchor is maintained and adjusted as the system configuration changes.
The “Hold” outcome is quantum-probabilistic and is realized across a huge number of independent trials; when averaged over a causally connected region, such patches emerge statistically uniformly. This preserves the observed isotropy and homogeneity on average, while simultaneously providing a realistic spectrum of large inhomogeneities.
“Dark matter”. Dimensionality gradients.
Deviations (“SER lags”) generate extended pockets. Their integrated effect is observed as “additional mass” in rotation profiles and lensing—what classical physics calls dark matter.
To reproduce the observed gravitational effects in halo regions, it is sufficient to have a stable local uplift of effective dimensionality at radii of order 8–10 kpc. In practice, this is realized as a “staircase” of fractions of elevated levels within the halo.
Scenario A (dense staircase): 5D ≈ 32%, 6D ≈ 12%, 7D ≈ 3.5%, 8D ≈ 1.0%, 9D ≈ 0.3%, 10D ≤ 0.03%.
Scenario B (moderate staircase): 5D ≈ 24%, 6D ≈ 8%, 7D ≈ 2.0–2.5%, 8D ≈ 0.5%, 9D ≈ 0.1–0.2%, 10D trace-level.
Other nearby combinations of fractions that yield a similar “additional mass” effect are also admissible. The presence of a denser inner core requires a small increase in the fractions of levels ≥7D in the central kiloparsecs while keeping the outer staircase unchanged. Such a stable positive deviation yields the correct order of additional “mass” for the flat tails of rotation curves and for weak/strong lensing, without postulating “dark matter” particles.
The mean background dimensionality is preserved (model-wise ⟨D⟩ ≈ 4.81); statistical isotropy and homogeneity of the background are not violated; the stability of the picture is supported by dynamic homeostasis.
For more detail, see Appendix 4. Relic Dimensionality Gradients.
“Black holes” — Astroscotomas
Local regions of space in which mass has reached such a degree of compactness that its gravitational field fully closes the trajectories of light and particles. From the outside, such regions manifest only through gravitational influence and accretion effects, while anything that crosses their boundary disappears from the observable world. Inside an astroscotoma, the density of substance is finite and increases toward the center, but does not become infinite. The substance is conserved and can transition into other phase states, including the breakdown of elementary particles into more elementary charge carriers.
There are two types of such objects.
- “Old” ones. Central galactic astroscotomas. They form in early epochs of evolution from primary density inhomogeneities and grow together with galaxies, concentrating a significant fraction of the mass of their nuclei.
- “New” ones. “Wandering” astroscotomas. They arise at later stages from collapsed stars and subsequent mergers of compact objects. They move through the interstellar and intergalactic medium, interacting with it via accretion and gravity.
An astroscotoma is not a hole or a singularity: it is a causally hidden but physically finite mass configuration. Its opacity is determined by the geometry of space and speed limits, not by the destruction of matter or the disappearance of time. For an external observer, it is a blind spot in the structure of the Universe, retaining all its mass and all physical laws within—simply hidden behind an opacity barrier.
For more detail, see Appendix 5. Astroscotomas.
“Dark energy” — Expansion of space — SER as such. Entropy
The global SER background (a statistical bias toward lower internal dimensionality with the birth of new SQ) leads to a global metric discharge—at the macro level, this appears as expansion. Local “islands” of elevated dimensionality on this background yield DM, while the smooth component of the process yields the Λ-effect.
By the “entropic trend” in SER we mean the directionality of cell dynamics between two regimes:
- Reverse (folding): coarsening of cells, growth of effective dimensionality. Driving force: gravity. In reverse, the cellular medium folds toward higher dimensionality due to gravitational attraction and SQ coalescence. This is a probabilistic process: high-dimensional cells form an “attraction” field for their neighborhood; they grow / burst. Overall, it resembles continuous “bubbling”.
- Forward (unfolding / SER): refinement of cells, dimensionality degradation. Driving force: cell charge. As long as charge is present in the system, it pushes SQ apart, leading to dimensionality degradation (refinement) and an increase in the number of cells.
- Substance pulls toward reverse, but cannot quickly “collapse” back into charge. For the full degradation of substance, the following are required:
- Dilution: cosmological expansion and a drop of SQ dimensionality below 3 must reduce the density of substance to a level compatible with the SQ “reception quanta”.
- Matching of the reception window: local cells must have sufficient information capacity (and suitable morphology) to rewrite substance into charge.
- In the presence of high matter density, large masses, and cell charge that significantly exceeds the elementary level, the overall process flow is directed toward reducing the residual SQ charge and, as a consequence, toward the expansion of space. The “windows” for transferring part of the charge into substance and the “windows” for the reverse return do not coincide in place or time; in aggregate this yields a predominance of unfolding. All else equal, the SQ network naturally moves toward states with a larger number of cells and a smaller mean charge.
Reverse-engineering the Universe
If the SER rule is applied in reverse mode, the parameters of the initial state can be reconstructed from the current number of Space Quanta (SQ) [9]. The reverse mode provides a quantitative estimate of the starting dimensionality of the fundamental SQ and formalizes the path from “today” back to the “beginning”.
Goal:
From the present-day known radius of the causally connected region, obtain:
- The current number of Planck-scale Space Quanta within the causal sphere;
- The degradation level index L under the SER rule;
- The number of levels that must be traversed “upward” (by folding) to reach a single quantum;
- Determine the internal dimensionality d of that single quantum;
- Determine the current macrodimensionality D of space.
Input data:
- Radius of the causally connected region today: Rhor0 = 4.36520×1026 m
- Number of Space Quanta (SQ) inside this region (current-space volume / Planck volume): Nhor0 = 8.25215×10184
- Folding rule (reverse SER): at a step with dimensionality d we apply 2 × d × SQd−1 → SQd
- Constraints: clearly, the starting dimensionality d0 cannot be below 3, as that would contradict the observed physics.
Result:
the number of SER “steps” from the current state to a merger into 1 SQ is 96 or 97. Added to the current SQ dimensionality, this yields the dimensionality of the “primordial” SQ.
With the minimally admissible (observational) macrometric of macroscopic space D0 ≈ 3 and an admissible d0 ≈ 3, we obtain a fractional dimensionality [10] of the single SQ: dstart = 99.36. With an integer dstart = 100, we obtain an estimate of the current macrodimensionality d0 ≈ 4.81.
That is, 97 full SER steps bring the causally connected SQ domain from the micro-metric state dstart (100–99.36) to the state d0 (4.81–3).
For a number of reasons, one cannot assert that these numerical estimates are the true characteristics of the current Universe, because:
- It is not fixed that the Universe consists only of the causally connected region, which makes an arbitrary dstart ≥ 100 possible.
- The space fabric accessible to us behaves as three-dimensional: locally, ordinary 3D geometry; globally, an almost flat FLRW [11]. This is consistent with the CMB [12] / BAO [13] and standard cosmology as a whole. However, it is not asserted that the current d0 ≈ 3, because SQ with d > 3 can form connected, stable subnets of any admissible macrodimensionality D. Yet the same logic implies a hard constraint: D ≤ d.
One may postulate that there exists a finite number of SER steps which, for an arbitrary dstart ≥ 100, under the unfolding rule SER SQd → 2 × d × SQd−1, brings the Universe’s causally connected region from a single SQ to the observed state Rhor0 without contradiction. In this case:
- The observational picture of the Universe is reproduced.
- The chronology of the Universe’s evolution is preserved (both its characteristic stages and its pace).
- The observed present-day morphology, composition, and structure of the Universe’s causally connected region are explained, as well as their evolution.
- There are no contradictions or “fine-tuning” required to match the observational effects of ΛCDM.
- There are no contradictions or “fine-tuning” required to match the Standard Model of particle physics and quantum field theories; the framework serves solely as their “battlefield.”
Note 9
A similar move—extrapolating the Friedmann metric backward in time—is precisely what enabled the Big Bang concept to be introduced as an initial state.
Note 10
The fractional dimensionality of the primary SQ dstart will be interpreted when we consider the initial stage of the Universe’s evolution. The fractional dimensionality d(0) is treated as the mean dimensionality of individual SQ across a causally connected domain, because SER does not proceed with non-uniformities and non-simultaneities.
Note 11
Friedmann–Lemaître–Robertson–Walker (FLRW) metric — the standard cosmological model metric (Friedmann–Lemaître–Robertson–Walker).
Note 12
CMB (Cosmic Microwave Background) — relic microwave radiation: light that “decoupled” from matter at recombination (≈380 thousand years after the beginning). Its small temperature “spots” and the peak in the anisotropy spectrum are a trace of acoustic waves in the early plasma.
Note 13
BAO (Baryon Acoustic Oscillations) — baryon acoustic oscillations: the same acoustic physics, but imprinted as a faint “rippling” in the galaxy distribution—a standard ruler of ~150 Mpc (comoving).
Model Dimensionality Parameters
Going forward, the range (dstart = 100 → d0 = 4.81) will be used as the “model” dimensionality parameters for the Universe’s evolution. If the Universe beyond the causally connected region is also homogeneous and isotropic, then other combinations of dstart and d0, consistent with SER logic, will yield proportionally equivalent results.