WHY SPACE IS 3D — AND WHY GRAVITY IS LATENCY
by John Gavel
What I Am Claiming (Up Front)
I am not proposing a new force, a new particle, or an alternative geometry.
I am making a more basic claim:
Space, time, mass, and relativity are not containers or primitives. They are bookkeeping consequences of a finite causal budget.
In Temporal Flow Physics (TFP), the universe does not exist in dimensions. Dimensions are serialized outcomes of how a fixed causal resource is spent.
This post presents a direct, equation-level argument for why:
- Space is exactly three-dimensional
- Lorentz symmetry emerges automatically
- Mass is stored causal remainder
- Attempts at higher-dimensional stability fail
No metaphors. No appeals to authority. Just constraints.
1. The One Invariant: The Handshake Budget
TFP begins with a single global invariant:
H = 132
This is the maximum number of causal handshakes a node can perform per full resolution cycle. Nothing can exceed this budget. There is no hidden reservoir.
This replaces the traditional role of:
- Energy conservation
- Action principles
- Background spacetime
All dynamics are budget reallocations.
2. Rank Closure: What It Means for Something to Exist
A causal state is only real if it is locally determinate.
In TFP, determinacy requires closure over a 12-point motif:
R_min = 12
Below rank 12, reality is underdetermined.
3. Dimension Is Not a Container — It Is a Sequence
Dimensions do not coexist. They serialize.
Define a causal cycle:
$$ \mathcal{C} = \{ t_n, t_{n+1}, t_{n+2} \} $$
Define directional resolution operators:
$$ \mathcal{R}_X(t_n), \quad \mathcal{R}_Y(t_{n+1}), \quad \mathcal{R}_Z(t_{n+2}) $$
Then a 3D volume is:
$$ V \equiv \mathcal{R}_Z \circ \mathcal{R}_Y \circ \mathcal{R}_X $$
No sequence → no volume.
4. Budget Partition in a Vacuum
In an isotropic vacuum, the budget distributes evenly:
$$ H_X = H_Y = H_Z = \frac{H}{3} = 44 $$
Each directional update has enough budget to maintain rank closure:
$$ 44 \ge R_{min} = 12 $$
So 3D space is stable.
5. Why a Fourth Dimension Fails (The Real Reason)
A common objection is: “But 132 / 4 = 33 > 12. Why not four dimensions?”
Because rank closure is not the limiting factor.
Let:
- D = number of serialized dimensions
- H_d = H / D
Latency per dimension scales as:
$$ \lambda_d \propto \frac{R_{min}}{H_d} $$
Total cycle latency:
$$ T_D \propto \sum_{d=1}^{D} \lambda_d = D \cdot \frac{R_{min}}{H/D} = \frac{D^2 R_{min}}{H} $$
Latency grows quadratically with dimension count.
6. The Stability Inequality
For a causal structure to persist:
$$ T_D < T_{max} $$
Substitute:
$$ \frac{D^2 R_{min}}{H} < T_{max} $$
With H = 132, R_min = 12:
$$ D^2 < 11 \cdot T_{max} $$
Empirically:
- D = 3 → stable
- D = 4 → unstable
Four dimensions do not fail geometrically. They fail temporally.
7. Velocity as Sequential Compression (Lorentz Emergence)
Motion is not movement through space. It is budget priority reassignment.
If an object moves along X:
$$ H_X \rightarrow H_X + \Delta H $$
Budget conservation:
$$ H_X + H_Y + H_Z = H $$
Cycle latency becomes:
$$ T(v) \propto \frac{1}{H_X} + \frac{2}{H - H_X} $$
Normalize with:
$$ \frac{H_X}{H} = \frac{v^2}{c^2} $$
Then:
$$ \frac{T(v)}{T(0)} = \frac{1}{\sqrt{1 - v^2/c^2}} = \gamma $$
Lorentz time dilation drops out automatically.
8. Length Contraction
Length is the number of successful handshakes across a dimension.
If budget is redirected into motion:
$$ L(v) \propto H_Y = H_Z = H \sqrt{1 - v^2/c^2} $$
Thus:
$$ L(v) = \frac{L_0}{\gamma} $$
9. The Mass Gap (The 1/12 Remainder)
After every full XYZ cycle:
- Rank closure completes
- Temporal closure does not
There is an irreducible remainder:
$$ \epsilon = \frac{1}{12} $$
This unresolved causal residue must be carried forward.
Define mass as accumulated remainder:
$$ m \propto \sum \epsilon $$
10. Gravity Without Geometry
Localized mass increases recursion depth, which increases local latency:
$$ \lambda_{local} > \lambda_{vacuum} $$
Define latency field:
$$ \Phi_\lambda(\vec{r}) $$
Curvature becomes:
$$ R_{\mu\nu} \sim \nabla_\mu \nabla_\nu \Phi_\lambda $$
Gravity is not bending space. It is refraction of causal flow.
11. Deriving the Schwarzschild Metric from Latency
11.1 Metric Mapping
In GR, the Schwarzschild interval is:
$$ ds^2 = -(1 - r_s/r)c^2 dt^2 + dr^2 / (1 - r_s/r) + r^2 d\Omega^2 $$
In TFP, we replace geometry with cycle completion latency:
Radial direction r <- t_n
Tangential directions <- t_{n+1}, t_{n+2}
11.2 Radial Budget Exhaustion
Total budget: H = 132
Mass M requires internal recursion cost:
$$ B_R(r) \sim GM / (r c^2) $$
Budget conservation:
$$ H = B_R + B_X + B_Y + B_Z $$
So radial budget:
$$ B_X(r) = H \cdot (1 - r_s/r), \quad r_s = 2GM / c^2 $$
11.3 Radial Delay
Latency inversely proportional to available budget:
$$ \lambda_r \sim 1 / B_X(r) $$
Radial distance requires more ticks → effective stretching.
11.4 Gravitational Time Dilation
Total cycle time:
$$ T = \lambda_r + \lambda_\theta + \lambda_\phi $$
Only lambda_r affected by mass:
$$ dt_{local} / dt = \sqrt{1 - r_s/r} $$
11.5 Reconstructing the Metric
Temporal term:
$$ c^2 dt^2 \rightarrow c^2 (1 - r_s/r) dt^2 $$
Radial term:
$$ dr^2 \rightarrow dr^2 / (1 - r_s/r) $$
Angular terms unchanged.
Result:
$$ ds^2 = -(1 - r_s/r)c^2 dt^2 + dr^2 / (1 - r_s/r) + r^2 d\Omega^2 $$
Schwarzschild metric recovered exactly.
11.6 Interpretation
Einstein: space is curved, clocks slow.
TFP: processing is delayed, distances appear longer. Same equations, different causality.
Final Statement
Traditional physics:
- Assumes dimensions
- Postulates Lorentz symmetry
- Treats mass and curvature as primitives
Temporal Flow Physics:
- Derives dimensions from budget limits
- Derives Lorentz symmetry from serialization
- Derives gravity from latency gradients
Space is three-dimensional because the universe cannot complete a stable causal cycle in four.
Not geometrically. Causally.
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