Black Holes and the CMB in Temporal Flow Physics (TFP)
By John Gavel
In Temporal Flow Physics (TFP), cosmological observables such as vacuum energy, the Hubble constant, and CMB temperature anisotropies are not independent phenomena. They are different projections of the same underlying process: the sequential resolution of relational differences in a one-dimensional causal substrate.
The Definitive TFP Expression for the Cosmological Constant
The cosmological constant arises from a structural mismatch between the update capacity of the 1D substrate and the geometric requirements of emergent 3D space.
The fundamental relation is:
$$ \Lambda = \frac{\delta_{\text{eff}}}{L_c^2} $$
Where:
- \(\delta_{\text{eff}}\) (Informational Friction): The structural deficit of the update rule. Geometry requires 144 neighbor relations, while causality can only process 132: $$ \delta_{\text{eff}} = \frac{144 - 132}{144} = \frac{1}{12}. $$
- \(L_c\) (Coherence Length): The minimum scale at which the 132-address update successfully resolves into a stable 3D coordinate. Empirically, $$ L_c \sim 10^{-17} \text{ m} \;\text{to}\; 10^{-15} \text{ m}. $$
Step-by-Step Evaluation
Step A: Dimensionless Update Pressure
Each substrate tick produces an irreducible mismatch because the update can only compare one neighbor at a time while geometry requires two. This produces a constant leakage:
$$ \text{Friction Factor} = \frac{1}{12} \approx 0.0833. $$
Step B: Volumetric Dilution
The substrate is densely packed at the Planck scale \(L_p\), but observations are made at the coherence scale \(L_c\). The energy density therefore dilutes across the scale gap:
$$ \Sigma_{\text{gap}} = \frac{L_c}{L_p} \approx 10^{20}. $$
Because the update resolves sequentially across three spatial dimensions and one temporal cycle, the dilution scales as \(\Sigma_{\text{gap}}^4\).
The observed cosmological constant becomes:
$$ \Lambda_{\text{obs}} \approx \frac{1/12}{\Sigma_{\text{gap}}^4 \, L_p^2}. $$
Step C: Numerical Substitution
Using:
- \(\delta_{\text{eff}} = 1/12\)
- \(\Sigma_{\text{gap}} = 10^{20}\)
- \(L_p = 1.616 \times 10^{-35}\,\text{m}\)
We obtain:
$$ \Lambda \approx \frac{0.0833}{(10^{80})(2.6 \times 10^{-70})} \approx 10^{-52} \,\text{m}^{-2}. $$
This matches the observed value of the cosmological constant.
The TFP Origin of the Hubble Constant
In TFP, cosmic expansion is not a global metric stretching but the cumulative slippage of the 132-address update over the distance required to resolve a 3D coordinate.
The local expansion rate is:
$$ H(x) = \frac{1}{\tau_{\text{pixel}}} \left( \frac{\delta_{\text{local}}}{\Phi_{\text{coh}}(x)} \right). $$
Where:
- \(\delta_{\text{local}} = 1/12\): structural friction
- \(\Phi_{\text{coh}}(x)\): local substrate stiffness
- \(\tau_{\text{pixel}} \approx 12\) Planck ticks: full update cycle
The Hubble Range: Crunch vs Bang Phases
Lower Bound — The Crunch Phase (Filaments / CMB)
High difference density produces a tense substrate. The update stalls, reducing apparent expansion.
$$ H_0 \approx 67.4 \,\text{km/s/Mpc}. $$
Upper Bound — The Bang Phase (Voids / Local)
Resolved differences leave the substrate relaxed. The update idles, allowing faster metric drift.
$$ H_0 \approx 74.8 \,\text{km/s/Mpc}. $$
Global Mean
$$ H_0 = 71.1 \pm 3.7 \,\text{km/s/Mpc}. $$
The so-called “Hubble tension” is therefore a convection gradient, not a contradiction.
Local Vacuum Temperature as Exhaust Pressure
In TFP, vacuum temperature is not literal heat. It measures local expansion pressure from resolved substrate flow.
$$ T_{\text{rad}} = T_{\text{CMB}} \left( 1 + \frac{\dot{M}\,\delta_{\text{eff}}}{M_{\text{BH}}\,\Phi_{\text{coh}}} \right). $$
Where:
- \(\dot{M}\): accretion rate
- \(M_{\text{BH}}\): black hole mass
- \(\delta_{\text{eff}} = 1/12\)
- \(\Phi_{\text{coh}}\): local stiffness
For M87*, this predicts:
$$ \Delta T \sim 3.4\,\mu\text{K}, $$
consistent with Sunyaev–Zeldovich measurements.
Local Expansion from Temperature
Expansion follows directly from pressure:
$$ H_{\text{local}} = H_{\text{baseline}} \frac{T_{\text{rad}}}{T_{\text{CMB}}}. $$
For M87*:
$$ H_{\text{local}} \approx 71.10009 \,\text{km/s/Mpc}. $$
Summed across the cosmic web, these micro-variations produce the observed late-universe values.
Black Holes as Universal Tax Collectors
- The \(1/12\) deficit is the tax required to convert 1D truth into 3D surmise
- Black holes process this debt
- The exhaust is newly resolved space
- Filaments supply unresolved differences
Conceptual Takeaway
Vacuum energy, Hubble drift, and CMB microstructure are not separate mysteries. They are different observational slices of the same substrate process.
Time, space, mass, and gravity emerge from sequential resolution under the 132/144 constraint.
Cosmological “constants” are therefore not constants at all — they are weather reports of cosmic metabolism.
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