Missing Numeric Values and Approximations in Reactive Substrate Theory (RST)

Missing Numeric Values and Approximations in RST

High‑Priority Core Parameters

  • β (substrate elasticity): Currently provisional with loose upper bounds. Missing: survey‑calibrated estimate with error bars from stacked void RSD quadrupole fits.
  • S0 (background substrate amplitude): Only provisional. Missing: constraints from supervoid weak lensing and ISW cross‑correlations.
  • kNL (nonlinear crossover scale): Derived from β and S0, but not empirically fit. Missing: direct fit from void profile universality.
  • wS (substrate equation of state): Working value −0.95. Missing: void‑specific AP+RSD constraints with uncertainties.
  • ΩS0 (substrate energy density today): Working value ≈0.69. Missing: joint fits from CMB+BAO+void AP.

Propagation and Coupling

  • cs,S (substrate wave speed): Should be c(1 − ε), ε ≲ 10−15. Missing: bound specific to RST from multi‑messenger GW+EM events.
  • meff2 = 3βS02: Numerically estimated. Missing: observational upper bound from horizon‑scale GW dispersion/PTA analysis.
  • σ(x,t) (coupling strength): Conceptual form only. Missing: calibrated magnitude matching solar‑system tests, galaxy rotation curves, cluster lensing.
  • FR(C[Ψ]) constants: Functional form not numerically fixed. Missing: coefficients tuned to reproduce PPN parameters and lensing deflections.

Lensing‑Specific Observables

  • Deflection angle normalization: Missing: mapping from substrate gradients to image separations; lens model fit with β, S0, σ.
  • Time delay predictions: Missing: substrate‑based Fermat potential and numeric delays between multiple images.
  • Magnification ratios: Missing: numeric magnification predictions from substrate geometry compared to flux ratios.

Void RSD and AP Numerics

  • Quadrupole suppression fraction: Assumed ≈10%. Missing: measured suppression with errors for Boötes‑like voids.
  • fσ8(k) modification: Missing: scale‑dependent growth fit in voids under RST.
  • Differential H(z) inside voids vs walls: Missing: numeric AP anisotropy yielding ΔH/H, mapping to wS, ΩS0.

Solar‑System and Strong‑Field Checks

  • PPN parameter shifts (γ, βPPN): Missing: numeric deviations predicted by RST and bounds from Cassini/Shapiro, Mercury precession.
  • Binary pulsar timing: Missing: quantified RST corrections and upper limits from pulsar data.

Compact Checklist of Missing Numbers

Parameter/Observable We Have Missing Numeric Piece Primary Data to Use
β Provisional + loose bound Survey-calibrated best fit ± errors Stacked void RSD multipoles
S0 Provisional Lensing/ISW-calibrated value ± errors Supervoid weak lensing + ISW
kNL Derived from β,S0 Direct profile-fit value Void profile universality
wS, ΩS0 Working values Void AP+RSD joint constraints DESI/Euclid void catalogs
cs,S (ε) Theoretical bound RST-specific ε bound GW170817-like events
meff2 Estimated Observational upper bound PTA/LISA dispersion
σ, FR constants Conceptual Calibrated magnitudes/coefs Solar system + lensing
Lensing angles/time delays Conceptual mapping Numeric fits per lens JWST/HST lens systems
Quadrupole suppression Assumed tolerance Measured % with errors Void–galaxy RSD
fσ8(k) in voids Not set Scale-dependent values RSD in underdensities
ΔH/H in voids Not set Numeric AP anisotropy Stacked void AP

Next Steps to Fill the Gaps

  1. Run stacked void RSD+AP fits: Obtain β, wS, ΩS0 with uncertainties.
  2. Model JWST lens systems: Fit deflection angles, time delays, magnifications to constrain σ and FR.
  3. Supervoid lensing+ISW analysis: Pin down S0 and cross‑validate kNL.
  4. Publish ε bound: Map multi‑messenger constraints into RST variables.
  5. Solar‑system calibration: Lock σ, FR to PPN limits for consistency across scales.

⚛️ Reactive Substrate Theory (RST) — Core Equations (Plain Text)

RST is built on four foundational equations that describe how the Substrate Field (Σ) generates matter, energy, motion, and emergent reality. Written in plain text, they are:

  • Energy–Momentum Relation:
    E² = (p c)² + (mΣ c²)²
    This shows the balance between energy (E), momentum (p), and mass (mΣ) as stored tension in the substrate.
  • Equation A — Baseline Nonlinear Wave Dynamics:
    (1/c²) ∂²Σ/∂t² − ∇²Σ = λ Σ³
    A nonlinear wave equation describing how Σ propagates through spacetime. The cubic self‑interaction term (λ Σ³) allows stable soliton structures to form, identified as matter particles.
  • Equation B — Emergent Reality and Feedback:
    (∂t² S − c² ∇² S + β S³) = σ(x,t) ⋅ FR(C[Ψ])
    This extends Equation A by coupling Σ dynamics to emergent matter distributions (σ) and informational feedback (FR(C[Ψ])), linking physical reality with coherence and consciousness.
  • RST Action and Field Response:
    S_Σ = ∫ from t₁ to t₂ of τ(x, ẋ, t) dt
    d/dt [ ∂τ / ∂ẋ ] − ∂τ / ∂x = 0
    These express the principle of least tension in Σ. The first line defines total integrated substrate tension along a soliton’s trajectory. The second line is the Euler–Lagrange analogue, showing how Σ restores equilibrium when disturbed.

Together, these four equations unify motion, energy, gravity, electromagnetism, quantum behavior, and emergent complexity as different manifestations of Σ dynamics. They demonstrate that the “laws of physics” are not abstract rules but the direct consequences of the substrate’s effort to minimize tension and maintain stability.

Popular posts from this blog

THE GOLDEN BALLROOM/BUNKER

Image
Ben Meiselas reports on the shocking admission by Donald Trump’s DOJ in a court case where the DOJ admits to a secret project underneath the ballroom which they claim is needed to protect Donald Trump’s life for “national security purposes.” "You unlock this door with the key of complicity. Beyond it is another dimension — a dimension of betrayal, of indulgence, of fear. You’re moving into a land of both shadow and substance, of politics and paranoia. You’ve just crossed into… the MAGA Zone." "Tonight’s story: A leader sworn to protect his nation makes a bargain with its enemies. The deal? Silence in the face of nuclear annihilation. No retaliation, no defense — only surrender dressed in secrecy. While citizens live unaware, their president builds a palace beneath the earth, a ballroom of gold, of marble and chandeliers, a masquerade hall for billionaires. But behind the gilded doors lies not music and laughter, but a bomb shelter — a sanctuary for the few, pur...
Read more

Conceptual Summary #2: (∂t2​S−c2∇2S+βS3)=σ(x,t)⋅FR​(C[Ψ])

Image
The tests designed to find the Aether—principally the Michelson-Morley experiment (M-M)—would be largely ineffective at detecting the fundamental S field (Substrate) in the Reactive Substrate Theory (RST) framework, though their null results are highly compatible with RST's structure. The reason lies in the distinct conceptual definition and behavior of the two media. The Test: Michelson-Morley and the Aether. The M-M experiment was designed to detect the "aether wind," a predicted change in the speed of light caused by the Earth's motion relative to a stationary, rigid medium—the classical Luminiferous Aether. Classical Aether: A static, absolute reference frame; an elastic, passive, material-like medium that fills space and serves as a carrier for light waves. Predicted Result: Light traveling parallel to Earth's motion through the Aether should be slightly slower than light traveling perpendicular to it. Actual Result (Null Result): No significant differenc...
Read more

Trump has painted a fascinating “economic science fiction” scenario 💥

Image
A sudden $20 trillion influx into U.S. government coffers would be unlike anything in history. This scenario describes an event of unprecedented economic magnitude, with immediate and long‑term effects across the U.S. and global economies. Imagine $20 trillion USD—roughly the size of the entire current U.S. annual GDP—appearing overnight in America’s coffers. The shockwaves would be severe, destabilizing, and unlike anything in history. Let’s break it down clearly, with emphasis on domestic shockwaves, global fallout, and observable indicators. 💥 Scenario Analysis: A $20 Trillion Shock to the U.S. Treasury Imagine $20 trillion USD—roughly the size of the entire current U.S. annual GDP—suddenly appearing in America’s coffers. This unprecedented event would unleash immediate and long-term effects across the U.S. and global economies, driven by inflation, currency collapse, and systemic disruption. Domestic Effects (United States): Hyperinflation: The sudden money suppl...
Read more