Deriving the RST Tension Equations: How Gravity Emerges from Substrate Mechanics

Recommended Video: Understanding Space-Time

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Deriving the RST Tension Equations: How Gravity Emerges from Substrate Mechanics

Reactive Substrate Theory (RST) proposes that the vacuum is not empty but is a continuous physical medium — the Substrate — with real tension and inertia. In this framework, gravity, time dilation, and redshift arise not from geometric postulates but from the mechanical behavior of this medium.

This article presents the first full derivation of the RST tension equations, showing how mass compresses the Substrate, how tension gradients form, and how these gradients reproduce the observable predictions of General Relativity.

1. The Physical Assumptions of RST

RST begins with three foundational assumptions:

  1. The vacuum is a continuous medium with baseline tension T0 and inertia ρ0.
  2. Mass compresses the Substrate, increasing both tension and inertia locally.
  3. Light is a shear ripple in the Substrate, with speed determined by the wave-speed equation:

c(r) = √( T(r) / ρ(r) )

This is the same equation that governs wave propagation in any physical medium. Unlike classical aether theories, RST’s Substrate is reactive: it changes state in response to matter and energy.

2. How Mass Modifies the Substrate

A mass M placed in the Substrate creates a compression field. The simplest physically consistent assumption is that the compression falls off with distance as an inverse-square law, just like gravitational force.

Thus, RST defines:

T(r) = T0 + kM / r²

ρ(r) = ρ0 + hM / r²

where k and h are coupling constants describing how strongly mass affects tension and inertia.

These equations are not arbitrary — they follow from the requirement that the Substrate must remain stable and isotropic, and that the influence of mass must diminish with distance.

3. Deriving the Local Speed of Light

Substituting the tension and inertia fields into the wave-speed equation gives:

c(r) = √( (T0 + kM / r²) / (ρ0 + hM / r²) )

This expression shows that the speed of light is not a universal constant but depends on the mechanical state of the Substrate. However, because T0 ≫ kM / r² and ρ0 ≫ hM / r² under normal conditions, the variation is extremely small — matching the empirical fact that c is nearly constant.

4. Deriving Gravitational Time Dilation

In RST, a clock is a soliton — a stable, self-reinforcing wave structure. Its oscillation frequency is proportional to the local wave speed:

f(r) ∝ √( T(r) / ρ(r) )

Therefore, the ratio of clock rates at two radii r₁ and r₂ is:

f(r₂) / f(r₁) = √( (T(r₂)/ρ(r₂)) / (T(r₁)/ρ(r₁)) )

This reproduces the qualitative behavior of gravitational time dilation in General Relativity:

  • Clocks run slower near mass (higher tension).
  • Clocks run faster farther away (lower tension).

But unlike GR, RST provides a physical mechanism for the effect.

5. Deriving Gravitational Redshift

A photon climbing out of a tension well loses frequency because the local wave speed changes. The redshift is:

z = √( T(r₂)/ρ(r₂) ) / √( T(r₁)/ρ(r₁) ) − 1

This matches the GR prediction for weak fields but diverges slightly in strong fields — a potential observational test of RST.

6. Deriving the Effective Gravitational Force

A tension gradient produces a force on solitons. The force per unit mass is:

g(r) = − (1 / 2ρ(r)) dT(r)/dr

Substituting the tension field:

dT/dr = −2kM / r³

gives:

g(r) = (kM) / (ρ(r) r³)

If we choose k / ρ0 = G, this becomes:

g(r) ≈ GM / r²

Thus, Newtonian gravity emerges naturally from Substrate mechanics.

7. Summary of the RST Tension Equations

The full set of RST equations derived above is:

  • T(r) = T₀ + kM / r²
  • ρ(r) = ρ₀ + hM / r²
  • c(r) = √(T(r)/ρ(r))
  • f(r) ∝ √(T(r)/ρ(r))
  • z = √(T₂/ρ₂) / √(T₁/ρ₁) − 1
  • g(r) = −(1/2ρ) dT/dr

These equations reproduce the observable predictions of General Relativity while providing a deeper physical explanation rooted in the mechanics of a continuous medium.

8. Why RST Works

RST succeeds because it:

  • Explains gravity as a mechanical effect, not a geometric postulate.
  • Derives time dilation and redshift from first principles.
  • Predicts measurable deviations from GR in strong fields.
  • Unifies wave propagation, soliton structure, and gravity under one framework.

In RST, the universe is not shaped by abstract geometry but by the tension landscape of a real, reactive medium. Space-time is the geometry of that medium — not a void, not a zero, but the dynamic stage on which all physical processes unfold.

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