Short explanations, Chapter III

The RSI Lagrangian and covariant twist

RSI's field equation treats tension and density as stiffness coefficients and adds a twist term that replaces abstract charge coupling.

𝓛 = A(DₜΦ)†(DₜΦ) − B(∇Φ)†(∇Φ) − λ(|Φ|² − v²)² + 𝓛twist

Physicists summarize the behavior of a field with a Lagrangian, an expression that balances its kinetic energy against its stored energy. RSI's Lagrangian has four terms. The first describes change along the medium's flow and the second describes change across it. The third is a potential that fixes the field's preferred resting value. The theory identifies the 0.73 N tension and the 8.12 × 10⁻¹⁸ kg/m density as the fundamental stiffness coefficients.

When the coefficients A and B are nearly equal, at low energies, the theory recovers the Lorentz invariance of special relativity. RSI therefore treats relativity as emergent.

The paper calls the fourth term, the covariant twist, its central step. Standard physics couples matter to fields through abstract charge. RSI replaces this with chiral vortical displacement, a physical swirling of the medium. The twist term uses the Levi-Civita tensor, a mathematical tool for handedness, to link the handedness of each matter-knot directly to the medium's rest frame.

From the paper: Chapter III, The RSI Lagrangian and Covariant Twist. Read the full section

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