Shukla Photonic Field Theory (SPFT-4) : SIPE as the Stiffness-Origin of Gravity

Abstract

We extend the Shukla Photonic Field Theory (SPFT-4) by introducing SIPE Vacuum stiffness, denoted as K_SIPE, as a fundamental physical origin of angular momentum in astrophysical systems. Observations show that planets, protostellar disks, stars, and galaxies rotate coherently, yet conventional theories rely on primordial spin or dark matter halos, leaving the origin of rotation unexplained. In contrast, SPFT proposes that the Vacuum possesses a finite stiffness due to the intrinsic Shukla Inherent Photon Energy (SIPE). The SIPE energy is extremely small, often expressed as an effective lower bound (~10⁻³⁰³⁰ eV) associated with the terminal stage of photon redshifting, whose scalar field energy fills the Vacuum, turning it into a stiff medium capable of mediating angular momentum. The Vacuum energy density is approximately ρ_vac ≈ 6 × 10^(-10) joule per cubic meter, and the corresponding Vacuum stiffness is K_SIPE = ρ_vac × c² ≈ 5.4 × 10⁷ Pascal, where c = 3 × 10⁸ m/s is the speed of light. This numerical scale is introduced here for the first time and provides a physically motivated, parameter-free measure of Vacuum rigidity. During gravitational collapse, random off-center mass infall interacts with this stiff Vacuum, producing Vacuum torque (τ) that converts radial motion into tangential motion. The emergent tangential velocity v_t is expressed as v_t(r) ≈ √(G × M_c(<r) / r) × (b / r) × √(K / K₀), where M_c(<r) is the cumulative mass enclosed within radius r, b is the impact parameter of infalling matter, K₀ = K_SIPE is the reference Vacuum stiffness, and G is the gravitational constant. The corresponding specific angular momentum j is given by j = r × v_t. Even when the system begins with total angular momentum L = 0, the interaction of off-center infall and Vacuum stiffness dynamically generates L > 0, giving rise to coherent rotation. This unified mechanism explains flat galactic rotation curves, planetary spin, angular momentum distribution, disk ring spacing (including retrograde rings), transient gaps in protoplanetary disks, and phase–material velocity decoupling. The SPFT–SIPE framework is causal, testable, and scale-independent, providing a single physical origin of rotation across planetary, stellar, and galactic systems. By linking Vacuum stiffness K_SIPE directly to angular momentum generation, it enables quantitative estimates of tangential velocities and angular momentum without invoking primordial spin or dark matter halos. “As photon frequencies redshift to zero, their vector modes vanish, and the persistent non-radiative photon residue (SIPE) continuously fills the Vacuum as a scalar field, with complete uncertainty regarding its timing, sources, and rate, naturally forming dark energy.”