Isotropic Radiation Pressure

$$P = \frac{\varepsilon}{3}$$

Status: Proven.

This is a standard, textbook result in relativistic kinetic theory and electromagnetism: for an isotropic distribution of radiation (or any ultra-relativistic gas, where particle momentum $p \approx E/c$), the pressure it exerts equals one-third of its energy density. It follows directly from the trace of the electromagnetic stress-energy tensor, or equivalently from averaging momentum flux over an isotropic (equal in all directions) distribution of massless or ultra-relativistic particles — one-third of the momentum flux acts along any given axis by symmetry.

Real, independent confirmation: this relation underlies the physics of the early radiation-dominated universe (used directly in the Friedmann equations during that era — see Standard Cosmology), stellar interiors where radiation pressure is significant, and is a standard derived result in any statistical mechanics or electrodynamics textbook treatment of a photon gas.

Used in: Paper 1, as the starting assumption for PBT’s “uniform pressure from isotropic flux.” The formula itself is real and correctly stated; what’s specific to PBT is applying it to a hypothesized subatomic particle flux rather than photons or an ordinary relativistic gas — see Hierarchical Energy Density Scaling for the unproven part of that extension.