On the finite-temperature quantum electrodynamics of gravitational acceleration

The temperature-dependent quantum-electrodynamic corrections to the Helmholtz free energy F of a particle at rest, and to its inertial mass $m_{\mathrm{inert}}$, are the same: ΔF=Δ$m_{\mathrm{inert}=\mathrm{\pi }{e}^2(\mathrm{kT}{)}^2/3\mathrm{}\mathrm{m}}$. By contrast, the correction to the total energy U=F+TS is ΔU=-ΔF. Donoghue, Holstein, and Robinett have pointed out that if (as the equivalence principle appears to imply) weight is proportional to total energy, then the gravitational acceleration of a particle inside a blackbody cavity becomes g(m+ΔU)/(m+ΔF)≊g(1-2ΔF/m)F represents the random kinetic energy of (and is thereby localized on) the particle, further analysis now suggests that the entropic energy difference TΔS=ΔU-ΔF is distributed over the cavity uniformly and independently of the particle position. If so, then the gravitational pull on TΔS cannot affect the motion of the particle well within the cavity, so that it will, after all, experience the universal Galilean acceleration g.