A sealed cavity contains blackbody radiation with pressure
PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Relativistic dynamics and fields in flat spacetime · Relativistic dynamics and fields in flat spacetime
The Geometry of Gravity, Ch The stress-energy tensor and relativistic continua
Problem
A sealed cavity contains blackbody radiation with pressure p=2.0×105Pa, satisfying p=ρ/3 as for any radiation field. Someone argues: The trace of the stress-energy tensor, Tμμ, is the natural relativistic measure of how much energy a source contains. Since blackbody radiation has Tμμ=−ρ+3p=0, this cavity's radiation carries no energy at all, only pressure.
((a)) Compute the radiation's energy density ρ from the given pressure.
((b)) Explain what is wrong with the claim, using the number found in part (a).
((c)) State, in one sentence, what a vanishing trace does tell about matter or a field, if not that its energy is zero.