Unruh Effect 3D: Rindler Trajectory & Vacuum Detection

This 3D companion to the Unruh-effect simulator makes the effect's cause visible: an observer's motion through spacetime, not the vacuum itself, decides whether it looks empty or thermal. The accelerated observer here traces a genuine hyperbolic Rindler worldline — x(τ) = (1/α)(cosh(ατ) − 1) — the real trajectory shape of constant proper acceleration in relativity, its path bending ever closer to the light cone. Its detector lights up with sparks at a rate set directly by the Bose–Einstein occupation number n̄(ω) computed from the real Unruh temperature T = ħa/(2πck_B), while an inertial observer drifting alongside — moving through the identical vacuum field, just without acceleration — stays dark for the entire run, exactly as quantum field theory predicts.