Accelerating Mirrors as a Physical Realization of the Kappa Plane-Wave Vacuum

Abstract: The kappa plane-wave vacuum is a family of kinematically defined quantum states whose thermal properties are well-understood, but whose physical origin has remained an open question. In this paper, we provide a concrete dynamical realization for this vacuum, demonstrating that it is physically and operationally equivalent to the quantum state produced by an accelerating Carlitz-Willey (CW) mirror on future null infinity. The equivalence is established through a three-pronged proof, showing that both systems exhibit identical Bogoliubov squeeze parameters, identical non-local thermal kernels in their Wightman functions, and identical Planckian responses in an Unruh-DeWitt detector. This result grounds an abstract kinematic construction in a well-understood dynamical model, identifying the parameter $\kappa$ with the mirror's physical acceleration. We further generalize our findings by deriving the complete class of mirror trajectories that reproduce the same asymptotic thermal state and show that only the pure exponential CW trajectory generates a constant, stationary flux.