= Lorentz invariance of optical cavity resonance
{c}
A <Lorentz transformation> of a resonant <optical cavity> transforms both the electromagnetic field and the mirror worldlines. Boundary conditions and event-by-event phase matching remain satisfied. For a longitudinal boost, a cavity of rest length $L$ has length $L/\gamma$ and unequal forward/backward frequencies $\gamma\omega_0(1\mp\beta)$. The coordinate round-trip time is $2\gamma L/c$, while the phase rate on a moving mirror is $\omega_0/\gamma$, so the round-trip phase is still $2\omega_0L/c$. A stationary-mirror resonance formula with only length contraction inserted describes the wrong boundary-value problem.
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