Slow clock transport synchronization ($\delta \sim Lu/(2c^2)$)

For ideal clocks in an inertial frame separated by fixed distance $L$, transporting a clock at small speed $u$ produces lag $\delta =(L/u)(1-\sqrt{1-u^2/c^2})\sim Lu/(2c^2)$. Hence the limit agrees with Einstein synchronisation, assuming the clock hypothesis. A relabelling $t_{\kappa }=t+\kappa x/c$ retains an endpoint offset $\kappa L/c$, so the result does not remove the choice of distant-time convention.