Operational Meaning of the Mandelstam-Tamm Time Scale in a Spin-1/2 Clock
Georgiev's analysis of a freely precessing spin correctly emphasizes that the Mandelstam-Tamm quantity $ΔT=Δ\hat A/|d\langle\hat A\rangle/d t|$ is not the variance of a time operator. He concludes, however, that its divergence near the extrema of the clock signal is devoid of physical meaning and that $ΔT$ does not disclose how well the system measures the passage of time. For the same projective $\hatσ_x$ readout, we show that $ΔT$ equals the inverse square root of the classical Fisher information in one binary outcome at regular operating points. Its divergence at submaximal-coherence extrema therefore identifies a loss of local sensitivity in the selected readout, not an infinite variance of physical time; a complementary $\hatσ_y$ measurement remains informative. This interpretation also separates Georgiev's exactly known tick--tock period from the statistical precision with which a tick can be located. It preserves his warning against a time-operator interpretation while qualifying his stronger conclusion that the Mandelstam--Tamm scale lacks physical content.