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Coordinate time labels events in a chosen spacetime chart. It is distinct from proper time, which is measured by a clock along its timelike path. For a stationary observer in a static metric with signature $(+---)$, the rate is $d\tau =\sqrt{g_{tt}}dt$ in units with light speed one. Different stationary observers can therefore accumulate different proper times during the same coordinate-time interval.

Two identical stationary devices counting operations at the same rate per proper time act as clocks. If the upper one sends start and finish light signals over a fixed path to the lower one in a stationary metric, both propagation delays are identical in coordinate time and cancel from the interval comparison. The lower elapsed proper time divided by the upper one is $\sqrt{g_{tt}(r_2)/g_{tt}(r_1)}$. In the weak field the relative lag is $g\Delta h/c^2$, giving the displayed operation deficit. A rate of $10^{12}$ operations per second, a week and a height difference of ten metres give a deficit of roughly $660$ operations. This observable tests the radial clock-rate factor; it does not independently determine the radial spatial metric coefficient because the common signal delay cancels.

Write $f(r)=1-2m/r$ and restore $c$ for the numerical estimate. A stationary clock at radius $r$ has $d\tau =\sqrt{f(r)}dt$. Let radii $r_1$ and $r_2=r_1-h$ denote the upper and lower computers. The metric is stationary and the same two fixed spatial points exchange both signals, so each signal has the same coordinate propagation time. Therefore the interval between reception events equals the interval between emission events in coordinate time: the common delay cancels.

For upper proper running time ${\tau }_1$, the lower computer has run forIn the weak gravitational field near Earth's surface, $m=GM/c^2$ andThe lower clock runs more slowly, so its remaining work isThus about 660 micro-operations remain; the proper-time shortfall is only about $6.6\times 10^{-10}$ seconds.

Successful comparison tests the gravitational dependence of stationary proper-clock rates, specifically the radial variation of $g_{tt}$ and its weak-field gravitational redshift prediction, assuming the computers execute equally per unit proper time. It also checks that this clock effect is independent of the chosen physical clock mechanism. It does not separately verify the Schwarzschild radial metric coefficient: although light propagation uses the null metric, the identical start and finish propagation delays cancel from this particular observable. This is Gravitational redshift measured by a computation counter.