The relevant version of the uncertainty principle here is the energy time one. \Delta E \Delta T <= \hbar. As time uncertainty tends to 0, energy uncertainty te

The relevant version of the uncertainty principle here is the energy time one. \Delta E \Delta T <= \hbar. As time uncertainty tends to 0, energy uncertainty tends to infinity. What does that mean? It means the clock system has to get an increasingly heavier pendulum, or increasingly tighter spring, or some analog thereof. When you make the pendulum Bob twice as heavy, it is half as sensitive to random stray influence, but whatever uncertainty you had about the bobs kinetic energy is multiplied by two. Infinite precision is only possible with an infinitely heavy pendulum.