Is the geopotential directly measurable (Gauss, Bruns, Einstein)

It has been pointed out by the great Swedish geodesist Arne Bjerhammar and others around1985 that it is possible to replace the classical method of spirit leveling for determining differences of the geopotential by a much more direct and elegant method, measuring the frequency of atomic clocks. This is impossible by classical physics and requires methods of Einstein's General Theory of Relativity. The principle is that the geopotential can be “felt” by the “proper time” of this theory, but there remained the problem that the measuring accuracies were unthinkably high in 1985 and even later. To get a leveling accuracy of 1 cm, we must measure these frequencies to a relative accuracy of 10-18. Reaching such accuracies provided a great challenge to high-precision time observation all over the world, from USA to China. Now it seems that the required frequency accuracy is being reached. The author tries to give a short introductory review accessible to geodetic students and surveyors. It is purely didactic.