Relativistic geodesy is an emerging field at the intersection of general relativity and quantum metrology. Its physical basis is the gravitational redshift: a clock at a lower gravitational potential runs slower than an identical clock at a higher potential, with the fractional frequency shift given by Δν/ν0 = ΔU/c2. While this effect was long confined to fundamental tests of general relativity, the emergence of optical lattice clocks with fractional frequency stability approaching 10–18 has turned it into a practical geodetic tool known as chronometric levelling.
This paper reviews the physical basis, historical development and practical implementation of chronometric levelling, and compares it with classical height-determination methods such as geometric levelling and the GNSS/geoid approach. Unlike classical levelling, whose accuracy degrades with the square root of the traverse length, chronometric levelling is essentially insensitive to the distance between stations. Demonstrated examples, including the comparison of transportable optical clocks at the Tokyo Skytree, already achieve centimetre-level height accuracy. We argue that continued development of transportable and satellite-borne optical clocks, together with ongoing efforts to refine national height systems and regional geoid models, will make chronometric levelling an increasingly important complement to classical geodetic techniques.
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