High Performance Clocks and Gravity Field Determination

Abstract

Time measured by an ideal clock crucially depends on the gravitational potential and velocity of the clock according to general relativity. Technological advances in manufacturing high-precision atomic clocks have rapidly improved their accuracy and stability over the last decade that approached the level of 10 −18 . This notable achievement along with the direct sensitivity of clocks to the strength of the gravitational field make them practically important for various geodetic applications that are addressed in the present paper.Based on a fully relativistic description of the background gravitational physics, we discuss the impact of those highly-precise clocks on the realization of reference frames and time scales used in geodesy. We discuss the current definitions of basic 2 J. Müller et al.geodetic concepts and come to the conclusion that the advances in clocks and other metrological technologies will soon require the re-definition of time scales or, at least, clarification to ensure their continuity and consistent use in practice.The relative frequency shift between two clocks is directly related to the difference in the values of the gravity potential at the points of clock's localization. According to general relativity the relative accuracy of clocks in 10 −18 is equivalent to measuring the gravitational red shift effect between two clocks with the height difference amounting to 1 cm. This makes the clocks an indispensable tool in high-precision geodesy in addition to laser ranging and space geodetic techniques.We show how clock measurements can provide geopotential numbers for the realization of gravity-field-related height systems and can resolve discrepancies in classically-determined height systems as well as between national height systems. Another application of clocks is the direct use of observed potential differences for the improved recovery of regional gravity field solutions. Finally, clock measurements for space-borne gravimetry are analyzed along with closely-related deficiencies of this method like an extra-ordinary knowledge of the spacecraft velocity, etc. For all these applications besides the near-future prospects, we also discuss the challenges that are related to using those novel clock data in geodesy.

Atomic clocks for geodesy

“…In this context, a comparison of equations (2.26) and (2.7) shows that the (classical) definition of the geoid as an equipotential surface is, to the level of approximation used above (roughly a few parts in 10 19 ), identical with a surface on which clocks tick with the same rate. However, with the advent of optical clocks with below the level of 10 -18 and corresponding links for their remote comparison, proposals for a new definition of a relativistic geoid based on optical clocks have become more and more realistic (Kopeikin et al 2011;Müller et al 2017;Phillip et al 2017).…”

“…along survey lines (along roads) crossing each other. Another geodetic application in this direction would be spaceborne clock measurements of the redshift effect with respect to some reference clock (optimally a master clock in space as described above) for gravity field recovery missions, as discussed, for instance, in (Mayrhofer and Pail 2012) and (Müller et al 2017).…”

“…Such clock networks could also help to establish a new global height reference system. Moreover, clock measurements for spaceborne gravity field recovery missions have been discussed in (Mayrhofer and Pail 2012) and (Müller et al 2017). Naturally, transportable optical clocks will typically follow their laboratory counterparts.…”

Comparing Optical Oscillators across the Air to Milliradians in Phase and 10−17 in Frequency

“…Carrier-phase OTWTFT achieves frequency comparisons with a residual instability of 1.2×10 -17 at 1 second across a turbulent 4-km free space link, surpassing previous OTWTFT by 10-20x and enabling future high-precision optical clock networks. Furthermore, by exploiting the carrier-phase, this approach is able to continuously track changes in the relative optical phase of distant optical oscillators to 9 mrad (7 attoseconds) at 1-sec averaging, effectively extending optical phase coherence over a broad spatial network for applications such as correlated spectroscopy between distant atomic clocks.2 Applications of future optical clock networks include time dissemination, chronometric geodesy, coherent sensing, tests of relativity, and searches for dark matter among others [1][2][3][4][5][6][7][8][9][10][11][12][13][14].This promise has motivated continued advances in optical clocks and oscillators [15][16][17][18][19] and in the optical transfer techniques to network them. In particular, time-frequency transfer over fiberoptic networks has seen tremendous progress [1,7,[20][21][22][23].…”

“…2 Applications of future optical clock networks include time dissemination, chronometric geodesy, coherent sensing, tests of relativity, and searches for dark matter among others [1][2][3][4][5][6][7][8][9][10][11][12][13][14].…”