C03  Clock network modeling
In general, networks of high precision clocks and their comparison enable the very precise determination of the relative gravitational potential (and the relative velocity). In this project we investigate the capabilities of such networks of the new generation of optical clocks connected by optical fiber links for a variety of applications such as Earth gravity field determination, time comparison or synchronization, navigation and positioning, and also fundamental physics tests. Since clocks directly measure the gravitational potential this opens up a fundamentally new concept for physical geodesy, that is, for e.g. geoid determination and the realization of a new global dynamic reference system. For the latter we will also make use of clocks in space.
For the thorough theoretical description of clocks and networks of clocks, one has to take into account all special and general relativistic effects like gravitational redshift, Doppler effect, gravitational time delay, Sagnac effect, and even the LenseThirring effect for clocks (gravitomagnetic clock effect). In fact, these effects give the information about the clocks’ relative motion and the gravitational field at their location. Based on this we then can model mass and height variations affecting the clock measurement, e.g., related to solid Earth tides.
We split this task into three main steps and an addon regarding tests of Special and General Relativity.
 Calculation of all (relativistic) effects within clock networks on Earth.
 Investigation of new and possibly more powerful and effective concepts for height determination over long distances or to remote areas (islands) based on networks of clocks on Earth (and possibly with the help of clocks in space).
 Development of fully relativistic notions for geodesy, e.g., a fully relativistic geoid based on clocks as well as on freely falling bodies (see figure 01).
 Geodetic modeling of timedependent gravitational fields, i.e. modeling of all relevant mass variations (mainly tidal effects) arising during the measurement time and between the epochs.
 As an addon we would like to analyze whether these high precision clocks in the gravitational field of the Earth can also be used for new high precision tests of Special and General Relativity.
This project will also prepare the theoretical foundations for the description of clocks with accuracies better than the present one and also serves as interface project between physics/General Relativity and geodesy.
Scientists working on this project
Dr. Dirk Pützfeld

phone: +49 421 21857934 
Dr.Ing. Hu Wu

phone: +49 511 7624891 
Selected Publications
PeerReviewed Literature
Müller, J., Dirkx, D., Kopeikin, S., Lion , G., Panet, I., Petit, G., Visser, P. (2018):
High Performance Clocks and Gravity Field Determination. ISSI book on High Performance Clocks, Space Science Reviews 214:5
DOI: 10.1007/s112140170431z
arXiv: 1702.06761
Müller, J., Dirkx, D., Kopeikin, S., Lion , G., Panet, I., Petit, G., Visser, P. (2017):
High Performance Clocks and Gravity Field Determination, Space Science Reviews 214:5
DOI: 10.1007/s112140170431z
arXiv: 1702.06761
Philipp D., Perlick V., Puetzfeld D., Hackmann E. and Lämmerzahl C. (2017):
Definition of the relativistic geoid in terms of isochronometric surfaces, Phys. Rev. D 95, 104037
DOI: 10.1103/PhysRevD.95.104037
arXiv: 1702.08412
Philipp D., Pützfeld D. and Lämmerzahl C. (2016):
On the applicability of the geodesic deviation equation in General Relativity (submitted)
arXiv: 1604.07173
Pützfeld D. and Obukhov Y.N. (2016):
Generalized deviation equation and determination of the curvature in General Relativity, Phys. Rev. D 93 (2016) 044073
DOI: 10.1103/PhysRevD.93.044073
arXiv: 1511.08465
Obukhov Y.N., PortalesOliva F., Pützfeld D. and Rubilar G.F. (2015):
Invariant conserved currents in generalized gravity, Phys. Rev. D 92 (2015) 104010
DOI: 10.1103/PhysRevD.92.104010
arXiv: 1507.02191
Pützfeld D. and Obukhov Y.N. (2015):
Equivalence principle in scalartensor gravity, Phys. Rev. D 92 (2015) 081502(R)
DOI: 10.1103/PhysRevD.92.081502
arXiv: 1505.01285
Obukhov Y.N. and Pützfeld D. (2014):
Equations of motion in scalartensor theories of gravity: A covariant multipolar approach, Phys. Rev. D 90 (2014) 104041
DOI: 10.1103/PhysRevD.90.104041
arXiv: 1404.6977
Non PeerReviewed Literature
Müller J. (2016):
Erdmessung mit Quanten und Relativität, BWG Jahrbuch 2016
arXiv: 1608.08407
Obukhov Y.N. and Pützfeld D. (2016):
Dynamics of test bodies in scalartensor theory and equivalence principle, Gravitation, Astrophysics, and Cosmology  Proceedings of the Twelfth AsiaPacific International Conference, Moscow, 28 Jun  5 July 2015, Eds. V. Melnikov and J.P. Hsu, World Scientific (Singapore), 2016, pp. 231235
DOI: 10.1142/9789814759816_0043
arXiv: 1603.09106
Obukhov Y.N. and Pützfeld D. (2015):
Multipolar test body equations of motion in generalized gravity theories, Equations of Motion in Relativistic Gravity, D. Pützfeld et. al. (eds.), Fundamental theories of Physics 179, pages 67119, Springer 2015
DOI: 10.1007/9783319183350_2
arXiv: 1505.01680
Philipp D. and Pützfeld D. (2015): On geodesic deviation in static spherically symmetric situations, April 2016, Proceedings of the 14th Marcel Grossmann Meeting, July 1218, 2015, Rome, Italy
Presentations, Talks and Posters
Müller J. and Wu H. (2017): Evaluation of the contribution of optical clocks to gravity field modelling, IAGIASPEI Joint Scientific Assembly, Kobe Japan, 30 July  4 August 2017, Oral presentation, Abstract G02203.
Pützfeld D. (2016): The Measurement of the Gravitational Field in General Relativity, Relativity seminar, University of Cologne, Germany.
Wu H., Müller J. and Brieden P. (2016): Benefit of GOCE gravity gradients at the lowered orbit on the global gravity field model, International Symposium on Gravity, Geoid and Height Systems 2016, Thessaloniki, Greece, September 1923, 2016
Wu H., Müller J. and Brieden P. (2016): The IfE global gravity field model from GOCEonly observations, International Symposium on Gravity, Geoid and Height Systems 2016, Thessaloniki, Greece, September 1923, 2016
Wu H., Müller J. and Brieden P. (2016): The latest IfE global gravity field model from GOCEonly observations, ESA Living Planet Symposium 2016, Prague, the Czech Republic, May 913, 2016, Abstract EART107
Wu H., Müller J. and Brieden P. (2016): The IfE global gravity field model from GOCEonly observations, International Symposium on Gravity, Geoid and Height Systems 2016, Thessaloniki, Greece, September 1923, 2016 more
Wu H., Müller J. and Brieden P. (2016): The latest IfE global gravity field model from GOCEonly observations, ESA Living Planet Symposium 2016, Prague, the Czech Republic, May 913, 2016, Abstract EART107 more