Imagine an experiment with a space-traveling clock. This clock travels in a satellite around Earth and broadcasts light pulses to a receiving station on Earth at very precise intervals of time. The arrival times of the light pulses are registered by a local clock and compared with the emitted times. Both the orbit of the satellite and the light traveling time are affected by the presence of the Earth, which bends space-time slowing down time. In John Wheeler's words: "matter tells space how to curve, and space tells matter how to move".

As the accuracy, reliability and portability of atomic clocks improves, such clock experiments will constrain general relativity, the mathematical theory that models the effects that matter has on space-time, more stringently. Spacecraft clocks offer us the opportunity to simultaneously probe different effects such as Shapiro delay, frame dragging and higher order relativistic effects all within the same astrophysical system.

In http://arxiv.org/abs/1402.6698, my collaborators and I have solved the forward problem where we determine which relativistic effects reach a magnitude above clock accuracy for a clock carrying satellite that orbits the Earth. The best space-qualified clock to date has been built for the Atomic Ensemble in Space (ACES) experiment - a Caesium fountain clock that is expected to reach frequency inaccuracy of 10-16. The best clocks on Earth have reached accuracies of the order of 10-18. We find that already at precisions of 10-16 several higher order relativistic effects are already relevant (see figure).

You may ask why are relativistic effects important. Firstly, relativistic effects are important for their own sake. General relativity is a beautiful theory. Few things can be more exciting than measuring the slow down of time, and understanding that our feet are slightly younger than our head by what is now a measurable amount. However, general relativity is not a complete theory of everything because it breaks down at small scales, and does not allow for a natural unification with quantum mechanics. We dream to unify relativity with quantum mechanics, and also to explain all observations including the nature of dark energy and dark matter. Observations of this dark sector, which is believed to comprise more than 95% of the universe, provide a sign of new physics that remains tantalizingly out of reach. No violations of general relativity have been observed to date.

Secondly, from a more practical perspective, atomic clocks can provide accurate space-craft tracking. As the clock accuracy and our treatment of the other errors improves, relativistic effects will become the dominant noise source, which has to be understood and modelled. Even though noise modelling is rarely the focus of an experiment, it is most often the dominant part of data analysis.

Our code is freely available as a supplement to the Physical Review D version of the paper. If you do not have access to PRD or are so excited about this that you want the code right now before the paper appears, you can email Ray (see his email address on the pdf of the paper) or another one of us. Once you install it, it has a user-friendly interface on which you can select orbit parameters, and the relativistic effect you want to compute the magnitude of. There are a number of simplifications that were made, which in principle could be relaxed, e.g., the satellite clock is assumed to communicate tick signals to one clock on Earth with the Earth being transparent to the clock signals. In reality there would be multiple clocks on Earth and the ticks from the space clock would be sent to the clocks on Earth within the field of view of the satellite. Additional terms could be added to the Hamiltonian to see if clocks in space can test your favourite alternative theory of gravity,

As the accuracy, reliability and portability of atomic clocks improves, such clock experiments will constrain general relativity, the mathematical theory that models the effects that matter has on space-time, more stringently. Spacecraft clocks offer us the opportunity to simultaneously probe different effects such as Shapiro delay, frame dragging and higher order relativistic effects all within the same astrophysical system.

In http://arxiv.org/abs/1402.6698, my collaborators and I have solved the forward problem where we determine which relativistic effects reach a magnitude above clock accuracy for a clock carrying satellite that orbits the Earth. The best space-qualified clock to date has been built for the Atomic Ensemble in Space (ACES) experiment - a Caesium fountain clock that is expected to reach frequency inaccuracy of 10-16. The best clocks on Earth have reached accuracies of the order of 10-18. We find that already at precisions of 10-16 several higher order relativistic effects are already relevant (see figure).

You may ask why are relativistic effects important. Firstly, relativistic effects are important for their own sake. General relativity is a beautiful theory. Few things can be more exciting than measuring the slow down of time, and understanding that our feet are slightly younger than our head by what is now a measurable amount. However, general relativity is not a complete theory of everything because it breaks down at small scales, and does not allow for a natural unification with quantum mechanics. We dream to unify relativity with quantum mechanics, and also to explain all observations including the nature of dark energy and dark matter. Observations of this dark sector, which is believed to comprise more than 95% of the universe, provide a sign of new physics that remains tantalizingly out of reach. No violations of general relativity have been observed to date.

Secondly, from a more practical perspective, atomic clocks can provide accurate space-craft tracking. As the clock accuracy and our treatment of the other errors improves, relativistic effects will become the dominant noise source, which has to be understood and modelled. Even though noise modelling is rarely the focus of an experiment, it is most often the dominant part of data analysis.

Our code is freely available as a supplement to the Physical Review D version of the paper. If you do not have access to PRD or are so excited about this that you want the code right now before the paper appears, you can email Ray (see his email address on the pdf of the paper) or another one of us. Once you install it, it has a user-friendly interface on which you can select orbit parameters, and the relativistic effect you want to compute the magnitude of. There are a number of simplifications that were made, which in principle could be relaxed, e.g., the satellite clock is assumed to communicate tick signals to one clock on Earth with the Earth being transparent to the clock signals. In reality there would be multiple clocks on Earth and the ticks from the space clock would be sent to the clocks on Earth within the field of view of the satellite. Additional terms could be added to the Hamiltonian to see if clocks in space can test your favourite alternative theory of gravity,

*etc*.