Testing General Relativity with Clocks in Space

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, etc. 

Impressions from ESA's Cosmic Vision meeting

On the 21st January 2014 I attended ESA's comic vision meeting in Paris. It involved listening to presentations of the five mission candidates: ECHO, Macro-Polo, LOFT and STE-QUEST. Out of these only PLATO was selected as the next medium size mission to be launched by ESA in 2022+. STE-QUEST was considered not yet ready from a technological perspective.

Note that, technically, this was a public event - i.e., anyone could attend as long as they registered in advance. However, most of the attendants seemed to be scientists who were somehow connected to the missions.

So, what were each of these new missions about?

 The Exoplanet Characterization Observatory (ECHO):  They propose to place satellite with a  very performant spectrograph in an L-2 orbit, over 1.5 million km away from our planet. The spectrograph separates incoming light into a frequency spectrum that covers visible to infrared wavelengths.  Such a mission could measure the chemical composition of the atmosphere of a wide range of extra-solar planets - from hot Jupiters to SuperEarths. Once the planets are found by TESS or PLATO it is natural to then want to study the composition of their atmosphere. It would be good to a have a mission that can both find the planets and perform an accurate spectrogram vs. one or the other.

PLAnetary Transits and Oscillations of stars (PLATO): This is the winning mission! It's a satellite that will take pictures of the sky from an orbit around the L-2 Lagrange point. It will search for planets with 32 small telescopes & cameras. Each camera covers 1100 square degrees (for comparison the moon is about 0.2 square degrees, the whole sky has about 40, 000 square degrees, and Kepler mission has a field of view of about 100 degrees).  They expect to find transiting planets, i.e., they find dips in the light given by a star when the planet passes in front of the star. They aim to find the planet's mass, radius and age, and also measure oscillations in brightness of the host star.

Large Observatory for X-ray Timing (LOFT) This would have been an X-ray satellite that covers an area over an order of magnitude larger than that of current detectors. It would provide high time resolution X-ray observations of matter in the presence of strong gravity, i.e., investigate the variability of light in X-rays emitted by matter orbiting black holes, neutron stars, active galactic nuclei, etc. Such a mission would severely constrain the range of possible neutron star equations of state. It would also provide measurements for the spin and mass of black holes, and investigate the behaviour of matter close to an event horizon and other aspects of strong gravity. Most of my colleagues favoured this mission.

Marco-Polo: was supposed to return a sample of 1999 JU₃ (a near Earth asteroid) to Earth for analysis. It is believed that asteroids are some of the oldest objects in the solar system, and understanding their composition might help us understand the origin of life. This is a mission that was quite popular, but had a time limit because this particular asteroid can only be reached when it is close enough to Earth. I agree that taking samples of asteroids is something we should be able to do as well as perhaps be able to blow them up if they come to close to Earth and endanger life here.

STE-QUEST: This is a fundamental physics mission that would have originally placed an atomic clock and an atom interferometer in an elliptical orbit around the Earth.   This orbit means that the spacecraft would test general relativity through varying gravitational fields. Due to a limited budget, the mission only kept the atom interferometer and a transponder that would reflect, amplify and re-transmit pulses of light sent by atomic clocks on Earth. However, it was decided the atom interferometer technology was not yet ready to be flown in space. STE-QUEST remains an exciting mission concept that in addition to answering fundamental physics questions provides very good technology tests for instruments that we want to able to put in space as part of other missions. Clocks are used for GPS, space-craft tracking, monitoring changes of the geopotential of the Earth, etc, and the atom interferometers would be the future gravimeters.

Overall impressions: 
This meeting felt like a conference with fewer young people than I am used to from an average US conference (both weddings and funerals feel like conferences to me with sometimes better cookies and no talks.) All presentations went well, and the science presented for each mission was very interesting, which made it difficult to choose. 

However, I am a bit depressed that when we have so much more technology than 15 years ago, the way we present has not changed. I would like to see ESA be at the forefront of outreach. For example, they could be a little more modern by having a short video describing each mission + a toy one could buy to show support for the mission, which can also be used to explain each mission to younger audiences. Instead they sport the same static websites with the occasional broken link. All these presentations of missions should also be recorded and accessible to the public via the internet.

 I cannot get away from the feeling that there is too much bureaucracy everywhere in science (and, of course, not just in science).  The missions drag on for too long. The approved concepts wait until the technology is outdated and the people proposing them are close to retirement. Instead of funding commissions to evaluate, re-evaluate, re...re...re evaluate maybe more science could be funded and more publicity for the existent and future missions could be done.  Of course, some evaluation process has to exist, but we seem to have long lost a sense of balance and forget to correlate the number of evaluations with the progress made. Everyone seems to believe that science should be more open with fewer bureaucratic hurdles. However, the answer to every problem just seems to be more bureaucracy with no direct plans for solving the problem. With better outreach and more of the science and discussions publicly available, perhaps the public will come up with new ideas that solve some of the existent problems of the system.