Quantum tests of the Einstein Equivalence Principle with the STE–QUEST space mission

Abstract

We present in detail the scientific objectives in fundamental physics of the Space–Time Explorer and QUantum Equivalence Space Test (STE–QUEST) space mission. STE–QUEST was pre-selected by the European Space Agency together with four other missions for the cosmic vision M3 launch opportunity planned around 2024. It carries out tests of different aspects of the Einstein Equivalence Principle using atomic clocks, matter wave interferometry and long distance time/frequency links, providing fascinating science at the interface between quantum mechanics and gravitation that cannot be achieved, at that level of precision, in ground experiments. We especially emphasize the specific strong interest of performing Equivalence Principle tests in the quantum regime, i.e. using quantum atomic wave interferometry. Although STE–QUEST was finally not selected in early 2014 because of budgetary and technological reasons, its science case was very highly rated. Our aim is to expose that science to a large audience in order to allow future projects and proposals to take advantage of the STE–QUEST experience.

Introduction

Our best knowledge of the physical Universe, at the deepest fundamental level, is based on two theories: Quantum Mechanics (or, more precisely, Quantum Field Theory) and the classical theory of General Relativity. Quantum Field Theory has been extremely successful in providing an understanding of the observed phenomena of atomic, particle, and high energy physics and has allowed a unified description of three of the four fundamental interactions that are known to us: electromagnetic, weak and strong interactions (the fourth one being gravitation). It has led to the Standard Model of particle physics that has been highly successful in interpreting all observed particle phenomena, and has been strongly confirmed with the recent discovery at the LHC of the Higgs (or, more precisely, Brout–Englert–Higgs) boson, which could in fact be viewed as the discovery of a fifth fundamental interaction. Although open questions remain within the Standard Model of particle physics, it is clearly the most compelling model for fundamental interactions at the microscopic level that we have at present.

On the other hand, Einstein’s theory of General Relativity (GR) is a cornerstone of our current description of the physical world at macroscopic scales. It is used to understand the flow of time in the presence of gravity, the motion of bodies from satellites to galaxy clusters, the propagation of electromagnetic waves in the vicinity of massive bodies, the evolution of stars, and the dynamics of the Universe as a whole. GR brilliantly accounts for all observed phenomena related to gravitation, in particular all observations in the Earth’s environment, the Solar system, in relativistic binary pulsars and, beyond that, on galactic and cosmological scales.

The assumed validity of GR at cosmological scales, and the fact that non-gravitational interactions are described by the Standard Model of particle physics, together with a hypothesis of homogeneity and isotropy of cosmological solutions of these theories, have led to the “concordance model” of cosmology, referred to as the $\mathrm{\Lambda }$-CDM (Cold Dark Matter) model, which is in agreement with all present-day observations at large scales, notably the most recent observations of the anisotropies of the cosmic microwave background by the Planck satellite (Ade, 2013). However, important puzzles remain, in particular the necessary introduction of dark energy, described by a cosmological constant $\mathrm{\Lambda }$, and of cold dark matter, made of some unknown, yet to be discovered, stable particle.

There is a potential conflict on the problem of dark matter between the concordance model of cosmology and the Standard Model of particles. On the one hand, there is strong evidence (Ade, 2013) that 26.8% of the mass-energy of the Universe is made of non-baryonic dark matter particles, which should certainly be predicted by some extension of the Standard Model of particles. On the other hand, there is no indication of new physics beyond the Standard Model which has been found at the LHC. For instance, the search of supersymmetry at LHC has for the moment failed.

Although very successful so far, GR as well as numerous other alternative or more general theories of gravitation are classical theories. As such, they are fundamentally incomplete, because they do not include quantum effects. A theory solving this problem would represent a crucial step towards the unification of all fundamental forces of Nature. Most physicists believe that GR and the Standard Model of particle physics are only low-energy approximations of a more fundamental theory that remains to be discovered. Several concepts have been proposed and are currently under investigation (e.g., string theory, loop quantum gravity, extra spatial dimensions) to bridge this gap and most of them lead to tiny violations of the basic principles of GR.

One of the most desirable attributes of that fundamental theory is the unification of the fundamental interactions of Nature, i.e. a unified description of gravity and the three other fundamental interactions. There are several attempts at formulating such a theory, but none of them is widely accepted and considered successful. Furthermore, they make very few precise quantitative predictions that could be verified experimentally. One of them is the Hawking radiation of black holes, which is however far from being testable experimentally for stellar-size black holes we observe in astrophysics.

Therefore, a fuller understanding of gravity will require observations or experiments able to determine the relationship of gravity with the quantum world. This topic is a prominent field of activity with repercussions covering the complete range of physical phenomena, from particle and nuclear physics to galaxies and the Universe as a whole, including dark matter and dark energy.

A central point in this field is that most unification theories have in common a violation at some (a priori unknown) level of one of the basic postulates of GR, which can be tested experimentally: the Einstein Equivalence Principle (EEP). Let us emphasize that the Weak Equivalence Principle (WEP) is not a fundamental symmetry of physics, contrary to e.g. the principle of local gauge invariance in particle physics. An important challenge is therefore to test with the best possible accuracy the EEP. This is then the main motivation of many experiments in fundamental physics, both on Earth and in space.

Precision measurements are at the heart of the scientific method that, since Galileo’s time, is being used for unveiling Nature and understanding its fundamental laws. The assumptions and predictions of GR can be challenged by precision experiments on scales ranging from micrometers in the laboratory to the Solar System size, in the latter case using spacecrafts or the orbiting Earth, Moon and planets. The implementation of tests with significantly improved sensitivity obviously requires the use of state-of-the-art technology, and in case of satellite-based experiments the challenge is to make such technology compatible with use in space, i.e. extremely robust, reliable, and automatized.

The satellite STE–QUEST (Space–Time Explorer and QUantum Equivalence Space Test) is specifically designed for testing different aspects of the EEP and searching for its violation with high precision. The Weak Equivalence Principle has been verified with high precision using torsion balances on ground (Schlamminger et al., 2008) and the Lunar laser ranging (Williams et al., 2004). It will be tested in Earth orbit by the CNES satellite $\mu$-SCOPE (Micro-Satellite à traînée Compensée pour l’Observation du Principe d’Equivalence) in 2016 (Touboul and Rodrigues, 2001). On the other hand, the gravitational red-shift, a different aspect of the EEP, was first measured using gamma ray spectroscopy in the laboratory (Pound and Rebka, 1960), and the most precise test so far was done in space with the GP-A experiment (Vessot and Levine, 1979). The ESA mission ACES (Atomic Clock Ensemble in Space) will test the gravitational red-shift with the highly accurate laser-cooled atomic clock PHARAO on the International Space Station (ISS) in 2016 (Cacciapuoti and Salomon, 2009).

Atomic clocks and high-performance time and frequency links, atom interferometers and classical accelerometers are today able to measure frequency, time, and distances, and furthermore to track the motion of massive bodies, quantum particles, and light to accuracy levels never reached before. These instruments achieve their ultimate performance in space, where the clean environment and the free-fall conditions become essential for identifying tiny deformations in space–time that might bring the signature of new physics or new fundamental constituents. From this point of view, it is not surprising that fundamental physics pervades all aspects of space science.

STE–QUEST was proposed in the fall of 2010 in response to ESA’s M3 call in the Cosmic Vision programme (with launch date in the 2022–24 time interval), by a science team under coordination by S. Schiller and E.M. Rasel with support from 67 colleagues from Europe and the USA. STE–QUEST is based on the earlier proposals EGE (Schiller, 2009) and MWXG (Ertmer, 2009), submitted to ESA’s M2 call. ESA performed a “concurrent design facility” study of a mission concept similar to EGE, named STE, in 2010. Previously, ESA had also convened a Fundamental Physics Advisory Team which in 2009–10 developed a roadmap on fundamental physics in space.

STE–QUEST, together with three other mission proposals, was selected in early 2011 by ESA’s advisory structure as one candidate mission. STE–QUEST went through an assessment phase study of the satellite and payload (see the Yellow Book of the mission¹). As a result of the assessment phase and in agreement with the national space agencies, STE–QUEST was removed from the candidate pool in late 2013, before the final selection of a single mission for the M3 slot, because of budgetary and technological reasons. Nevertheless, ESA’s advisory committees evaluated the science aspects of STE–QUEST in early 2014 (together with the remaining M3 candidates) and ranked them highly. It is likely that STE–QUEST will recompete for the M4 launch slot.

The primary science objectives of STE–QUEST is testing the different aspects of the Einstein Equivalence Principle with quantum sensors. The payload consists of a differential atom interferometer comparing the free propagation of matter waves of different composition under the effect of gravity and a frequency comparison link in the microwave domain for comparing atomic clocks on ground. STE–QUEST performs a direct test of the WEP by comparing the free fall of quantum objects of different composition. The Eötvös ratio between the matter waves of two isotopes of the Rubidium atom is measured in a differential atom interferometer down to the $2\times {10}^{-15}$ uncertainty level. While present limits on WEP tests involving classical objects reach an uncertainty of a few parts in ${10}^{13}$, measurements performed on quantum objects (matter waves in states which have no classical counterpart, e.g. spatio-temporal quantum superpositions) are still at the level of a few parts in ${10}^7$ (Fray et al., 2004, Schlippert et al., 2014, Tarallo et al., 2014). From this point of view, STE–QUEST will explore the boundaries between gravitation and quantum mechanics, significantly improving existing measurements and complementing experiments such as $\mu$-SCOPE, designed for a classical WEP test in space to the level $1\times {10}^{-15}$.

STE–QUEST also tests another complementary aspect of the Einstein Equivalence Principle, one of the most fascinating effects predicted by GR and other metric theories of gravity: the gravitational red-shift or gravitational time dilation effect. As direct consequence of the EEP, time runs (or clocks tick) more slowly near a massive body. This effect can be detected when comparing the time intervals measured by identical clocks placed at different depths in a gravitational field. The microwave link (MWL) of the STE–QUEST satellite allows comparing ground clocks down to the $1\times {10}^{-18}$ uncertainty level. Such measurements, far beyond the capabilities of existing intercontinental time and frequency transfer systems, will perform clock red-shift tests in the field of the Sun and the Moon, respectively at the $2\times {10}^{-6}$ and $4\times {10}^{-4}$ uncertainty levels. For comparison, existing measurements of the Sun red-shift effect are at the few % uncertainty level while, to our knowledge, no such tests have ever been performed in the field of the Moon. An optional (depending on available funding) onboard clock allows additionally a red-shift measurement in the Earth field by taking advantage of the high apogee and high eccentricity of the orbit. The clock under consideration is derived from the PHARAO cold atom Cs clock to be flown on the ISS (Cacciapuoti and Salomon, 2009). The version planned for STE–QUEST is designed to reach an uncertainty in the Earth field red-shift test of $2\times {10}^{-7}$, one order of magnitude better than the objective of ACES. The relativistic theory for time and frequency transfer needed for frequency links in space missions such as ACES and STE–QUEST is described in Ref. Blanchet et al. (2001).

Clock red-shift measurements obtained in the field of the Earth, the Sun or the Moon test the Local Position Invariance (LPI) principle and search for anomalous couplings depending on the composition of the source of the gravitational field. LPI is a constituent of EEP together with WEP and the Local Lorentz Invariance (LLI) principle, see Section 2.1. As we shall discuss in Section 5.1, in generic frameworks modeling a possible violation of EEP, WEP and clock red-shift tests are complementary and need to be pursued with equal vigor as, depending on the model used, either one of the tests can prove significantly more sensitive than the other. Improving the accuracy of these tests will bring significant progress in restricting the parameters space and discriminating between theories seeking to unify quantum mechanics with gravity. The eventual detection of an EEP violation would carry the signature of new fundamental constituents or interactions in the Universe (e.g. scalar fields for dark energy, particles for dark matter, fundamental strings, etc.). In this case, STE–QUEST tests would have a significant impact not only for fundamental physics research, but also for cosmology and particle physics. The ensemble of fundamental physics science objectives of STE–QUEST is summarized in Table I and Fig. 1.

STE–QUEST has also important applications in domains other than fundamental physics, in particular in the fields of time and frequency metrology and for geodesy studies. As mentioned, the STE–QUEST high-performance MWL provides the means for connecting atomic clocks on ground in a global network, enabling comparisons down to the $1\times {10}^{-18}$ fractional frequency uncertainty level. Clock comparisons via STE–QUEST will contribute to the realization of international atomic time scales (UTC, TAI, etc.) and to the improvement of their stability and accuracy. Synchronization of clocks, space-to-ground and ground-to-ground, to better than 50 ps can be achieved through STE–QUEST for distributing time scales to unprecedented performance levels. Common-view comparisons of ground clocks, primarily used for gravitational red-shift tests in the field of Sun or Moon, also provide direct information on the geopotential differences at the locations of the two ground clocks. STE–QUEST will therefore contribute to establishing a global reference frame for the Earth gravitational potential at the sub-cm level through local measurements. This method is complementary to current and future satellite gravimetry missions such as CHAMP, GRACE and GOCE as well as to altimetry missions like JASON and Envisat in defining the Global Geodetic Observing System (GGOS). The Table IV (relegated in the conclusion Section 6) summarizes the list of topics other than fundamental physics that shall be investigated by STE–QUEST.

The present paper is an adapted version of the fundamental physics science objectives of STE–QUEST extracted from the Yellow Book of STE-QUEST (see also the Ref. Aguilera (2013)). The Yellow Book also gives an overview of science objectives in other fields (geodesy, time/frequency metrology, reference frames) and details on the mission and payload, which are however beyond the scope of this paper that focuses on the fundamental physics objectives. In Section 2 we shall review in more detail the EEP and its different facets. In Section 3 we shall discuss the status of EEP in Physics today and particularly in the contexts of cosmology and particle physics. Quantum mechanics and the EEP and the potential interest of quantum tests of the EEP will be analyzed in Section 4. The specific tests of the EEP which will be achieved by STE–QUEST will be presented in Section 5. The paper ends with the main conclusions in Section 6.