Einstein's Theory of General Relativity is a cornerstone of our current description of the physical world. It is used to describe 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 presence of massive bodies; and the dynamics of the Universe as a whole.

Although successful so far, the Theory of General Relativity, 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 that solves this problem by accounting for both relativistic and quantum effects  would represent a crucial step towards the unification of all the fundamental forces of Nature.

Several approaches have been proposed and are currently under investigation: examples are string theory, quantum gravity, extra spatial dimensions. All of these tend to lead to tiny violations of basic principles. Therefore, a full understanding of gravity will require observations or experiments which can determine the relationship of gravity with the quantum world. This is currently a 'hot' topic and includes the study of dark energy.

Improvements in technology mean that several experiments can now be performed in space with significantly improved accuracy. Taking advantage of this, STE-QUEST is designed to test the different aspects of Einstein's Equivalence Principle using quantum sensors.

Einstein's Equivalence Principle (EPP) can be expressed as follows:

1. Weak Equivalence Principle (WEP): The trajectories of freely falling test bodies are independent of their structure and composition;
2. Local Lorentz Invariance (LLI): In local freely falling frames, the outcome of any non-gravitational test experiment is independent of the velocity of the frame;
3. Local Position Invariance (LPI): In local freely falling frames, the outcome of any non-gravitational test experiment is independent of where and when in the Universe it is performed.

 
Primary Scientific Objectives of STE-QUEST 
 
 

Gravitational Redshift Tests

A direct consequence of Einstein's Equivalence Principle is that time passes (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 positions in a gravitational field, or when their tick rates (frequencies) are compared. Time and frequency can be transferred between remote locations using electromagnetic waves generated directly from the local clock and transmitted to a particular detection position (denoted by x').

The comparison of two clocks (i = 1, 2) with identical oscillation frequency and operating at different locations x₁ and x₂ yields a frequency ratio:

In this gravitational redshift formula, ν_i(x') is the frequency of clock i located at x_i, as observed (measured) at the particular location x' where the comparison between the two clocks takes place (see Figure below); U is the gravitational potential. According to Einstein's Theory of General Relativity, this frequency ratio is universal, and independent of the nature of the clocks. 

A two-way link compares the clock on-board the STE-QUEST spacecraft (νsc) with two clocks on the ground (ν1 and ν2). The link transfers the clock signals in both directions (space-to-ground and ground-to-space) allowing the received signal to be compared with the local clock at both ends. Credit: ESA

 STE-QUEST will search for a possible violation of the gravitational redshift formula. Phenomenologically, such a violation may be described by a dependence on the gravitational potential of one or more of the fundamental constants that determine the clock frequency:  X = X(U l c²), where X is a generic dimensionless fundamental constant or a dimensionless combination of fundamental constants. Such dependence would correspond to a violation of the Local Position Invariance principle (LPI).

The Earth's gravitational redshift was measured with an accuracy of 7×10^-5 by the 1976 Gravity Probe-A experiment by comparing the frequency of a clock on the ground with the frequency of a clock on a rocket, as the height changed. The Atomic Clock Ensemble in Space (ACES) mission, planned to fly on the International Space Station (ISS) in the 2014-2015 timeframe, seeks to improve this test by a factor 10 to 30, with its Projet d'Horloge Atomique par Refroidissement d'Atomes en Orbite (PHARAO) cold atom clock.

STE-QUEST will make use of the latest cold atom clocks – the technology has made substantial progress recently - and an orbit optimized for such measurements, resulting in improvements in sensitivity by 1 to 2 orders of magnitude.

STE-QUEST will also perform a comparison of clocks on ground, by measuring the daily variation of the redshift effect in the Sun's gravitational field. This will provide a means to search for the neutron’s scalar charge and to test the anomalous coupling of matter to the Standard Model quantum fields.

Weak Equivalence Principle Tests

Testing the Universality of Free Fall with Matter Waves

The Weak Equivalence Principle (WEP) postulates that the world line of a freely falling test body is independent of its structure and composition. This hypothesis is a cornerstone not only of Einstein's Theory of General Relativity, but also for almost all modern theories of gravitation.

Experimental tests of this principle are therefore based on the detection of tiny differential accelerations between test masses of different structure and composition.

The Eötvös parameter (η) is historically used to quantify a deviation from the WEP of two test bodies with different compositions (A and B), inertial mass m_i, and gravitational mass m_g:

An experiment measuring a value of η not equal to zero would disprove the universality of free fall and violate the Equivalence Principle.

In tracking the free propagation of matter waves, free-fall experiments extend into the domain of quantum objects. This approach is conceptually different from all other free-fall tests based on classical bodies. As per the principles of quantum mechanics, particles have to be described as wave packets; in the context of an atom interferometer (as adopted by STE-QUEST) this introduces the concept of coherence of the different partial matter waves.

STE-QUEST will compare the free-fall of the two isotopes of rubidium (⁸⁵Rb and ⁸⁷Rb) while the spacecraft orbits around perigee (see Figure below), in order to conduct a quantum test of the Weak Equivalence Principle with an accuracy down to 1×10^-15.

  
Additional Science with STE-QUEST

In addition to the science goals outlined above, STE-QUEST has applications in areas of research other than fundamental physics:

• Time and frequency metrology: STE-QUEST will connect atomic clocks on Earth in a worldwide network, bringing important contributions to the generation of atomic time scales and to the synchronization of clocks on ground and in space.
• Relativistic geodesy: The comparison of clocks on Earth will give access, via the redshift formula, to differential geopotential measurements on the Earth's surface. A resolution at the level of 1 centimetre on the differential geoid height can be achieved by STE-QUEST.
• Cold-atom and matter wave physics in conditions of weightlessness: STE-QUEST will study the evolution of ultra-cold atomic samples in an environment free from perturbations, over long free-propagation times.
• Optical and microwave ranging: The optical and microwave links will allow the cross-comparison of different ranging techniques and the measurement of differential atmospheric propagation delays in the optical and microwave domains.