Satellite Test Of The Equivalence Principle Research Articles

STEP as a Decisive Test of MOND on Earth

We review and emphasize the importance of the Satellite Test of the Equivalence Principle (STEP) in probing one of the most successful and popular alternative theories to dark matter known as Modified Newtonian Dynamics (MOND), on Earth. This would be achieved with no modification of STEP’s current design and sensitivity and if MOND exists STEP could in principle easily detect it.

Satellite Test of the Equivalence Principle as a Probe of Modified Newtonian Dynamics.

The proposed satellite test of the equivalence principle (STEP) will detect possible violations of the weak equivalence principle by measuring relative accelerations between test masses of different composition with a precision of one part in 10^{18}. A serendipitous by-product of the experimental design is that the absolute or common-mode acceleration of the test masses is also measured to high precision as they oscillate along a common axis under the influence of restoring forces produced by the position sensor currents, which in drag-free mode lead to Newtonian accelerations as small as 10^{-14}  g. This is deep inside the low-acceleration regime where modified Newtonian dynamics (MOND) diverges strongly from the Newtonian limit of general relativity. We show that MOND theories (including those based on the widely used "n family" of interpolating functions as well as the covariant tensor-vector-scalar formulation) predict an easily detectable increase in the frequency of oscillations of the STEP test masses if the strong equivalence principle holds. If it does not hold, MOND predicts a cumulative increase in oscillation amplitude which is also detectable. STEP thus provides a new and potentially decisive test of Newton's law of inertia, as well as the equivalence principle in both its strong and weak forms.

STEP and fundamental physics

The Satellite Test of the Equivalence Principle (STEP) will advance experimental limits on violations of Einstein's equivalence principle from their present sensitivity of two parts in 1013 to one part in 1018 through multiple comparison of the motions of four pairs of test masses of different compositions in a drag-free earth-orbiting satellite. We describe the experiment, its current status and its potential implications for fundamental physics. Equivalence is at the heart of general relativity, our governing theory of gravity and violations are expected in most attempts to unify this theory with the other fundamental interactions of physics, as well as in many theoretical explanations for the phenomenon of dark energy in cosmology. Detection of such a violation would be equivalent to the discovery of a new force of nature. A null result would be almost as profound, pushing upper limits on any coupling between standard-model fields and the new light degrees of freedom generically predicted by these theories down to unnaturally small levels.

Electrostatic patch effect in cylindrical geometry: I. Potential and energy between slightly non-coaxial cylinders

We study the effect of any uneven voltage distribution on two close cylindrical conductors with parallel axes that are slightly shifted in the radial and by any length in the axial directions. The investigation is especially motivated by certain precision measurements, such as the Satellite Test of the Equivalence Principle. By energy conservation, the force can be found as the energy gradient in the vector of the shift, which requires determining potential distribution and energy in the gap. The boundary value problem for the potential is solved, and energy is thus found to the second order in the small transverse shift, and to lowest order in the gap to cylinder radius ratio. The energy consists of three parts: the usual capacitor part due to the uniform potential difference, the one coming from the interaction between the voltage patches and the uniform voltage difference and the energy of patch interaction, entirely independent of the uniform voltage. Patch effect forces and torques in the cylindrical configuration are derived and analyzed in the next two parts of this work.

Cryogenic tilt table

We describe the design and development of a cryogenic tilt table that will be used to test the flight hardware for NASA’s Satellite Test of the Equivalence Principle (STEP). Our table can tilt the hardware around two axes and is part of a test bed that has 6-degree-of-freedom controllability. The goal was to build a tilt table with a resolution better than ∼5 μrad (1 arcsec). Our table consists of three aluminum plates. The outermost plate is attached to the cryogenic probe and is fixed. The middle and inner plates rest on the outer and middle plates, respectively, using knife edges and knife edge holders made of silicon nitride that are glued to the aluminum plates. A cryogenic tilt sensor was also developed and integrated with the table. The sensor consists of an electrically grounded copper cube hanging from a support, and is placed between two pairs of capacitive electrodes. Any motion of the cube caused by tilting is measured differentially using a Wheatstone bridge circuit. The table is connected to the bottom of a cryogenic probe. A voice coil actuator, located on top of the probe at room temperature, is used to create the necessary tilt. A thin fiber is used to connect the actuator and the table. The system is controlled using a dSPACE control card. A test of the table at cryogenic temperatures (4.5 K) and low pressure (1 μTorr) showed a noise level of ∼0.7 μrad (150 marcsec), which is nearly an order of magnitude better than the required resolution.

Satellite Test of the Equivalence Principle Uncertainty Analysis

STEP, the Satellite Test of the Equivalence Principle, is intended to test the apparent equivalence of gravitational and inertial mass to 1 part in 1018 (Worden et al. in Adv. Space Res. 25(6):1205–1208, 2000). This will be an increase of more than five orders of magnitude over ground-based experiments and lunar laser ranging observations (Su et al. in Phys. Rev. D 50:3614–3636, 1994; Williams et al. in Phys. Rev. D 53:6730–6739, 1996; Schlamminger et al. in Phys. Rev. Lett. 100:041101, 2008). It is essential to have a comprehensive and consistent model of the possible error sources in an experiment of this nature to be able to understand and set requirements, and to evaluate design trade-offs. In the following pages we describe existing software for such an error model and the application of this software to the STEP experiment. In particular we address several issues, including charge and patch effect forces, where our understanding has improved since the launch of GP-B owing to the availability of GP-B data and preliminary analysis results (Everitt et al. in Space Sci. Rev., 2009, this issue; Silbergleit et al. in Space Sci. Rev., 2009, this issue; Keiser et al. in Space Sci. Rev., 2009, this issue; Heifetz et al. in Space Sci. Rev., 2009, this issue; Muhlfelder et al. in Space Sci. Rev., 2009, this issue).

The Science Case for STEP

The Satellite Test of the Equivalence Principle (STEP) will advance experimental limits on violations of Einstein’s Equivalence Principle (EP) from their present sensitivity of 2 parts in 10 13 to 1 part in 10 18 through multiple comparison of the motions of four pairs of test masses of different compositions in an earth-orbiting drag-free satellite. Dimensional arguments suggest that violations, if they exist, should be found in this range, and they are also suggested by leading attempts at unified theories of fundamental interactions (e.g., string theory) and cosmological theories involving dynamical dark energy. Discovery of a violation would constitute the discovery of a new force of nature and provide a critical signpost toward unification. A null result would be just as profound, because it would close off any possibility of a natural-strength coupling between standard-model fields and the new light degrees of freedom that such theories generically predict (e.g., dilatons, moduli, quintessence). STEP should thus be seen as the intermediate-scale component of an integrated strategy for fundamental physics experiments that already includes particle accelerators (at the smallest scales) and supernova probes (at the largest). The former may find indirect evidence for new fields via their missing-energy signatures, and the latter may produce direct evidence through changes in cosmological equation of state—but only a gravitational experiment like STEP can go further and reveal how or whether such a field couples to the rest of the standard model. It is at once complementary to the other two kinds of tests, and a uniquely powerful probe of fundamental physics in its own right.

SATELLITE TEST OF THE EQUIVALENCE PRINCIPLE: OVERVIEW AND PROGRESS

STEP, the Satellite Test of the Equivalence Principle, is reviewed and the current status of the project is discussed. This space-based experiment will test the universality of free fall and is designed to advance the present state of knowledge by over five orders of magnitude. The international STEP collaboration is pursuing a development plan to improve and verify the technology readiness of key systems. We discuss recent advances with an emphasis on accelerometer fabrication and tests. Critical technologies successfully demonstrated in flight by the Gravity Probe B mission also contribute to progress.

DETECTING LORENTZ INVARIANCE VIOLATIONS IN THE 10-20 RANGE

In recent years the possibility has been raised of Lorentz invariance violations arising from physics beyond the Standard Model. Some of these effects manifest themselves as small anisotropies in the velocity of light, c. By comparing the resonant frequencies of cavity modes with different spatial alignments, limits on the order δ c/c < 10-15 have been set and some further improvement can be expected. However, the largest Lorentz violations originating at the Planck scale are expected to manifest themselves as a fractional frequency variation at the 10-17 level in the absence of suppression factors. Space experiments have been proposed to approach the 10-18 level. Here we explore the possibilities for pushing further and show that it is possible in principle to reach well into the 10-20 range with existing technology. This could be done in a very quiet cryogenic environment, such as the drag-free orbiter being developed for the Satellite Test of the Equivalence Principle (STEP).

Effect of Surface Roughness on Thin Film Niobium Coatings

Satellite Test of the Equivalence Principle (STEP) proposes to use niobium thin film strip-line circuits on precision quartz assemblies to achieve on-orbit differential acceleration sensitivities of 10-18 g. The acceleration is determined from a displacement measurement under known spring stiffness. Currents trapped in niobium circuits (400 nm thick, 100 mum wide) provide magnetic spring forces, and in conjunction with a SQUID magnetometer, the displacement measurement. We have studied the effect of substrate surface roughness on the critical current and temperature of niobium thin film strip-line circuits. We have observed a critical current that decreases with increasing surface roughness, with no change in critical temperature. We attribute the decrease in critical current to a flux penetration barrier at the strip-line edge that decreases with increasing surface roughness. This is a significant finding for the development of the STEP instrument, since anomalous flux penetration at the edge of circuits can degrade performance, add SQUID sensor noise, and lead to trapped flux instabilities.

STEP payload development

The Satellite Test of the Equivalence Principle, STEP, will test what is arguably the most fundamental principle of physics to unprecedented accuracy. The experiment will enhance our knowledge of the identity of mass and inertia by five or more orders of magnitude, to one part in 10 18, by comparing the rate of fall of test masses in earth orbit. The equivalence principle is the cornerstone of General Relativity, and detection of any violation would be an unambiguous sign of new physics. This paper describes progress toward the payload design for STEP.

Aerogel: Space exploration applications

The unique physical properties of aerogel have proven to be enabling to a variety of both flight and proposed space exploration missions. The extremely low density and highly porous nature of aerogel makes it suitable for stopping high velocity particles, as a highly efficient thermal barrier, and as a porous medium for the containment of cryogenic fluids. The use of silica aerogel as a hypervelocity particle capture and return media for the Stardust Mission has drawn the attention of many in the space exploration community. Aerogel is currently being used as the thermal insulation material in the 2003 Mars Exploration Rovers. The SCIM (Sample Collection for the Investigation of Mars) and the STEP (Satellite Test of the Equivalence Principle) Missions are both proposed space exploration missions, in which, the use of aerogel is critical to their overall design and success. Composite materials comprised of silica aerogel and oxide powders are under development for use in a new generation of thermoelectric devices that are planned for use in many future space exploration mission designs. Work is currently ongoing in the development and production of non-silicate and composite aerogels to extend the range of useful applications envisioned for aerogel in future space exploration projects.

The confrontation between general relativity and experiment

We review the experimental evidence for Einstein’s general relativity. Tests of the Einstein equivalence principle support the postulates of curved space-time and bound variations of fundamental constants in space and time, while solar system experiments strongly confirm weak-field general relativity. The binary pulsar provides tests of gravitational wave damping and of strong-field general relativity. Future experiments, such as the gravity probe B gyroscope experiment, a satellite test of the equivalence principle, and tests of gravity at short distance to look for extra spatial dimensions could further constrain alternatives to general relativity. Laser Interferometric Gravitational Wave Observatories on Earth and in space may provide new tests of scalar-tensor gravity and graviton-mass theories via the properties of gravitational waves.

Gravitational Experiments in Space: Gravity Probe B and STEP

We describe two space based gravitational physics experiments, the Gravity Probe B Relativity Mission (GPB) and the Satellite Test of the Equivalence Principle (STEP). GP-B will perform precision tests of two independent predictions of general relativity, the geodetic effect and frame dragging. STEP will provide a precision test of a foundation of general relativity, the Equivalence Principle.

ESA's STEP assessment and phase a studies for M2 and M3

STEP (Satellite Test of the Equivalence Principle) was studied by ESA at Assessment and Phase A level as a candidate for the second medium-size project (M2) and, after its non-selection, again at Assessment and Phase A level for M3. During the M2 cycle, STEP was studied as an ESA/NASA collaborative project, during the M3 cycle as a European-only project. During both cycles, the payload consisted not only of several differential accelerometers to test the Equivalence Principle, but also of accelerometers to measure the Constant of Gravity, to test the inverse square law of gravity, to search for a hypothetical force between spin-polarised and ordinary matter, and to perform a high-precision geodesy experiment. In the end, STEP was not selected as M3 either. The studies carried out by ESA for M3 complemented similar studies performed at about the same time by NASA and by CNES. Over the last couple of years a variety of mission options was studied by the three space agencies with the result that a low-cost, cryogenic option that exclusively focuses on the Equivalence Principle test is the best way forward. This mission (MiniSTEP) is now under study as a NASA/ESA collaborative project.

The NASA-ESA MiniSTEP payload

The Equivalence Principle, which states that gravitational mass and inertial mass are different ways of measuring the same property, is the experimental foundation for modern gravitational theory. Modern theory cannot reconcile gravity with the other fundamental forces. One possibility is that the present theory of gravity, general relativity, is incomplete or incorrect. If this is the case, the Equivalence Principle may be violated at some level beyond the one part in 10 12 that has been experimentally verified. The goal of the Satellite Test of the Equivalence Principle (STEP) is to improve this result to better than one part in 10 18. In STEP two or more concentric, cylindrical test masses “fall” around the Earth in a drag-free satellite. The masses are cooled to < 2K and supported by frictionless, superconducting, linear bearings. Ultra-sensitive SQUID position detectors measure their relative motion. A confirmed violation could provide key information toward the possible unification of the four fundamental forces; conversely, a null result can rule out competing theories or constrain new theories. MiniSTEP is the least expensive mission proposed to date that still achieves STEP's basic scientific goal. It compares four different materials in four differential accelerometers. Cost saving is achieved by operating the accelerometers sequentially, thereby avoiding duplicated equipment. The drag-free satellite will be built around an existing superfluid helium dewar and a small, semi-production spacecraft. A small commercial launch vehicle will place the satellite in a 400 km, sun-synchronous, polar, Earth orbit. Nominal mission lifetime is four months - but a six to eight month life is expected.

The NASA/ESA MiniSTEP project

The Equivalence Principle states that gravitational mass and inertial mass are identical quantities. However, modern theory cannot reconcile gravity with the other three fundamental forces found in nature. One possibility is that the present theory of gravity, rooted in general relativity, is incomplete or incorrect. As a consequence of this, the Equivalence Principle may be violated at some level beyond the one part in ∼10 12 that has been experimentally verified. The objective of the Satellite Test of the Equivalence Principle (STEP) is to extend the range of experiment to one part in 10 18. This is accomplished by allowing two concentric, cylindrical test masses to “fall” around the Earth in a drag-free satellite. The test masses are cooled to < 2K and are supported by frictionless, superconducting, linear bearings. Relative motion between the test masses is measured by ultra-sensitive SQUID position detectors. The consequences of a confirmed violation will be to provide key information toward the possible unification of the four fundamental forces. A null result may rule out several competing theories and set better limits for new theories. Of the several STEP missions studied, MiniSTEP is the least expensive mission to date that still achieves the basic scientific goals. It uses four pairs of test masses (four differential accelerometers) to compare at least four different materials. An existing superfluid helium dewar, containing the four differential accelerometers, will be used along with a small, semi-production spacecraft to form the drag free satellite. The satellite will be placed in a 400 km, sun-synchronous, Earth orbit by a small commercial launch vehicle early in 2002. The nominal mission lifetime is four months.

Test mass design for the EP experiment on M3 STEP

The design strategy for pairs of test-masses for the Satellite Test of the Equivalence Principle is discussed. Limitations are placed on the possible density ratios for the materials used in each test-mass pair, leading to the conclusion that a fully cyclical test for systematic errors is not possible. The immunity of test-masses to local gravitational influences is considered, and a figure of merit, the ‘differential acceleration susceptibility’ χ(R, θ, ϕ)= Δa z/a, is introduced for any test-pair, such that different designs may usefully be intercompared. The electrostatic patch-effect is described in the context of its potential influence on the STEP test-masses, and the need to prevent azimuthal rotation of the masses is underlined. Two schemes for frictionlessly preventing such azimuthal rotation are discussed: longitudinal grooves, and chordal ‘flats’ on the masses. It is found that the minimum number of grooves (or ‘flats’) that may be used on the STEP test-masses is 6.

The Confrontation between General Relativity and Experiment

We review the experimental evidence for Einstein's general relativity. Tests of the Einstein Equivalence Principle support the postulates of curved spacetime and bound variations of fundamental constants in space and time, while solar-system experiments strongly confirm weak-field general relativity. The Binary Pulsar provides tests of gravitational-wave damping and of strong-field general relativity. Future experiments, such as the Gravity Probe B Gyroscope Experiment, a satellite test of the Equivalence principle, and tests of gravity at short distance to look for extra spatial dimensions could further constrain alternatives to general relativity. Laser interferometric gravitational-wave observatories on Earth and in space may provide new tests of scalar-tensor gravity and graviton-mass theories via the properties of gravitational waves.

The STEP mission: principles and baseline design

The Satellite Test of the Equivalence Principle (STEP) will test the equality of fall of objects in Earth orbit to anaccuracy approaching one part in 108 by measuring the difference in rate of fall of test cylinders incryogenic differential accelerometers in a drag-free satellite. This paper describes the current baseline design andprinciples used in the design of the STEP mission.