Paul Worden

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 an accuracy approaching one part in 108 by measuring the difference in rate of fall of test cylinders in cryogenic differential accelerometers in a drag-free satellite. This paper describes the current baseline design and principles used in the design of the STEP mission.

The Science Case for STEP

Abstract 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.

The Gravity Probe B test of general relativity

The Gravity Probe B mission provided two new quantitative tests of Einsteins theory of gravity, general relativity (GR), by cryogenic gyroscopes in Earths orbit. Data from four gyroscopes gave a geodetic drift-rate of −6601.8 ± 18.3 marc-s yr−1 and a frame-dragging of −37.2 ± 7.2 marc-s yr−1, to be compared with GR predictions of −6606.1 and −39.2 marc-s yr−1 (1 marc-s = 4.848 × 10−9 radians). The present paper introduces the science, engineering, data analysis, and heritage of Gravity Probe B, detailed in the accompanying 20 CQG papers.

STEP: A Status Report

This paper presents an overview of the current technical status of STEP, the Satellite Test of the Equivalence Principle. STEP was originally presented as a candidate for ESA’s M2 mission as a joint mission with NASA, and has since been studied as an M3 candidate, and under NASA as QuickSTEP and MiniSTEP. Studies especially during the last two years have resolved some long standing issues such as control of helium tide, improved the mission definition and error analysis, and have resulted in an improved baseline design which should be capable of comparing rates of fall to an accuracy approaching 10-18.

STEP and fundamental physics

The Satellite Test of the Equivalence Principle (STEP) will advance experimental limits on violations of Einsteins 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.

STEP error model development

We describe the ongoing development of a comprehensive error model for the satellite test of the equivalence principle, STEP. The goal is to employ a model of the experiment and apparatus as a self-consistent whole. The model uses a set of input parameters based on experiment design and the measured characteristics of STEP sensor systems. The output of the model evaluates specific disturbances to the test masses in the general categories of thermal noise, gas pressure forces, electrical forces, magnetic forces, gravitational forces, radiation pressure and vibration. Use of the model to set experiment requirements and to evaluate design trade-offs are briefly discussed. PACS number: 0480C (Some figures in this article are in colour only in the electronic version; see www.iop.org)

The step payload and experiment

Abstract The foundation of modern gravitational theory is the Equivalence Principle. General Relativity is incompatible with theories of other fundamental forces such as QED, suggesting that it is incomplete. For example, there may be additional forces coupled to baryon number or spin. In this case the Equivalence Principle may be violated below the experimentally verified level of one part in 10 12 . A violation could provide crucial information for new theories. A team of US and European scientists has assembled to do the Satellite Test of the Equivalence Principle (STEP) with the goal of improving this measurement to 1 part in 10 18 . In STEP two or more test masses “fall” around the earth in a drag free satellite. A difference in the rate of fall appears as a periodic difference in their acceleration. The test masses are cooled to less than 2K and are supported by frictionless superconducting bearings. Ultra-sensitive SQUID position sensors measure their relative motion and their common motion is removed by adjustments during acceleration maneuvers. Any Equivalence Principle signal is separated from major disturbances by rotation of the spacecraft. STEP is planned to be launched by 2004, with nominal mission lifetime of 6 months.

Gravity Probe B data analysis: II. Science data and their handling prior to the final analysis

The results of the Gravity Probe B relativity science mission published in Everitt et al (2011 Phys. Rev. Lett. 106 221101) required a rather sophisticated analysis of experimental data due to several unexpected complications discovered on-orbit. We give a detailed description of the Gravity Probe B data reduction. In the first paper (Silbergleit et al Class. Quantum Grav. 22 224018) we derived the measurement models, i.e., mathematical expressions for all the signals to analyze. In the third paper (Conklin et al Class. Quantum Grav. 22 224020) we explain the estimation algorithms and their program implementation, and discuss the experiment results obtained through data reduction. This paper deals with the science data preparation for the main analysis yielding the relativistic drift estimates.

Gravity Probe B data analysis: I. Coordinate frames and analysis models

Gravity Probe B (GP-B) was a cryogenic, space-based experiment testing the geodetic and frame-dragging predictions of Einsteins theory of general relativity (GR) by means of gyroscopes in Earth orbit. This first of three data analysis papers reviews the GR predictions and details the models that provide the framework for the relativity analysis. In the second paper we describe the flight data and their preprocessing. The third paper covers the algorithms and software tools that fit the preprocessed flight data to the models to give the experimental results published in Everitt et al (2011 Phys. Rev. Lett. 106 221101–4).

Nanohertz frequency determination for the gravity probe B high frequency superconducting quantum interference device signal

In this paper, we present a method to measure the frequency and the frequency change rate of a digital signal. This method consists of three consecutive algorithms: frequency interpolation, phase differencing, and a third algorithm specifically designed and tested by the authors. The succession of these three algorithms allowed a 5 parts in 10^10 resolution in frequency determination. The algorithm developed by the authors can be applied to a sampled scalar signal such that a model linking the harmonics of its main frequency to the underlying physical phenomenon is available. This method was developed in the framework of the Gravity Probe B (GP-B) mission. It was applied to the High Frequency (HF) component of GP-Bs Superconducting QUantum Interference Device (SQUID) signal, whose main frequency fz is close to the spin frequency of the gyroscopes used in the experiment. A 30 nHz resolution in signal frequency and a 0.1 pHz/sec resolution in its decay rate were achieved out of a succession of 1.86 second-long stretches of signal sampled at 2200 Hz. This paper describes the underlying theory of the frequency measurement method as well as its application to GP-Bs HF science signal.In this paper, we present a method to measure the frequency and the frequency change rate of a digital signal. This method consists of three consecutive algorithms: frequency interpolation, phase differencing, and a third algorithm specifically designed and tested by the authors. The succession of these three algorithms allowed a 5 parts in 10(10) resolution in frequency determination. The algorithm developed by the authors can be applied to a sampled scalar signal such that a model linking the harmonics of its main frequency to the underlying physical phenomenon is available. This method was developed in the framework of the gravity probe B (GP-B) mission. It was applied to the high frequency (HF) component of GP-Bs superconducting quantum interference device signal, whose main frequency f(z) is close to the spin frequency of the gyroscopes used in the experiment. A 30 nHz resolution in signal frequency and a 0.1 pHz/s resolution in its decay rate were achieved out of a succession of 1.86 s-long stretches of signal sampled at 2200 Hz. This paper describes the underlying theory of the frequency measurement method as well as its application to GP-Bs HF science signal.