Relativity's Subtlety

On April 20, 2004, a Boeing Delta II rocket launched from Vandenberg Air Force Base carried Gravity Probe B into orbit and so initiated the next step in a 40-year quest to verify a corollary of the General Theory of Relativity. First conceived in 1960, and initially funded in 1964 but delayed by financial, physics, and implementation challenges, this experiment embodies the ultimate in accurate measurement while canceling or eliminating error sources. As with so many engineering and science projects, GP-B (Gravity Probe B) is elegant in concept but brutal in details of its execution.

We now accept Einstein's Theory of Relativity as fact—and with good reason. Since he put forth the Special Theory in 1905, and followed it in 1916 with the General Theory, which links space, time, and gravity, both theories have been confirmed by innumerable tests, observations, and their ability to predict and explain large- and atomic-scale phenomena. Special relativity, summarized by the elegant formula E=mc², has the greatest impact on what most engineers and scientists do, along with quantum theory, of course.

But one subtlety of the General Theory has evaded direct experimental confirmation (see sidebar "Is Your Frame Dragging?"). The effect that the theory predicts is so subtle that only one observation, the Hulse-Taylor binary-pulsar discovery of the mid-1970s, has indirectly confirmed it.

The GP-B experiment has little resemblance to what goes on in a scientist's lab. The entire unit is encased in a 3-ton, 21-ft-long housing and is now in polar orbit at a 400-mile altitude. Typical of the experiment's requirement for exceptional precision, the launch window each day for liftoff was just 1 second. Miss it, and the unit would be unable to achieve the precise polar orbit that aligns it with its guide star.

Many experienced partners are contributing to the $700 million GP-B project: Prime contractor Stanford University built the science instrument, working with the NASA Marshall Space Flight Center; Lockheed Martin Missiles and Space has a major subcontract; and the Harvard Smithsonian Astrophysical Observatory provided key guide-star measurements. (Note: Gravity Probe A was launched on June 18, 1976, for a planned 115-min suborbital flight, solely to test some of the concepts and verify some critical data.)

The heart of GP-B is a set of four gyroscopes, but they have little resemblance to the crude ones sold as toys or even the precise ones used for missile guidance. The gyros are electrically spun spheres the size of ping-pong balls (with a 1.5-inch diameter), spinning in a vacuum at 10,000 rpm, housed in a 9-ft-long chamber.

The principle is simple: A perfect gyro stays pointed in the same direction in space. Any frame dragging distorts the space-time fabric and affects the gyro's pointing. But this experiment poses two problems. First, imperfections in the gyro assembly cause it to drift. Second, the simple phrase "same direction" loses meaning in the context of the curvature of space-time, frame-dragging, and relativistic effects. To complicate the experiment, the geodetic effect of the gyros traveling through the space-time curvature is much larger than the frame-dragging effect.

The experiment had to have six major characteristics:

• A drift-free gyroscope with absolute drift from nonrelativistic effects of less than 10^-11 degrees/ hr (one-millionth the drift of the best guidance gyros)

• A gyro readout to determine changes in spin angle to 0.1 milliarc-second

• A stable reference, based on a telescope, to relate the gyro and its assembly to a guide star

• A guide star in the right area of the sky with well-known optical and radio-emission characteristics

• A way to separate the two relativistic factors of frame-dragging and geodetic effects

• A way to calibrate the entire assembly after launch to eliminate larger scale instrumentation errors that may obscure the signals that indicate the desired effects

The core of the GP-B is a 21-inch-long block of fused quartz, which is bonded to a quartz telescope and contains the four gyros. It also houses a proof mass—in this case, a quartz sphere the same size as the gyro rotors—that floats in a vacuum cavity at the center of mass of the spacecraft. The role of the proof mass is to follow the ideal gravitational orbit. Sensing its position in the cavity and making compensating adjustments to the satellite based on position changes cancel out the geodetic effect.

The spinning heart of the Gravity Probe B experiment comprises the most perfect sphere ever fabricated (right) and its housing (left); four identical units exist.

The four gyro rotors are made of fused quartz, fabricated to an extreme level of material homogeneity and then ground to the near-absolute sphericity (Figure 1). The spheres are round to within 40 atomic layers, which is proportionally equivalent to an Earth-sized sphere with surface height variations of only 16 ft. (Reference 1 explains the manufacturing of the fused quartz and the fabrication and testing of these spheres—an amazing story in itself.) Four gyros provide redundancy, and, by spinning two of the gyros in one direction and two in the opposite direction, the system can cancel some error sources.

It's one thing to have a virtually perfect gyro rotor, but that alone does not provide the necessary performance for this experiment. The designers had to solve three design puzzles: how to suspend these rotors in their cavity without disturbing their spin, how to get and keep the rotors spinning, and how to read out the spin direction of a perfect, unmarked sphere.

They solved the first problem by levitating the rotors with three pairs of saucer-shaped electrodes. The electric fields center the rotors to a few millionths of an inch. They did not perform the spinning up electrically, however. Instead, they directed a precise stream of helium gas, traveling at nearly Mach 1, at the rotors. It takes about half an hour for the rotor to reach full speed, and it loses less than 1 percent of this speed over 1,000 years in the super-vacuum of the cavity.

A SQUID (superconducting quantum interference device) pickup and the quantum-physics London effect sense the angular shift in the rotor spin asix, without physical contact or interference.

But the third problem proved the most challenging. The designers used superconductivity as the basis of a noninterfering pointer readout based on the SQUID (superconducting quantum interference device). When a superconductor spins, it generates a magnetic field due to the London moment (named after Fritz London, the physicist who predicted it). To read the rotor-spin direction, the designers coated the rotors with a superthin, precise layer of niobium. The rotors generate a tiny electric field due to differences in electron motion in their lattice; this effect, the London moment, exactly aligns with the spin axis.

A thin, superconducting loop connected to a SQUID circles each of the rotors (Figure 2). When the rotor tilts, due to the anticipated frame-dragging, the London moment also tilts, changing the magnetic field through the loop. The SQUID-based London-moment readout can detect changes in magnetic field of 5x10^-14 gauss, corresponding to a gyro tilt of 0.1 milliarc-second. By comparison, the Earth's magnetic field is 13 orders of magnitude larger than this level of detection.

Packaging is Everything—Almost

Engineers know that the difference between a basic project and one that works in the final application is the packaging. It's the same with GP-B. Any outside disturbances, especially magnetic fields, affect the readings. To prevent any such impact, the gyro rotor and SQUID assembly is housed in a lead balloon—literally. Otherwise, external magnetic fields would penetrate the superconducting shell. GP-B uses a series of four lead bags or balloons. The designers inserted the gyro assembly into the first bag and then cooled it to superconducting temperatures and expanded it, further lowering the magnetic field. They inserted the first bag into the next bag, which undergoes the same cooling and expansion, and so on. This technique results in an enclosure with extraordinarily low (10^-6 gauss) and stable magnetic field.

One more element is necessary to make the experiment viable: The gyro assembly must know which way it is pointing, for a calibration reference. The change in angle between the gyro rotor pointing and the reference direction indicates possible frame-dragging.

The reference technique most satellites and missiles use is to aim a telescope at a star. GP-B uses this same method, with enhancements (see sidebar "In Space, You Can't Ask for Directions"). The entire SIA (science instrument assembly) comprises the gyro and its spin detectors, which are referenced to the telescope, which in turn is referenced to the guide star.

Supercooling and superconductivity are critical to the experiment. The main body of the probe structure—the SIA—is housed in a 650-gallon Dewar flask, or thermos bottle, which contains the supercooled liquid helium and thus maintains the probe at 1.65K, or -271.4C (Figure 3). Nothing is wasted, because the boil-off of this helium initially brings the rotors up to speed and subsequently fuels the spacecraft thrusters. The supercooled helium, as a passive container, must provide the proper environment for two years without "refills."

The designers tested many subparts of this complex experiment in other, unrelated projects or in specially designed tests. In addition, the project used extensive modeling and simulation to shape the design, assess various operational and control strategies, generate code, and analyze the effect of error sources. Among other tools, the design team at Stanford used standard versions of Matlab and Simulink from The MathWorks. According to Jennifer Petrosky, industry marketing manager at The Mathworks, "These tools facilitate prelaunch planning, analyze the probability of success and reliability issues, and investigate calibration and data analysis choices."

What's the outcome of the GP-B experiment? According to Francis Everett of Stanford, principal investigator on GP-B, "The background effects are going to be five or six orders of magnitude smaller [than the Einstein effects the experiment is looking for], so it will be an extraordinarily strong test."

It is too soon to report on the final results. Thus far, every aspect of the satellite is performing at, or exceeding, target specifications. However, it will take at least one year and likely two of data collection followed by data analysis to determine whether the "music of the spheres" can confirm the frame-dragging hypothesis that derives from the General Theory of Relativity.

Regardless of the results, the entire experiment has pushed the technological and experimental boundaries of instrumentation precision, as well as some more seemingly mundane challenges. Gravity Probe B has inspired advances in gyro fabrication, suspension, spin, and readout; near-perfect elimination of interfering magnetic fields; telescope pointing and control; large-scale Dewar technology; design simulation of every aspect, including modeling and control of supercooled helium sloshing and boil-off (see sidebar "Who Can Plug This Hole?"); and component fabrication, calibration, and test. For more physics, technical details, and insight, see references 2 and 3.