From Gravity Probe B to STEP: Testing Einstein in Space
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From Gravity Probe B to STEP: Testing Einstein in Space James Overduin1 1Gravity Probe B, Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA 94305, USA Abstract I summarize the history, current status and preliminary findings of the Gravity Probe B (GPB) mission, which seeks to make the first direct measurements of the geodetic and frame-dragging effects predicted by Einstein's theory of general relativ- ity. I then discuss the planned Satellite Test of the Equivalence Principle (STEP), which will test the underlying assumption of Einstein's theory, the equivalence of gravitational and inertial mass. STEP will place important constraints on theories that seek to go beyond general relativity, such as unified field theories based on higher dimensions (string theory) and theories of dynamical dark energy (quintessence), both of which predict the existence of new fields that may violate the equivalence principle. 1 Background to the Gravity Probe B Experiment By coincidence, the successful launch of Gravity Probe B on 20 April 2004 (Fig. 1) came exactly 100 years after the earliest published accounts of frame-dragging experiments, by August F¨opplin Munich in 1904 [1]. F¨oppl,working as he was before general (and for that matter special) relativity, was investigating the possibility of a coupling between the spin of the Earth and that of a pair of heavy flywheels whose rotation axis could be aligned along either lines of latitude or longitude (Fig. 2). He was probably inspired by earlier experiments of countrymen Immanuel and Benedict Friedlaender (1896) involving torsion balances in the vicinity of spinning millstones, and by the writings of Ernst Mach, who famously speculated in 1883 that water in a spinning bucket might not exhibit the effects of centrifugal force \if the sides of the vessel increased in thickness and mass until they were ultimately several leagues thick." A sufficiently Figure 1: Launch of Gravity Probe B 1E-mail:[email protected] 1 80 Benedict Friedlaender August Foppl Foppl's experimental setup Figure 2: Experiments in frame-dragging before general relativity massive bucket, in other words, might carry the local inertial frame of the water around with it. Mach's Principle, as this idea came to be known, has proved to be of limited scientific value (Ref. 1 lists 21 different formulations of it in the literature, some mutually contradictory). Nevertheless Gravity Probe B (GPB) can be seen as a modern-day realization of Mach's proposal with an earth-sized bucket and the role of water played by orbiting gyroscopes more than a million times more sensitive than the best inertial navigation gyros on earth. Albert Einstein was strongly influenced by Mach's ideas, and his early attempts at gravitational field theories all exhibited frame-dragging effects. It is somewhat surprising, therefore, that he did not attempt to work out the Machian implications of general relativity himself. That was left to Hans Thirring and Josef Lense (1918), after whom the general relativistic frame-dragging effect is often named. (In a nice reversal of the usual course of events, Thirring had wanted to build an improved F¨oppl-type experiment and only reluctantly settled for doing the theoretical calculation after he was unable to obtain funding [1].) The terms \frame-dragging" and \Lense-Thirring" are sometimes used interchangeably with \gravitomagnetic", based on the close analogy between Maxwell's equations and a subset of Einstein's field equations in the low-velocity, weak-field limit [2]. Such analogies did not begin with general relativity; their existence was already suspected in 1849 by Michael Faraday, who designed experiments to search for \gravitational induction." The terminology must be used with care, however; for just as in ordinary electrodynamics, the distinction between gravitomagnetic and gravitoelectric is frame-dependent, and other phenomena besides frame-dragging are at least partly "gravito-electromagnetic." An example is the geodetic effect, which involves the transport of angular momentum through a gravitational field and was already studied two years before the Lense-Thirring effect by Willem de Sitter (1916). He showed that the earth-moon system would precess in the field of the sun, an effect now called the solar geodetic effect (although \heliodetic" might be more descriptive). De Sitter's calculation was extended to rotating test bodies such as the earth by Jan Schouten (1918) and Adriaan Fokker (1920), and the solar geodetic effect is now sometimes referred to as the de Sitter or Fokker-de Sitter effect. These effects became widely known when they were mentioned by Arthur Eddington in his textbook of 1924. The idea of attempting to observe them with terrestrial gyroscopes was briefly considered in the 1930s by P.M.S. Blackett, who discarded it as impractical [3]. Technological progress during World 2 81 Leonard Schiff George Pugh Dan Debra, Bill Fairbank, Francis Everitt and Bob Cannon with a model of GPB, 1980 Figure 3: Genesis of Gravity Probe B War II, however, brought the problem back into the realm of possibility. An advertisement for a new \cryogenic gyroscope" in the December 1959 issue of Physics Today stimulated Leonard Schiff to revisit some earlier calculations involving tests of Mach's Principle and led to his elegant re-derivation of both the geodetic and frame-dragging effects in the form now known as the Schiff formula: 3GM GI 3~r ~ ~ ~ − × ~ · − ~ ΩGR = Ωgeo + Ωf d = 2 3 (~r ~v) + 2 3 2 S ~r S ; (1) 2c r c r r where M, I and S~ refer to the mass, moment of inertia and angular momentum of the central body and r and ~v are the orbital radius and instantaneous velocity of the gyroscope. In a nice example of scientific synchronicity, essentially the same results were arrived at independently months earlier by George Pugh, a researcher at the Pentagon who also contributed the ingenious suggestion of shielding an orbiting gyroscope from non-gravitational disturbances inside a drag-free satellite. Frame-dragging arises due to a spin-spin interaction between the gyroscope and rotating earth, anal- ogous to the interaction of a magnetic dipole with a magnetic field. In a polar orbit 642 km above the earth, it causes a gyroscope's spin axis to precess in the east-west direction by 39 milliarcsec/yr, an angle so tiny that it is equivalent to the angular width of the object Pluto as seen from earth. The geodetic effect is somewhat larger; it arises partly as a spin-orbit interaction between the spin of the gyroscope and the \mass current" of the moving earth in the gyro rest frame. This is the analog of Thomas precession in electromagnetism. The spin-orbit interaction accounts for one-third of the total geodetic precession; the other two-thirds are not gravito-electromagnetic in origin, but arise due to space curvature around the massive earth (an effect sometimes referred to as the \missing inch" [2]). In a 642 km polar orbit, the geodetic effect causes a gyroscope's spin axis to precess in the north-south direction by 6606 mil- liarcsec/yr, an angle comparable to that subtended by the planet Mercury as seen from earth. The measurement of precessions this small would eventually pose immense technical and scientific challenges, an obstacle which fortunately did not deter Schiff (a theorist), Bill Fairbank (a low-temperature experi- mentalist) and Bob Cannon (a gyroscope specialist) when they met one sunny afternoon in 1960 in the Stanford university swimming pool to discuss the idea seriously for the first time (Fig. 3). GPB received its first NASA funding in March 1964. 2 The Gravity Probe B Mission and Preliminary Results In concept the experiment is simplicity itself: a gyroscope, a readout mechanism to monitor its spin axis, and a telescope to compare this axis with the line of sight to a distant guide star (Fig. 4). In practice GPB 3 82 telescope guide star gyroscopes dewar direction to guide star thrusters for gyro spin axis drag−free control Figure 4: Gravity Probe B concept grew into one of the most complex experiments ever flown, requiring at least a dozen new technologies that did not exist when it was conceived. Among these are the world's roundest and most homogeneous gyroscope rotors and a suspension system operating to levitate and maintain them within microns of their housings over a dynamic range of eleven orders of magnitude in force. A novel readout scheme based on the superconducting London moment was developed using ultra-sensitive superconducting quantum interference device (SQUID) magnetometers. Expandable nested lead shields were employed to reduce the ambient magnetic field. New techniques were invented to spin up the gyros, reduce vacuum pressure and remove charge buildup on the rotors. Perturbing forces were suppressed by a drag-free control system whereby any one of the gyroscopes could be isolated as an inertial \plumb line"; the rest of the spacecraft was made to follow its motion by means of helium boiloff vented through a revolutionary porous plug and specially designed thrusters. (This porous plug has since proved vital to other NASA missions including COBE, IRAS, WMAP and Spitzer.) The resolution of the onboard telescope, fastened to the gyro assembly by a novel quartz bonding technique, was enhanced by means of a beam splitter and image dividers. Non-inertial motions of the guide star, IM Pegasi, were compensated by the use of long-baseline radio interferometry to monitor its position relative to distant background quasars. Once in orbit, GPB underwent an initial orbit checkout phase, which lasted until 27 August 2004 and has been described in detail elsewhere [4]. The science phase which followed lasted until 14 August 2005 (or 353 days, just under the original goal of one full year).