The Experimental Verdict on Spacetime from Gravity Probe B James Overduin Abstract Concepts of space and time have been closely connected with matter since the time of the ancient Greeks. The history of these ideas is briefly reviewed, focusing on the debate between “absolute” and “relational” views of space and time and their influence on Einstein’s theory of general relativity, as formulated in the language of four-dimensional spacetime by Minkowski in 1908. After a brief detour through Minkowski’s modern-day legacy in higher dimensions, an overview is given of the current experimental status of general relativity. Gravity Probe B is the first test of this theory to focus on spin, and the first to produce direct and unambiguous detections of the geodetic effect (warped spacetime tugs on a spin- ning gyroscope) and the frame-dragging effect (the spinning earth pulls spacetime around with it). These effects have important implications for astrophysics, cosmol- ogy and the origin of inertia. Philosophically, they might also be viewed as tests of the propositions that spacetime acts on matter (geodetic effect) and that matter acts back on spacetime (frame-dragging effect). 1 Space and Time Before Minkowski The Stoic philosopher Zeno of Elea, author of Zeno’s paradoxes (c. 490-430 BCE), is said to have held that space and time were unreal since they could neither act nor be acted upon by matter [1]. This is perhaps the earliest version of the relational view of space and time, a view whose philosophical fortunes have waxed and waned with the centuries, but which has exercised enormous influence on physics. The opposing absolutist view, that space and time do possess independent existence apart from matter, has an equally distinguished history that might be traced back to the Stoics’ philosophical rivals, the Epicureans, whose founder Leucippus of Abdera (active c. 450 BCE) introduced the concept of a pre-existing void as the “emptiness between atoms” [2]. The earliest explicit statement of the absolutist view has been attributed by Max Jammer to the Pythagorean philosopher Archytas (428-347 BCE): “Since everything which is moved into a certain place, it is plain that the place where the thing moving or being moved shall be, must exist first” [3]. V. Petkov (ed.), Space, Time, and Spacetime, Fundamental Theories of Physics 167, 25 DOI 10.1007/978-3-642-13538-5 2, c Springer-Verlag Berlin Heidelberg 2010 26 J. Overduin Aristotle (384-322 BCE) constructed a hybrid of the absolute and relational views. He accepted arguments similar to that of Archytas, but was deeply unhappy with the atomistic idea of void, “since no preference can be given to one line of motion more than to another, inasmuch as the void, as such, is incapable of differ- entiation . how [then] can there be any natural movement in the undifferentiated limitless void?” To get around this difficulty Aristotle developed the arguably rela- tional idea that space is defined by that which contains it. He was led in this way (in the Physics) to his influential picture of a cosmos pinned simultaneously to the center of the earth and the firmanent of fixed stars: “The center of the universe and the inner surface of the revolving heavens constitute the supreme ‘below’ and the supreme ‘above’; the former being absolutely stable, and the latter constant in its position as a whole.” Such was Aristotle’s authority that few questioned it for two millenia. An exception was John Philoponus (c. 490-570), who argued for a more purely absolute picture and reacted in particular against the idea that space is somehow defined by that which contains it: “Place is not the adjacent part of the surrounding body . It is a given interval, measurable in three dimensions; it is distinct from the bodies in it, and is, by its very nature, incorporeal. In other words, it is the dimensions alone, devoid of any body.” Claudius Ptolemy (c. 85-165) elaborated on Aristotle’s system, using only cir- cular motions and uniform speeds so as to “save the phenomena” in the face of increasingly accurate observations. However, the way in which he did so points up the limited extent to which Aristotle’s thinking can truly be considered relational. The fact that the “firmanent of fixed stars” and “center of the earth” defined the rest frame of Aristotle’s cosmos did not mean that space was physically anchored to the matter making up the earth or stars. Rather it so happened that these refer- ents stood still in a background space that was more properly conceived as existing absolutely. Thus, adopting an earlier idea of Hipparchus, Ptolemy first detached the sun’s “orbit” from the center of the earth (giving it an “eccentricity”). Later he added planetary “deferents,” “epicycles” and finally “equants”–all reference points or paths in empty space (some of them even with inherent motions of their own). These so-called “void points” make sense only with respect to absolute space–or perhaps to “matter” of a divine kind, as hinted at in the Almagest: “The first cause of the first motion of the universe, if one considers it simply, can be thought of as an invisible and motionless deity.” Here Ptolemy anticipated Newton, who would later refer to absolute space (in the Opticks) as the “sensorium” of God. The nature of time as well as space was eagerly debated in this way by the ancients. The Epicurean philosopher Lucretius (c. 99-55 BCE) may have been the first to argue explicitly for a relational view of time, writing in The Nature of the Universe that: “Time by itself does not exist . It must not be claimed that any- one can sense time by itself apart from the movement of things.” Saint Augustine (354–430) put a theological twist on this argument in his Confessions, emphasizing that “God created the world with time, not in time.” Nicolaus Copernicus (1473–1543) relocated the center of Aristotle’s universe from the earth to the sun. This step was not quite so daring as often thought, for Hipparchus and Ptolemy had already nudged the sun’s “orbit” away from the center of the earth by introducing “eccentricity.” As Copernicus himself noted near the The Experimental Verdict on Spacetime from Gravity Probe B 27 beginning of De Revolutionibus: “Nothing prevents the earth from moving . For, it is not the center of all the revolutions.” Furthermore, although he re-centered the cosmos kinematically on the sun, Copernicus did not attach space dynamically to the rest frame of the sun or any other physical body, but followed Aristotle in associating it with the metaphysical “sphere of the fixed stars,” which (he wrote): “contains itself and everything, and is therefore immovable. It is unquestionably the place of the universe, to which the motion and position of all the other heavenly bodies are compared.” Fifty years later, the notion of rigid planetary spheres could no longer be rec- onciled with astronomical observations, leading Johannes Kepler (1571–1630) to declare: “From henceforth the planets follow their paths through the ether like the birds in the air. We must therefore philosophize about these things differently.” Thoughts such as these led him to the radical idea of attaching the rest frame of space to physical bodies rather than a metaphysical construct such as absolute space (he conceived of forces extending outward from the sun and sweeping the planets along in their orbits). The laws of planetary motion that he subsequently derived have been wonderfully characterized by Julian Barbour as a “pre-Machian triumph of Mach’s Principle” [2]. A similar shift in thinking is apparent in Galilei Galileo (1564–1642). Rather than identifying the fixed stars with the rest frame of space in an abstract sense, he asserted (in the Dialogo) that they are physically at rest in space: “The fixed stars (which are so many suns) agree with our sun in enjoying perpetual rest.” However, Galileo did not further define this state of “rest,” and appears to have implicitly adopted the absolutist view. In fact he was the first to use the actual term “abso- lute motion,” in his theory of the tides. R´en´e Descartes (1596–1650) also relied on the concept of absolute space (which he referred to as a “plenum”) in arriving at something similar to Newton’s eventual first law of motion. After learning of Galileo’s trial by the Inquisition, however, he put off publishing his results by more than a decade and eventually prefaced them (in the Principia Philosophiae)bya disclaimer stating that all motion was, after all, relative. He may have been the first to hold both absolutist and relational views at the same time. This inconsistency irritated Isaac Newton (Fig. 1), who complained in De Grav- itatione that if all motion was really relative as Descartes said, then “it follows that a moving body has no determinate velocity and no definite line in which it moves.” It was partly to do away with any such confusion that he expressed himself so Fig. 1 Isaac Newton (1643–1727) and his bucket experiment: the concavity of the water’s surface indicates that the water is rotating with respect to “absolute space” 28 J. Overduin categorically in the famous opening of his Principia: “Absolute, true and mathe- matical time, of itself and from its own nature, flows equably without relation to anything external . absolute space, in its own nature, without relation to anything external, remains always similar and immoveable.” He added that the existence of absolute space could be demonstrated by watching the water in a spinning bucket.