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2 Basic Issues in Gravitation TESTS OF FUNDAMENTAL PRINCIPLES The principle of equivalence led Einstein to the geometriza- tion of gravity. The principle in its weakest form states that the ratio of the inertial mass the tendency of a body to resist accelerationto the passive gravitational mass the tendency of a body to respond to a gravitational field is the same for all bodies. This is a weD-known result that is often trivialized in elementary mechanics courses. It is a profound statement when one considers that masses are not simple but composed of a host of different particles experiencing different interactions, each of which contributes to the mass. Gravity appears to be oblivious to this complexity. The ratio of the inertial to the gravitational mass is known from terrestrial experiments to be the surge for all bodies to one part in 10~. This implies that gravity does not differentiate between the strong and the electromagnetic interac- tions. Using laser ranging to the corner reflectors left on the Moon by the Apollo program, precision measurements of the motion of the Moon and Earth as they orbit the Sun have determined that the contribution to the mass of the gravitational binding energy of the Earth shares in this equivalence of the masses. The equivalence of the masses leads directly to the inability 8
9 to distinguish locally between a gravitational field and an accel- eration: the principle of equivalence. It was through the appli- cation of special relativity to the kinematics and dynamics in a rotating system that Einstein was led to curved space and the geometric description of gravitation. The way that the principle of equivalence is incorporated in the general theory of relativity goes further than merely the equivalence of inertial and gravita- tional mass. The indistinguishability of gravity and acceleration implies that all physics in a local region experiencing free fall is the same whether free fall occurs near a massive object such as a black hole or far from other matter; in other words the gravitational potential does not enter local physics in any measurable way. The theory asserts the still bolder generalization that the formulation and numerical content of the laws of physics locally in a free falling region are independent of epoch and the physical conditions in the universe. The principle of equivalence is at the foundation of gravita- tion. Violations of the principle would indicate the presence of new interactions in nature and would be evidence against the met- ric interpretation of gravity. New tests with increased accuracy are qualitatively different from prior measurements as they probe new regimes that could cause a violation of the principle. Space experiments in low g and g are expected to be able to improve the accuracy of the tests. WEAK FIELD A measure of the strength of the gravitational interaction is provided by the dunensionIess constant GM/Rc2, where G is the Newtonian gravitational constant, M the mass of the source body, R the distance to the observer, and c the velocity of light. On the surface of the Earth this quantity is 7 x 10~~°, while at the limb of the Sun it ~ 2 x 10-6. The value at the location of the pulsar in the binary pulsar system is almost the same as at the limb of the Sun. These are all weak fields. On the surface of a neutron star it is close to ~ x 10-i, and at the horizon of a black hole it nears unity. All of the detailed tests of relativistic gravitation have been carried out in fields where the constant is lem than 10-6. The tests in the solar system have established the bending of electromagnetic waves by the distortion of space due to the Sun to within an error of 1 percent of the value predicted by general
10 relativity. The retardation of electromagnetic waves by the field of the Sun has been established to 0.1 percent by ranging to Mars during the Viking program as the line of sight passed close to the Sun. These effects are first order in the field strength and when cast into the formalism of the parametric post-Newtonian (PPN) parameters show that gravity distorts space (i.e., these ejects measure the PPN parameter, 7~. The advance of the perihelion of Mercury is an effect that depends both on spatial curvature ~ and on the time part of the metric to second order in the dimensionless field quantity ,8. The perihelion advance is in agreement with general relativity to an error of 0.5 percent providing that no corrections have to be applied for a possible mass quadrupole moment of the Sun and that other of the PPN parameters can be assumed to have known values. The perihelion advances of Mars and the asteroid Icarus have also been measured and are in agreement with general relativity to an error of 20 percent. The gravitational red shift is now confirmed to 0.01 percent uncertainty in the field of the Earth using atomic clock compar- isons between a ground-based and a suborbital space platform. The measurements of the red shift can be interpreted as a test of the principle of equivalence and the hypothesis that gravitation is a metric phenomenon. The same term in the PPN expansion that provides the Newtonian limit also ~ responsible for the red shift in first order of the field strength. The binary pulsar system is an elegant system in which to test weak-field gravity. The field strengths are comparable to those at the surface of the Sun. More importantly, the period of the motion of one neutron star around the other is a mere ~ h. The periastron advance of the orbit is 4 degrees per year (Mercury's advance is 40 seconds per century), while the relativistic time delay across the orbit is measured in milliseconds rather than hundreds of mi- croseconds as in the solar system. The continuing program to monitor the binary pulsar will be enormously profitable. However, should anomalies be found, one must be sure they are not a prom erty of the timekeeping of the pulsar or an effect of the interaction of the binary system with other stellar systems or components of the interstellar medium. The binary pulsar system is not a substitute for solar system tests in which all the parameters can be directly measured. The continuation of the precision measurements of planetary ephemer-
11 ides and the opportunities provided in the space program to im- prove planetary range data through planetary orbiters and landers leave a rich legacy for experimental tests of weak-field gravity. The value of the data base improves with time because some of the effects due to relativistic corrections~uch as determinations of perihelia advances and possible variations in the gravitational constantgrow with time. In addition, many of the Newtonian corrections due to perturbations by other bodies in the solar sys- tem become more reliably estimated with sane. The technology has advanced to the point that one can con- sider carrying out direct tests in a weak field to second order in the field strength. Although it does not follow that the strong- field behavior of relativistic gravitation would be determined by establishing the second-order terms, it must be true that if vio- lations are observed the strong-field solutions would have to be modified. A measurement of the gravitational red shift near the Sun to second order would give an independent estimate of the PPN parameter A. The determination of the gravitational bend- ing of light by the Sun to the second! order would yield both new est~rnates of ,B and the second-order term in the metric responsible for spatial curvature. Both of these experiments are candidates ~ · ~ for space missions. ST1tONG FIELD A profound prediction of general relativity is that regions of spac~time exist in which the gravitational field ~ so strong that they are cut off from our direct observation and that, once entered, there is no escape from them. These regions include sufficient mass, m, in a spatial dimension, r, that GM/Rc2 approaches 1 On a surface called the horizon that separates the outside and the inside worlds. Observers viewing the formation of a horizon from the outside would see the interior vanish in a finite time (an observer at the horizon of a region containing a solar mass would see the interior vanish in about 10 ps). Once the horizon has formed, phenomena near the horizon appear frozen to a distant observer owing to the large gravitational red shift. To a local observer the horizon behaves as a one-way membrane that permits entry but no exit. Because of this property these regions have been dubbed black holes. Theoretical work during the past two decades has discovered
12 that black holes are completely cnaracterized by their mass, elec- tric charge, and angular momentum. All previous history of their constituents is lost during the formation. The black holes may change their charge and angular momentum ~ interactions with their surroundings, but the intrinsic mass of the black holes never decreases. This Is not strictly true, as discovered by Hawking, inasmuch as a black hole has a finite entropy; it will emit ther- mal radiation by quantum mechanical tunneling at the horizon. Through this process, small black holes will evaporate (and save the second law of thermodynamics). The evaporation time is pro- portional to the cube of the mass of the hole; a 10~~8 solar mass hole will evaporate in a time equal to the age of the universe. Aside from limits imposed by the lifetime due to thermal evade oration, there is no a priori reason intrinsic to gravitational theory to choose masses for black holes. One has to apply astrophysical reasoning to estimate the probability that nature will create black holes and to place limits on their masses. Black holes may have been created in the primeval universe or subsequently in the cores of galaxies by accretion. A strong possibility for creation occurs in the collapse of stars that have spent their nuclear fuel and in which the stellar cores are more massive than can be maintained against gravity by neutron degeneracy pressure. Current wisdom holds that compact objects with masses greater than a few solar masses are black holes. Black holes are the most efficient converters of rest mass to energy posited in nature. Objects falling into spinning holes could release up to 10 percent of their rest mass into the exterior world. Much of the energy would be released as gravitational radiation due both to the acceleration of the infalling object and the exci- tation of oscillations of the metric normal modes of the hole. The high conversion efficiency is the main reason why black holes are invoked as the power source for quasars and active galaxies. A technique to search for black holes is to find dynamical sys- terns in which one has to infer the existence of a dark compact object to explain the motions of surrounding bodies. Searches of this nature have been made in the optical, infrared, ends radio wavelengths using high spatial resolution coupled to spectroscopy. The Great observatories" proposed by the space program will play an important role in this search. The most promising black hole candidates have been uncovered in x-ray astronomy. The Cygnus X1 source is part of a binary system in which one component
13 is a visible star that appears to be feeding a compact object of greater than 3 solar masses. The x-ray emitter must be of small size since the source is seen to fluctuate on time scales as short as milliseconds. The Advanced X-ray Astrophysics Facility (AXAF) will uncover more such systems, and large area x-ray detectors will be useful in measuring the fast time fluctuations. One of the more dramatic prospects for gravitational wave astronomy is the detection of the metric ringing of a black hole after excitation by the infall of matter. The signatures of the signals are directly cal- culable; the oscillation periods are proportional to the mass of the hole. A l~solar-mass black hole wait produce a pulse with strong 1-kHz components and is detectable using terrestrial instruments. The search for signals from holes with mass larger than 104 so- lar masses is best carried out by space-borne gravitational wave detectors. NONSTATIC FIELDS When the sources of a gravitational field are in motion, new phenomena occur in relativistic gravitation that have no analogs in Newtonian gravity but can be thought of as having closer analogies to electromagnetism. In particular, magnetic gravitational effects and gravitational radiation are two phenomena that are amenable to measurement. The weak-field solution of the gravitational metric outside of a spinning sphere was presented by Thirring and Lense in 1918. The spinning sphere, in addition to producing spatial curvature, causes the inertial frame in its vicinity to be dragged along with the rota- tion by an amount of the order of the gravitational field strength multiplied by the rotation rate. In an analogy with electromag- netism, the spinning sphere produces an ~electric" gravitational interaction due to its mass, represented by the pure time part of the metric, which yields the ordinary Newtonian potential. It also generates a ~magnetic" gravitational interaction due to the mass currents that produce a gravitational vector potential represented by the crossed time-space terms in the metric. The gravitational magnetic terms interact with mass currents much as magnetic fields interact with ordinary currents. At the time, Thirring and L`ense looked at the possibilities of determining "magnetic" gravi- tational effects on the satellites of Jupiter, but concluded that the ejects on the orbits would be too small to measure. In the early
14 1960s, L. Schiff analyzed the motion of a gyro (a gravitational mag- netic moment) in the field of the spinning Earth and realized that the precession of the gyro could be large enough to measure. An attempt to do this is embodied in the experiment known as Gravity Probe B. which will be discussed below. The experiment wiD be a fundamental measurement of a new phenomenon in gravitation, which is expected to play an unportant role in some astrophysical problems. Present-day models of double-Iobe radio sources invoke a spinning black hole that powers the radio source and gives di- rectional stability to the plasma jets connecting the lobes. Frame dragging at the hole may be the mechanism providing the power. An interesting sidelight is Thirring's analysis of the weak- field solutions inside a spinning shell of mass in which Coriolis and centrifugal forces are generated by the spinning shell. He alluded to the possibility that Mach's principle could be directly incorporated into relativistic gravitation if one were able to solve the cosmological boundary value problem. In 191S, Einstein established that time-dependent free field solutions to the gravitational field equations should exist. These are gravitational waves traveling at the speed of light that distort space-time transverse to their propagation direction. The plane wave solutions are visualized as strains in space that contract space in one dimension and expand it in an orthogonal dimen- sion, both of which are transverse to the wave propagation. Two polarizations are possible, differing only in that their strain axes are rotated by 45 degrees. The waves carry energy away from their sources and, just as in electromagnetism, exert damping on the radiating systems. Strong evidence for gravitational radia- tion damping has now been observed in the binary neutron star system PSR 1913+16. The sources of the gravitational radiation are accelerating masses. Since there is only one sign of the mass and since the center of mass of an isolated radiating system must remain fixed, the lowest order of the radiation is derived from the time-varying quadrupole moment of the source. In a quantum mechanical description of general relativity, which is a tensor the- ory of rank 2, the field particle the gravitation will have a spin of 2. The direct detection of a gravitational wave may be accom- plished by several methods. One method is the mensuration of space between free bodies that "ride" the wave. This is done by measuring changes in the time it takes electromagnetic waves
15 to travel between a configuration of free masses. An alternative method is to measure the time-dependent distortions of extended bodies under the influence of the gravitational wave reexpressed in terms of "tidal forces." Both techniques are being actively pursued in current research and will be described more extensively later. The direct experunental confirmation of the wave solutions by laboratory experiments using a terrestrial source and receiver, in analogy to the Hertz experiment for electromagnetic waves, appears to be impossible with present technology or that of the forseeable future. As a consequence, the direct detection of grav- itational waves has become an astrophysical problem, for it is in this realm that we expect to observe phenomena in which the coherent motions of large masses at high velocity will make mea- surable gravitational wave strains at the Earth. The coupling of astrophysics to the fundamental study of the gravitational inter- action makes the search for gravitational radiation a particularly exciting field. Not only will we test gravitational theory by inves- tigating the wave solutions and gather evidence of the behavior of strong-field gravity at the sources, but we expect to gain a new view of the universe through the gravitational wave window. The space program offers a particularly important opportunity for this research, as it enables observation of gravitational radiation in the low-frequency bands, which may be inaccessible or unobservable from the ground (see Chapter 3~. COSMOLOGY In principle, the large-scale properties of the universe are described by a solution of the field equations of relativistic gravity coupled to the equation of state for matter and a set of initial conditions. At present, the grand synthesis of cosmological theory is still only a dream, but the essential ingredients are expected to involve the unification of the forces known in nature and a viable quantization of gravitation. The realization that understanding the origin and evolution of the universe will require a deeper understanding of all of physics has long been suspected, but the observational and theoretical discoveries of the past two decades have given the notion real substance. Cosmological studies have always been a singular branch of science. There is only one universe to observe, and so the standard techniques of classification and comparative studies, familiar and
16 so useful in astronomy, do not apply. We must perform our obser- vations from within; there Is no way to step outside and observe the entire system. Cosmology, in common with the rest of astron- omy, does not permit us to alter conditions in the system and then observe the effect of our tinkering, a practice that is so important in an experunental science. For ad of these reasons cosmological research is more dependent on the interaction of theoretical de- velopment with observation than most other branches of natural science. The only hard discrim~nants indicating that one is on the right track come through the consistency of one cosmological observation as related to another through a theoretical framework. The explosive origin of the universe is strongly suggested by the red shift distance relation first discovered in the 1920s. It is also consistent with the discovery of the 3K cosmic background radiation in the 1960s. Although the "big bang" mode! ~ not unique in relating the known cosmological observables, it is at present the mode! making the least ad hoc assumptions and serves as a useful and possibly correct framework to describe cosmological studies. An overview of the issues in cosmology is conveniently given by the epochs in this model. In the modern epoch the universe is endowed with stars and galaxies, the arena of astronomy. The explored part of this epoch extends back In time to when the universe was approximately half its present size and twice as hot. The evolution and geometry of the universe In this epoch are expected to be dominated by the matter density. The research associates] with this epoch is crudely characterized by cartography and by taking inventory of the mass. One aim is to relate the global geometry to the matter distribu- tion through the Einstein field equations. A longstanding hope is to measure the geometry with sufficient freedom from systematic errors such as evolutionary effects to determine whether the uni- verse is opened or closed. The observational problem is to estate fish the cosmic distance scale by coupling red shift measurements with reliable absolute sizes or luminosities of astronomical objects. Advances in detector technology and the planned large-aperture, ground-based and space-borne observatories are expected to make significant progress in this program by observing larger and fainter parts of the universe. Associated with determining the global geometry of the uni- verse is the exploration of its large-scale structure. The clustering of matter and the fixing of local velocity fields may be remnants of
17 primeval large-scale density fluctuations, if these phenomena were not extensively modified by dynamical processes occurring at later times. The converse problem of determining the mass in the mod- ern universe seems more difficult. A longstanding observation is that the luminous matter accounts for less than 10-2 of the mass required to close the universe. Dynamical methods of measuring mass indicate much larger values. The rotation curves of individ- ual galaxies imply that at least twice as much mass is invisible (dark mass). The dynamics of galactic clusters imply that 30 to 100 times the amount of luminous mass is dark. The nature of the dark matter ~ the universe is a major puzzle. Dark matter can- didates must be consistent with other cosmological observables, in particular the measurements of the 3K cosrn~c background and the measured isotopic abundances of light elements. Space-borne astronomy may provide the critical clue by opening up the entire electromagnetic spectrum. A poorly understood epoch ~ the transition from the time when the 3K background was last scattered by matter to the for- mation of the modern universe. The expectation is that during this time the first stars or galaxies were formed out of density fluc- tuations that already had to exist in earlier epochs. An observable remnant of this period could be the radiation emitted by the re- lease of energy due to nuclear burning. Although it is not expected that the 3K background is strongly perturbed by the plasma in this period, it is possible that fine-scale anisotropies are washed out by Thomson scattering, thereby invalidating conclusions now being drawn from the isotropy of the 3K background. Space-borne oh servations, especially in the infrared, may shed light on this epoch, if the emission from foreground sources is not overwheIrning. The 3K background was last scattered by matter at the time when the pruneval plasma condensed into atoms, at a tempera- ture of 104 degrees when the universe was 10-4 of its present size. Epochs prior to this are not observable directly by electromagnetic astronomies. The 3K background is therefore one of the few relics conveying information on earlier epochs of cosmic evolution. The radiation has been measured over three decades of the electromag- netic spectrum, including both the Rayleigh and the Jeans and Wien parts of a thermal source. The data, of varying quality, are represented by a single temperature to approximately 10 percent uncertainty. The precision of the measurements is not sufficient to
18 set meaningful limits on likely processes in the early universe that might not have equilibrated. Conventional wisdom holds that the spectrum laid not be easy to perturb because the heat capacity of the radiation so overwhelms that of matter in the early universe. The photon to baryon ratio is of the order of {O9. Measurements of the angular distribution of the 3K have pre- sented a challenge to cosmology. A large-scale anisotropy ~nter- preted as being due to the motion of the observer relative to the last scatterers of the radiation has been measured. The veloc- ity of our galaxy determined from this anisotropy is larger than expected. More important, it has set a benchmark for mapping velocity fields in the modern universe. No other anisotropy on angular scales extending from 90 degrees to a few minutes of arc has been measured to a level of t0-4. The most stringent upper limit is 2 x 10-5 at an angular scale close to 3 minutes. The absence of an~sotropy raises at least two questions. The first, more philosophical than the second, ~ how might the uni- verse be created so that large-scale regions (l degree or larger) that could not have been causally connected throughout the expansion would have the same temperature? An answer ~ proposed by the inflationary universe model. The second question is how did galaxies form in the short time after decoupling of the radiation from the matter? The initial expectation was that galaxy forma- tion would be the end result of the growth of adiabatic density fluctuations in the pruneva] plasma. The fluctuations would leave imprints of smalI-scale anmotropy in the 3K background at a level of 10-4 or larger. The high degree of Isotropy has led to specu- lations that the primary density fluctuations are isothermal and due to condensations of nonbaryonic unknown particles. The new particles, if long-lived, could be candidates for the invisible mass, but must be tailored to have properties that would not upset the isotopic abundances determined in the earlier epoch of primeval nucleosynthesis . The space program offers important opportunities for the oh servation of the 3K background. Measurements of the spectrum and large-scale anisotropy will be carried out by the Cosmic Back- ground Explorer (COBE) satellite. Should the results of this m~s- sion indicate that foreground emission does not compromise fur- ther observations at higher sensitivity, such observations should be considered for future missions. A new possibility for 3K oh servations is the use of space-borne millimeter dishes to measure
19 smaB-scale anisotropy. The millimeter-wave region lies at frequen- cies above the contamination by galactic synchrotron radiation and below the emission of interstellar dust but ~ perturbed by atmospheric emission in ground-based telescopes. A constraint is imposed on cosmic modem by the epoch of nucleo-synthesis. As the universe cooled, it spent a few minutes at a temperature where fusion of baryons was possible. The pri- mordial abundance ratios of the light elements was established at this time. The relative abundances are calculated by nuclear reaction theory with the cosmic temperature, the baryon density, and the expansion time as input variables. The abundances of H2, He3, He4, anil [i7 measured in the interstellar medium and in the spectra of old stars is in remarkable agreement with the cosmic model, providing that the photon to baryon ratio is not smaller than a few times 109. Of the more abundant isotopes, the primordial abundance of H2 is particularly sensitive to the mass density, decreasing with increasing mass density. On the other hand, He4 has little sensitivity. Should the measurements of primeval isotopic abundances hold as more regions of the universe are observed, it will place strong constraints on the constituents of hidden matter, indicating that no more than 10 percent of the mass in the universe is baryonic. The epoch of nucleosynthesis is the earliest from which any hard evidence of cosmic evolution is available at present. Two other relic backgrounds have been hypothesized. The first is a thermal bath of neutrinos, now near 1K, which decoupled from matter at a temperature of 10~iK when the muons annihilated. The second is a stochastic background of gravitational radiation that might have originated during the Planck epoch when the universe was opaque to gravitational radiation. The realization that the explosive universe may have experi- enced temperatures as high as 106~K (1057 eV) and mass densities as high as 1093 g/cm3 in the Planck era, when a still unformulated quantum theory of gravitation dominated the microphysics, and that the universe subsequently passed through all imagined and known domains of high-energy physics, has led to a synthesis of theoretical cosmology and quantum field theory. Several new ideas have emerged from this synthesis. One is a speculation that at suf- ficiently high energies (1024 eV) all the interactions in nature (but not gravity) have comparable strengths. It has been suggested that at these energies, through the mediation of a new boson that
20 couples the quark and lepton fields (responsible for proton decay), it ~ possible to violate baryon conservation. If this is true, it could offer an explanation for the antunatter/matter asymmetry seen in the universe and furthermore would account for the development of the baryon to photon ratio we observe, rather than Repose it as an initial condition. Another idea, which grew out of theoretical work associated with gauge fields, is that of the inflationary universe. In this mode! of the very early universe there Is no matter or radiation density at the beginning, but a large fixed energy stored in a symmetric state of the vacuum. The cosmological metric evolves exponentially, just as the de Sitter (empty) universe with a positive cosmological constant, until the vacuum has undergone a transition to a lower energy state (assumed to be zero) with broken symmetry. At this point the universe has expanded by a factor of 1028, and the latent energy of the initial vacuum state has been transformed into the matter and radiation fields that from then on determine the more conventional evolution of the universe. The inflationary universe mode! provides an explanation of the large-ecale isotropy of the 3K background by having the entire universe expand rapidly from a single causally connected region of the vacuum. Furthermore, the mode} predicts that the mass density should be exactly equal to the closure density. The coupling of field theory with cosmology is only beginning. The unification of gravitation with the other fields in nature will be a key ingredient in theories of the very early universe. It is too early to tell if the space program will play a direct role in this aspect of cosmological research. One could imagine that some compelling candidate particle that might only be detectable above the Earth's atmosphere will be proposed as a constituent of the dark matter. At present this does not seem to be the case.
