The Confrontation between General Relativity and Experiment

Abstract

The status of experimental tests of general relativity and of theoretical frameworks for analyzing them is reviewed and updated. Einstein's equivalence principle (EEP) is well supported by experiments such as the Eötvös experiment, tests of local Lorentz invariance and clock experiments. Ongoing tests of EEP and of the inverse square law are searching for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, the Nordtvedt effect in lunar motion, and frame-dragging. Gravitational wave damping has been detected in an amount that agrees with general relativity to better than half a percent using the Hulse-Taylor binary pulsar, and a growing family of other binary pulsar systems is yielding new tests, especially of strong-field effects. Current and future tests of relativity will center on strong gravity and gravitational waves.

Keywords: Gravitational radiation; Post-Newtonian limit; Tests of relativistic gravity; Theories of gravity.

Figure 1

Selected tests of the weak equivalence principle, showing bounds on η, which measures fractional difference in acceleration of different materials or bodies. The free-fall and Eöt-Wash experiments were originally performed to search for a fifth force (green region, representing many experiments). The blue band shows evolving bounds on η for gravitating bodies from lunar laser ranging (LLR).

Figure 2

Selected tests of local Lorentz invariance showing the bounds on the parameter δ, which measures the degree of violation of Lorentz invariance in electromagnetism. The Michelson-Morley, Joos, Brillet-Hall and cavity experiments test the isotropy of the round-trip speed of light. The centrifuge, two-photon absorption (TPA) and JPL experiments test the isotropy of light speed using one-way propagation. The most precise experiments test isotropy of atomic energy levels. The limits assume a speed of Earth of 370 km s⁻¹ relative to the mean rest frame of the universe.

Figure 3

Selected tests of local position invariance via gravitational redshift experiments, showing bounds on α, which measures degree of deviation of redshift from the formula Δν/ν = ΔU/c². In null redshift experiments, the bound is on the difference in α between different kinds of clocks.

Figure 4

Geometry of light deflection measurements.

Figure 5

Measurements of the coefficient (1+γ)/2 from light deflection and time delay measurements. Its GR value is unity. The arrows at the top denote anomalously large values from early eclipse expeditions. The Shapiro time-delay measurements using the Cassini spacecraft yielded an agreement with GR to 10⁻³ percent, and VLBI light deflection measurements have reached 0.01 percent. Hipparcos denotes the optical astrometry satellite, which reached 0.1 percent.

Figure 6

Constraints on masses of the pulsar and its companion from data on B1913+16, assuming GR to be valid. The width of each strip in the plane reflects observational accuracy, shown as a percentage. An inset shows the three constraints on the full mass plane; the intersection region (a) has been magnified 400 times for the full figure.

Figure 7

Plot of the cumulative shift of the periastron time from 1975–2005. The points are data, the curve is the GR prediction. The gap during the middle 1990s was caused by a closure of Arecibo for upgrading. Image reproduced with permission from [409], copyright by AAS.

Figure 8

Constraints on masses of the pulsar and its companion from data on J0737-3039A, B, assuming GR to be valid. The inset shows the intersection region magnified by a factor of 80. Image courtesy of M. Kramer.

Figure 9

Bounds on the scalar-tensor parameters α₀ and β₀ from solar-system and binary pulsar measurements. Bounds from tests of the Nordtvedt effect using lunar laser ranging and circular pulsar-white-dwarf binary systems are denoted LLR and SEP, respectively. Image reproduced with permission from [164], copyright by the authors.

Figure 10

The six polarization modes for gravitational waves permitted in any metric theory of gravity. Shown is the displacement that each mode induces on a ring of test particles. The wave propagates in the +z direction. There is no displacement out of the plane of the picture. In (a), (b), and (c), the wave propagates out of the plane; in (d), (e), and (f), the wave propagates in the plane. In GR, only (a) and (b) are present; in massless scalar-tensor gravity, (c) may also be present.