"The Confrontation between General Relativity and Experiment"
Clifford M. Will 

1 Introduction

When general relativity was born 100 years ago, experimental confirmation was almost a side issue. Admittedly, Einstein did calculate observable effects of general relativity, such as the perihelion advance of Mercury, which he knew to be an unsolved problem, and the deflection of light, which was subsequently verified. But compared to the inner consistency and elegance of the theory, he regarded such empirical questions as almost secondary. He famously stated that if the measurements of light deflection disagreed with the theory he would “feel sorry for the dear Lord, for the theory is correct!”.

By contrast, today experimental gravitation is a major component of the field, characterized by continuing efforts to test the theory’s predictions, both in the solar system and in the astronomical world, to detect gravitational waves from astronomical sources, and to search for possible gravitational imprints of phenomena originating in the quantum, high-energy or cosmological realms.

The modern history of experimental relativity can be divided roughly into four periods: Genesis, Hibernation, a Golden Era, and the Quest for Strong Gravity. The Genesis (1887 – 1919) comprises the period of the two great experiments which were the foundation of relativistic physics – the Michelson–Morley experiment and the Eötvös experiment – and the two immediate confirmations of general relativity – the deflection of light and the perihelion advance of Mercury. Following this was a period of Hibernation (1920 – 1960) during which theoretical work temporarily outstripped technology and experimental possibilities, and, as a consequence, the field stagnated and was relegated to the backwaters of physics and astronomy.

But beginning around 1960, astronomical discoveries (quasars, pulsars, cosmic background radiation) and new experiments pushed general relativity to the forefront. Experimental gravitation experienced a Golden Era (1960 – 1980) during which a systematic, world-wide effort took place to understand the observable predictions of general relativity, to compare and contrast them with the predictions of alternative theories of gravity, and to perform new experiments to test them. New technologies – atomic clocks, radar and laser ranging, space probes, cryogenic capabilities, to mention only a few – played a central role in this golden era. The period began with an experiment to confirm the gravitational frequency shift of light (1960) and ended with the reported decrease in the orbital period of the Hulse–Taylor binary pulsar at a rate consistent with the general relativistic prediction of gravitational-wave energy loss (1979). The results all supported general relativity, and most alternative theories of gravity fell by the wayside (for a popular review, see [421]).

Since that time, the field has entered what might be termed a Quest for Strong Gravity. Much like modern art, the term “strong” means different things to different people. To one steeped in general relativity, the principal figure of merit that distinguishes strong from weak gravity is the quantity 𝜖 ∼ GM ∕Rc2, where G is the Newtonian gravitational constant, M is the characteristic mass scale of the phenomenon, R is the characteristic distance scale, and c is the speed of light. Near the event horizon of a non-rotating black hole, or for the expanding observable universe, 𝜖 ∼ 1; for neutron stars, 𝜖 ∼ 0.2. These are the regimes of strong gravity. For the solar system, − 5 𝜖 < 10; this is the regime of weak gravity.

An alternative view of “strong” gravity comes from the world of particle physics. Here the figure of merit is 3 2 −2 GM ∕R c ∼ ℓ, where the Riemann curvature of spacetime associated with the phenomenon, represented by the left-hand-side, is comparable to the inverse square of a favorite length scale ℓ. If ℓ is the Planck length, this would correspond to the regime where one expects conventional quantum gravity effects to come into play. Another possible scale for ℓ is the TeV scale associated with many models for unification of the forces, or models with extra spacetime dimensions. From this viewpoint, strong gravity is where the curvature is comparable to the inverse length squared. Weak gravity is where the curvature is much smaller than this. The universe at the Planck time is strong gravity. Just outside the event horizon of an astrophysical black hole is weak gravity.

Considerations of the possibilities for new physics from either point of view have led to a wide range of questions that will motivate new tests of general relativity as we move into its second century:

  • Are the black holes that are in evidence throughout the universe truly the black holes of general relativity?
  • Do gravitational waves propagate with the speed of light and do they contain more than the two basic polarization states of general relativity?
  • Does general relativity hold on cosmological distance scales?
  • Is Lorentz invariance strictly valid, or could it be violated at some detectable level?
  • Does the principle of equivalence break down at some level?
  • Are there testable effects arising from the quantization of gravity?

In this update of our Living Review, we will summarize the current status of experiments, and attempt to chart the future of the subject. We will not provide complete references to early work done in this field but instead will refer the reader to selected recent papers and to the appropriate review articles and monographs, specifically to Theory and Experiment in Gravitational Physics [420*], hereafter referred to as TEGP; references to TEGP will be by chapter or section, e.g., “TEGP 8.9”. Additional reviews in this subject are [40, 361, 392]. The “Resource Letter” by the author [428], contains an annotated list of 100 key references for experimental gravity.

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