Chapter 7: Experimental Tests of General Relativity

In the previous chapters, we have seen how Einstein's general theory of relativity radically changed our understanding of gravity, space, and time. The theory makes a number of striking predictions that deviate from Newtonian gravity, such as the bending of starlight by the Sun, the precession of Mercury's orbit, and the gravitational redshift of light. In this chapter, we will explore these predictions in detail and examine the observational evidence that has accumulated over the past century to test general relativity. We will start with the three "classical tests" that were proposed by Einstein himself, and then move on to more modern tests involving phenomena like gravitational lensing, gravitational waves, and black holes. As we will see, general relativity has passed every test with flying colors, solidifying its position as our best theory of gravity to date.

The Three Classical Tests

Shortly after Einstein published his general theory of relativity in 1915, he proposed three observational tests that could potentially confirm or refute the theory. These tests, which came to be known as the "classical tests" of general relativity, were:

1. The precession of Mercury's perihelion
2. The deflection of starlight by the Sun
3. The gravitational redshift of light

Let's examine each of these tests in turn.

The Precession of Mercury's Perihelion

The planet Mercury has a highly elliptical orbit around the Sun, with its closest approach (perihelion) precessing by a small amount each orbit. According to Newtonian gravity, this precession should be entirely accounted for by the gravitational tugs of the other planets. However, precise observations in the late 19th century revealed a small discrepancy: Mercury's perihelion was advancing by about 43 arcseconds per century more than Newton's theory predicted.

This anomaly had puzzled astronomers for decades, and some had even suggested the existence of an unseen planet ("Vulcan") near the Sun to explain it. But in 1915, Einstein showed that his general theory of relativity naturally accounted for Mercury's excess precession. According to GR, the curvature of spacetime around the Sun causes Mercury's orbit to precess by an extra 43 arcseconds per century, in perfect agreement with observations.

This was a major triumph for Einstein's theory. It explained a longstanding mystery and provided compelling evidence for the existence of spacetime curvature. Today, the precession of Mercury's perihelion is considered one of the key observational pillars of general relativity.

The Deflection of Starlight by the Sun

Another prediction of general relativity is that light should be deflected by gravitational fields. According to the theory, a ray of starlight passing near the Sun should be bent by a small angle, with the deflection being twice as large as Newtonian gravity would predict.

Einstein realized that this effect could be tested during a total solar eclipse, when stars near the Sun become visible in the darkened daytime sky. By comparing the apparent positions of stars during the eclipse to their normal positions at night, astronomers could measure the deflection and see if it matched GR's prediction.

The first attempt to measure this effect was made during the total solar eclipse of 1919, by two expeditions led by British astronomer Arthur Eddington. One team traveled to the island of Principe off the coast of Africa, while the other went to Sobral, Brazil. Despite challenges posed by weather and equipment, both teams succeeded in photographing the eclipse and measuring the positions of stars.

When the results were analyzed, they showed that starlight was indeed deflected by the Sun, with a magnitude closely matching Einstein's prediction. The news made headlines around the world and catapulted Einstein to international fame. The bending of starlight by the Sun was seen as a dramatic confirmation of general relativity and the existence of curved spacetime.

Since 1919, the light deflection test has been repeated many times with increasing precision, using radio telescopes as well as optical ones. The most accurate measurements to date, made with very-long-baseline interferometry (VLBI), have verified general relativity to within 0.02%.

The Gravitational Redshift of Light

The third classical test of general relativity involves the gravitational redshift of light. According to GR, light emitted in a gravitational field should be redshifted (i.e., its wavelength should be increased) as it climbs out of the potential well. The stronger the gravitational field, the greater the redshift.

Einstein proposed that this effect could be measured using spectral lines from the Sun. The light emitted by atoms in the Sun's atmosphere should be slightly redshifted compared to the same lines produced in a laboratory on Earth, due to the Sun's strong gravitational field.

Measuring this gravitational redshift proved to be quite challenging, due to the need for extremely precise spectroscopy and the presence of other effects that can shift spectral lines (such as the Doppler shift from the Sun's rotation). The first successful measurement was made in 1925 by Walter Adams, using a spectrograph on the 100-inch telescope at Mount Wilson Observatory. Adams found a gravitational redshift that was consistent with Einstein's prediction, although with a fairly large uncertainty.

More precise tests of the gravitational redshift have been made since then, using the Mössbauer effect and atomic clocks. In the 1960s, Robert Pound and Glen Rebka measured the redshift of gamma rays traveling up and down a 22-meter tower at Harvard University, confirming GR to within 1%. Later experiments using rocket-borne hydrogen maser clocks have verified the redshift to within a few parts in 10^5.

The gravitational redshift is not only a key test of general relativity, but also a practical concern for GPS satellites, which experience a significant redshift due to Earth's gravity. Without correcting for this effect, GPS navigation would be off by several kilometers per day.

Modern Tests of General Relativity

While the three classical tests provided the first strong evidence for general relativity, many more tests have been devised and carried out in the century since Einstein's theory was published. These modern tests probe GR in new and extreme regimes, and take advantage of advanced technologies that were undreamt of in Einstein's day.

Gravitational Lensing

One of the most striking predictions of general relativity is the phenomenon of gravitational lensing. Just as a glass lens bends light rays passing through it, a massive object (like a galaxy or galaxy cluster) can bend the path of light from a background source, acting as a "gravitational lens."

There are three main regimes of gravitational lensing:

1. Strong lensing: This occurs when the lens is massive enough and well-aligned enough to produce multiple images, arcs, or rings of the background source. The first strong lens was discovered in 1979, in the form of twin quasars that were actually two images of the same quasar, lensed by a foreground galaxy. Hundreds of strong lenses are now known, and they provide a way to map the distribution of dark matter and to test GR on kiloparsec scales.

2. Weak lensing: This is a more subtle effect that occurs when the lensing mass is not strong enough to produce multiple images, but still distorts the shapes of background galaxies. By statistically analyzing these shape distortions over large areas of the sky, astronomers can map the large-scale structure of the universe and test GR on cosmic scales. Weak lensing has become a key probe of cosmology in recent years, with major surveys like the Dark Energy Survey and the Kilo-Degree Survey providing increasingly precise measurements.

3. Microlensing: This occurs when a compact object (like a star or planet) passes in front of a background star, causing a temporary brightening of the latter due to lensing. Microlensing has been used to discover exoplanets and to probe the population of black holes and other dark objects in our galaxy. It also provides a test of GR on stellar scales.

Gravitational lensing has provided some of the most spectacular confirmations of general relativity to date. The observed number, distribution, and properties of lensed systems are in excellent agreement with GR's predictions, and have placed stringent constraints on alternative theories of gravity.

Gravitational Waves

Perhaps the most exciting development in testing general relativity in recent years has been the direct detection of gravitational waves. These are ripples in the fabric of spacetime itself, produced by accelerating masses and propagating outward at the speed of light. Einstein predicted the existence of gravitational waves in 1916, but he doubted that they would ever be detected due to their extremely small amplitude.

A century later, the Laser Interferometer Gravitational-Wave Observatory (LIGO) succeeded in measuring the minuscule spacetime distortions produced by passing gravitational waves. The first detection, made in September 2015, came from the merger of two black holes about 1.3 billion light years away. The observed waveform matched the predictions of general relativity to within a few percent, providing a stunning confirmation of the theory in the strong-field, high-velocity regime.

Since then, dozens more gravitational wave events have been detected by LIGO and its European counterpart, Virgo. These have included mergers of binary black holes, binary neutron stars, and even a possible neutron star-black hole merger. Each event provides a new test of GR under extreme conditions, and so far the theory has passed with flying colors.

Gravitational wave astronomy has opened up a whole new window on the universe, allowing us to probe regions and events that are invisible to electromagnetic radiation. It has also provided some of the most stringent tests of GR to date, confirming key predictions like the existence of black holes, the propagation of gravitational waves at the speed of light, and the "no-hair" theorem (which states that black holes are completely characterized by their mass, charge, and spin).

Observational Evidence for Black Holes

Black holes are perhaps the most extreme and enigmatic predictions of general relativity. These are regions of spacetime where the curvature becomes so strong that nothing, not even light, can escape from within the event horizon. Black holes are a direct consequence of Einstein's equations, but for many years they were considered a mathematical curiosity rather than a physical reality.

Today, however, there is overwhelming observational evidence for the existence of black holes. This evidence comes from several different lines of inquiry:

1. X-ray binaries: These are systems where a black hole or neutron star is pulling matter from a companion star. As the matter spirals in and heats up, it emits X-rays that can be detected by telescopes. The properties of these X-ray emissions, particularly the rapid variability and high energies involved, provide strong evidence for the presence of a compact object like a black hole.

2. Supermassive black holes: At the centers of most galaxies, including our own Milky Way, there are compact objects with masses millions to billions of times that of the Sun. These objects are too massive and compact to be explained by clusters of stars or other known objects, and their properties match those expected for supermassive black holes. The best evidence comes from observations of stars orbiting the Galactic Center, which have allowed astronomers to measure the mass and size of the central object with great precision.

3. Gravitational waves: As mentioned above, the gravitational wave signals detected by LIGO and Virgo match the predictions for merging black holes. The masses, spins, and other properties inferred from these signals are consistent with black holes and inconsistent with other compact objects like neutron stars.

4. Event Horizon Telescope: In 2019, the Event Horizon Telescope collaboration released the first direct image of a black hole. By linking radio telescopes around the world to form an Earth-sized virtual telescope, they were able to resolve the event horizon of the supermassive black hole at the center of the galaxy M87. The observed size and shape of the black hole shadow matched the predictions of general relativity, providing a stunning visual confirmation of the theory.

The observational evidence for black holes is now so strong that their existence is considered a near certainty. They provide some of the most extreme tests of general relativity, probing the theory in regions of strong curvature and high velocities. So far, GR has passed all of these tests, further solidifying its status as our best theory of gravity.

Conclusion

A century after its birth, general relativity remains our most accurate and well-tested theory of gravity. From the classic tests proposed by Einstein to the cutting-edge observations of gravitational waves and black holes, the theory has been subjected to increasingly precise and rigorous tests, and has emerged victorious every time.

The confirmation of general relativity is not just a triumph for the theory itself, but for the scientific method as a whole. GR made a number of bold, counterintuitive predictions that differed sharply from Newtonian gravity and common sense. Yet when these predictions were tested by carefully designed experiments and observations, they were found to be correct. This is the essence of science: making testable predictions and letting nature be the ultimate arbiter of truth.

Of course, no scientific theory is ever complete or final. There are still many open questions and unanwered issues.