Classical Tests of General Relativity

Abanonded steam engine in Uyuni train cemetery
Figure 1. An abandoned steam engine with Einstein’s field equations painted on it. Image due to Jimmy Harris.

Last Wednesday, November 25, was the 100 year anniversary of general relativity. It was the precise day that Einstein presented his field equations, shown in figure 1, to the world. In celebration of this anniversary, today I present to you some of the early triumphs of general relativity, classical predictions of the theory that have been precisely tested and where theory has exquisitely matched experiment. This is the sixth instalment of my howgrworks series. Let’s get started.

The Perihelion of Mercury

Before Einstein, we believed that the motion of planets in the solar system were governed by Kepler’s laws of planetary motion. These can be derived from Newton’s laws of motion and universal gravitation, but Kepler discovered them before Newton, through the power of careful observation.

Kepler’s laws are very good. To an extremely good approximation, they do describe the motion of a single planet orbiting the sun. They tell us that the orbit of a planet around the sun has the shape of an ellipse, like that shown in figure 2. The point where the planet is closes to the sun is called the perihelion of the planet.

an elliptic orbit
Figure 2. The orbit of a small planet around the sun, The orbit is elliptical. The orbit of Mercury, and most planets, is actually ALMOST circular. So the eccentricity of the orbit is greatly exaggerated in this image. (Credit due to Wikimedia commons contributor Brandir.)

But planets don’t actually follow perfect, closed, elliptical orbits. The ellipse slowly rotates, or precesses over the course of time, meaning that the perihelion of the planet moves over time, as shown in figure 3.

precessing Kepler orbit
Figure 3. In actuality, a planet doesn’t quite obey Kepler’s laws. The ellipse isn’t quite closed, so the perihelion of the orbit itself moves around the sun over long periods of time. (Image due to Wikimedia commons contributor WillowW.)

This precession is caused by a number of factors. The gravitational influence of other planets, for instance, contributes. Indeed, for most planets, the gravity of the rest of the solar system adequately explains the precession. But there’s one planet where this isn’t the case: Mercury. If you work out the numbers, the precession of Mercury’s orbit is too big to be explained only by the gravitational effects of the other planets.

For several decades, the perihelion of Mercury was a mystery. People hypothesized that there was a tenth planet (or dwarf planet) in the solar system closer to the sun than Mercury, called Vulcan. The planet Vulcan turns out not to exist, but its legacy lives on, as shown in figure 4.

Spock
Figure 4. Live long and prosper, Vulcan.

When Einstein developed general relativity, he knew about the mystery of the perihelion of Mercury, and he believed he had the answer. Einstein worked out some of the corrections to a Keplerian orbit due to general relativity, and found they perfectly predicted Mercury’s perihelion.

General relativity was off to a great start!

The Deflection of Light

But Einstein wasn’t content with explaining observations we’d already made. He wanted to make a prediction. Ever since Newton proposed his law of universal gravitation, people have wondered if gravity should effect the path of a beam of light. In 1784, the brilliant Henry Cavendish calculated the gravitational pull of a planet on a small particle moving at the speed of light. At the time, people didn’t know that photons are massless, but it turns out not to matter. The change in the path is independent of the mass of the particle.

General relativity also predicts that gravity should bend light, but for very different reasons. In general relativity, a massive object distorts spacetime itself, and light simply takes the straightest path. You have to work through the numbers, but if you do, you discover that this means light bends twice as much in general relativity as in  Newtonian gravity.

But how to test this prediction? Einstein proposed that we could use the sun itself. The sun should bend the path of starlight from the stars behind it. This is an example of gravitational lensing, which I’ve discussed before. Of course, usually the light from the sun masks any starlight one might wish to observe. But during a total solar eclipse, like the one shown in figure 5, the moon completely obscures the sun, and the stars should be visible.

2012 total solar eclipse
Figure 5. The 2012 total solar eclipse, viewed from Australia. (Image credit: NASA.)

After hearing Einstein’s prediction, Sir Arthur Standley Eddington lobbied strongly for an expedition to test it. Eddington saw the expedition both as an exciting scientific opportunity and as a way to heal the wounds of the first world war, which was still raging when he began lobbying for the expedition. After a long legal battle, Eddington avoided the draft and was granted a grant of 1000 pounds sterling for the expedition. As gravitational physicist Clifford Will writes in his article on the event:

The decision reeks of irony: a British government permitted a pacifist scientist to avoid wartime military duty so that he could go off and try to verify a theory produced by an enemy scientist.

But in March 1919, Eddington set sail for an island off the coast of Guinea and his collaborator, Andrew Claude de la Cherois Crommellin sailed to northern Brazil. Each expedition aimed to observe the deflection of light in 1919 total solar eclipse. This is a very difficult measurement to make and, due to inclement weather, the Crommelin team was unable  to make a definitive measurement. The Eddington team, however, was able to make a definitive measurement, one that confirmed Einstein!

Eddington’s result was widely publicized, and it sky-rocketed Einstein to fame. In 1919, as now, general relativity captured the public’s imagination. After Eddington announced his result, the Illustrated London News ran a major spread, describing the experiment, shown in figure 6.

The Illustrated London News
Figure 6. The Illustrated London News describes the Eddington expedition.

In science, it is not enough to explain observed phenomena, one must make a new, testable prediction. And Einstein’s prediction of the bending of light did just that. It was this victory that convinced the scientific community, and the world, that general relativity was right.

Gravitational Redshift

At the core of Einstein’s theory is the idea of gravitational redshift. If you take a beam of light at the surface of the earth, and somehow transport it up to the top of a tower, it will appear redder in colour than it did at the surface. This is because spacetime is stretching out as we move away from the surface and the wavelength of the light is stretching out with it. I’ve described this in great detail before.

It turns out that we can actually experimentally test this prediction! In 1959, Robert Pound and Glen Rebka used atomic nuclei in a crystal lattice to measure the wavelength of a beam of x-ray light, which they transported from the top of a tower, shown in figure 7 in a Harvard physics building to the basement, 74 feet below. This is the now famous Pound-Rebka experiment.

robert pound
Robert Pound at the top of the tower for the Pound-Rebka experiment. Image taken from Pound’s review article, Weighing Photons.

Of course, even with an extremely precise understanding of the light and the atomic transitions, this experiment would be impossible without some clever tricks. The experiment deserves an article all by itself. So for now, I will point you to this wonderful article in Physical Review. Suffice to say Pound and Rebka’s experiment confirmed Einstein’s predictions in exquisite detail.

And Many More…!

There are many more tests of general relativity, and I plan to tell you about them in another post. So Stay tuned!

Related Reading

This is the sixth part of my series on general relativity. Here are the first parts:

Further Reading

I’m far from the first person to write about this.

  • Ethan Siegel has a great article on the Perihelion of Mercury and the bending of light.
  • Brian Koberlein has an excellent article on Eddington’s measurement during the total solar eclipse.

Sources

For the brave or very interested, here peer-reviewed articles of interest. You will notice a preponderance of articles by Clifford Will. This is no accident, as he’s the world’s foremost expert on experimental tests of general relativity. (He’s also Canadian! Go Canada!)

 

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