A few hours ago the longest total solar eclipse of the Century swept across Asia. And a few days ago Evalyn Gates provided a wonderful guest post on gravitational lensing. This seems like an opportune time to note that gravitational lensing and total solar eclipses are inextricably linked.
One of the most interesting predictions of Einstein’s new theory of relativity was that gravity would cause light to bend. Imagine you are looking at a distant source of light, for example a star, or a faraway galaxy, or a quasar at the edge of the Universe. And let’s assume that, along the line-of-sight to the distant source there’s a massive object, for example the Sun, or a black hole, or a galaxy, or a cluster of galaxies. The gravity from the massive object will “pull” on the photons as they pass, shifting their paths, and thereby affecting the image that we see in our telescopes. In the simple case of a distant point source of light (e.g., a far away star), and a compact spherically symmetric lens (e.g., a black hole), the bending angle is given by
$latex displaystyle theta=(G/c^2)4M/r$
In this equation M is the mass of the lens, r is the minimum distance between the (unperturbed) line-of-sight to the source and the lens, G is the gravitational constant, and c is the speed of light. This was a crucial prediction of Einstein’s new theory, and one way to test it was to see if the stars on the sky “jump” as the Sun (which is quite massive, and traverses the sky quite briskly) comes nearby on the sky. If you plug in the appropriate numbers above ((G/c^2)*M_sun = 1.5 km [geometric units], R_sun = 700,000 km), you find that a star should shift on the sky by 1.75 arcseconds (8.57e-6 radians) as the Sun approaches. There’s one slight snag in measuring this effect: the Sun is sort of bright. When it’s up in the sky it can be a little hard to see what the stars are doing. By the time it’s dark and you can see stars, the Sun is far away on the sky (e.g., below the horizon), and there’s no longer a measurable effect. But nature conveniently provides a very elegant solution to this problem: the total Solar eclipse. In one of the more mysterious coincidences (or is it an argument for “intelligent design”?), it turns out that the Moon and the Sun have very similar angular sizes, when seen from Earth. So every now and then the Moon crosses right in front of the Sun and blocks it out. The sky goes dark. The stars come out in the middle of the day. It even becomes possible to see stars near the very edge of the Sun. Nature conveniently provides the perfect system in which to validate the general relativity prediction of gravitational lensing.
We have a habit in science of simplifying the historical progression. Einstein’s initial 1911 prediction was off by a factor of two (giving hope to us mere mortals). Over the next few years a number of expeditions were mounted to test his prediction, but all of them failed (e.g., bad weather, World War I). This gave Einstein time to discover his error, and in 1915 he fixed his result, arriving at the equation above. The definitive (though subsequently controversial) measurement was performed by Sir Arthur Eddington in 1919. He observed the positions of stars during a total eclipse, claimed to confirm Einstein’s prediction, and vaulted Einstein to fame. In one of the best newspaper headlines ever, the New York Times
front page page 17 announced: “LIGHTS ALL ASKEW IN THE HEAVENS; Men of Science More or Less Agog Over Results of Eclipse Observations”.
We’ve come a long way. Gravitational lensing is now one of our best probes of the Universe, revealing the presence of dark matter, and maybe eventually becoming a sensitive probe of dark energy. I’m super bummed I didn’t get to see the total eclipse a few hours ago. But I have every confidence that the stars were all appropriately askew, and that people were appropriately agog.