Is God a Mathematician_ - Mario Livio [103]
The fact that Einstein had turned warped four-dimensional spacetime into the cornerstone of his new theory of the cosmos meant that he badly needed a mathematical theory of such geometrical entities. In desperation, he turned to his old classmate the mathematician Marcel Grossmann (1878–1936): “I have become imbued with great respect for mathematics, the more subtle parts of which I had previously regarded as sheer luxury.” Grossmann pointed out that Riemann’s non-Euclidean geometry (described in chapter 6) was precisely the tool that Einstein needed—a geometry of curved spaces in any number of dimensions. This was an incredible demonstration of what I dubbed the “passive” effectiveness of mathematics, which Einstein was quick to acknowledge: “We may in fact regard [geometry] as the most ancient branch of physics,” he declared. “Without it I would have been unable to formulate the theory of relativity.”
General relativity has also been tested with impressive accuracy. These tests are not easy to come by, since the curvature in spacetime introduced by objects such as the Sun is measured only in parts per million. While the original tests were all associated with observations within the solar system (e.g., tiny changes to the orbit of the planet Mercury, as compared to the predictions of Newtonian gravity), more exotic tests have recently become feasible. One of the best verifications uses an astronomical object known as a double pulsar.
A pulsar is an extraordinarily compact, radio-wave-emitting star, with a mass somewhat larger than the mass of the Sun but a radius of only about six miles. The density of such a star (known as a neutron star) is so high that one cubic inch of its matter has a mass of about a billion tons. Many of these neutron stars spin very fast, while emitting radio waves from their magnetic poles. When the magnetic axis is somewhat inclined to the rotation axis (as in figure 61), the radio beam from a given pole may cross our line of sight only once every rotation, like the flash of light from a lighthouse. In this case, the radio emission will appear to be pulsed—hence the name “pulsar.” In one case, two pulsars revolve around their mutual center of gravity in a close orbit, creating a double-pulsar system.
There are two properties that make this double pulsar an excellent laboratory for testing general relativity: (1) Radio pulsars are superb clocks—their rotation rates are so stable that in fact they surpass atomic clocks in accuracy; and (2) Pulsars are so compact that their gravitational fields are very strong, producing significant relativistic effects. These features allow astronomers to measure very precisely changes in the light travel time from the pulsars to Earth caused by the orbital motion of the two pulsars in each other’s gravitational field.
Figure 61
The most recent test was the result of precision timing observations taken over a period of two and a half years on the double-pulsar system known as PSR J0737-3039A/B (the long “telephone number” reflects the coordinates of the system in the sky). The two pulsars in this system complete an orbital revolution in just two hours and twenty-seven minutes, and the system is about two thousand light-years away from Earth (a light-year is the distance light travels in one year in a vacuum; about six trillion miles). A team of astronomers led by Michael Kramer of the University of Manchester measured the relativistic corrections to the Newtonian motion. The results, published in October 2006, agreed with the values