Is God a Mathematician_ - Mario Livio [104]
Incidentally, both special relativity and general relativity play an important role in the Global Positioning System (GPS) that helps us find our location on the surface of the Earth and our way from place to place, whether in a car, airplane, or on foot. The GPS determines the current position of the receiver by measuring the time it takes the signal from several satellites to reach it and by triangulating on the known positions of each satellite. Special relativity predicts that the atomic clocks on board the satellites should tick more slowly (falling behind by a few millionths of a second per day) than those on the ground because of their relative motion. At the same time, general relativity predicts that the satellite clocks should tick faster (by a few tens of millionths of a second per day) than those on the ground due to the fact that high above the Earth’s surface the curvature in spacetime resulting from the Earth’s mass is smaller. Without making the necessary corrections for these two effects, errors in global positions could accumulate at a rate of more than five miles in each day.
The theory of gravity is only one of the many examples that illustrate the miraculous suitability and astonishing accuracy of the mathematical formulation of the laws of nature. In this case, as in numerous others, what we got out of the equations was much more than what was originally put in. The accuracy of both Newton’s and Einstein’s theories proved to far exceed the accuracy of the observations that the theories attempted to explain in the first place.
Perhaps the best example of the astonishing accuracy that a mathematical theory can achieve is provided by quantum electrodynamics (QED), the theory that describes all phenomena involving electrically charged particles and light. In 2006 a group of physicists at Harvard University determined the magnetic moment of the electron (which measures how strongly the electron interacts with a magnetic field) to a precision of eight parts in a trillion. This is an incredible experimental feat in its own right. But when you add to that the fact that the most recent theoretical calculations based on QED reach a similar precision and that the two results agree, the accuracy becomes almost unbelievable. When he heard about the continuing success of QED, one of QED’s originators, the physicist Freeman Dyson, reacted: “I’m amazed at how precisely Nature dances to the tune we scribbled so carelessly fifty-seven years ago, and at how the experimenters and the theorists can measure and calculate her dance to a part in a trillion.”
But accuracy is not the only claim to fame of mathematical theories—predictive power is another. Let me give just two simple examples, one from the nineteenth century and one from the twentieth century, that demonstrate this potency. The former theory predicted a new phenomenon and the latter the existence of new fundamental particles.
James Clerk Maxwell, who formulated the classical theory of electromagnetism, showed in 1864 that the theory predicted that varying electric or magnetic fields should generate propagating waves. These waves—the familiar electromagnetic waves (e.g., radio)—were first detected by the German physicist Heinrich Hertz (1857–94) in a series of experiments conducted in the late 1880s.
In the late 1960s, physicists Steven Weinberg, Sheldon Glashow, and Abdus Salam developed a theory that treats the electromagnetic force and weak nuclear force in a unified manner. This theory, now known as the electroweak theory, predicted the existence of three particles (called the W, W–, and Z bosons) that had never before been observed. The particles were unambiguously detected in 1983 in accelerator experiments (which smash one subatomic particle into another at very high energies) led by physicists Carlo Rubbia and Simon van der Meer.
The physicist Eugene Wigner, who coined the phrase “the unreasonable effectiveness of mathematics,” proposed to call all of these unexpected achievements