Once Before Time - Martin Bojowald [5]
Such success stories, in which an elegant mathematical description explains and predicts a multitude of phenomena, can be found throughout physics; they are indeed the landmarks of its progress. Reliving such insights is often so gratifying that scientists employ the term “beauty”—a pragmatic kind of beauty whose core, the mathematical formulation, can be seen only by the initiated, but which in its concrete successes can also be appreciated by outsiders.1
Concretely, Newton’s law of gravity describes the attractive force between two bodies caused by their masses. The force increases proportionally with the amounts of the masses: The attraction between two heavy bodies is larger than that between two light ones. It is also inversely proportional to the squared distance between the bodies; it weakens considerably when the bodies are farther apart. In addition to these proportionalities, the exact quantitative strength of the force is determined by a mathematical parameter, now called Newton’s gravitational constant. In this value one can see the unification of earthly and heavenly phenomena. The gravitational constant can be derived from the tiny attraction of two masses on Earth, as was first accomplished in Henry Cavendish’s laboratory in 1797 and ’98; using the same value to calculate the force exerted by the sun on the planets shows exactly the right nudge required to hold the planets on their observed orbits.
In contrast to its clear dependence on distance, Newton’s gravitational force is completely independent of time. Time independence sounds plausible, for a fundamental law of nature should, after all, be valid at all times in the same way. It is also consistent with the dominant understanding of space and time in Newton’s age and long thereafter, not to mention our everyday conceptions of them. Although one can easily change the positions and distances of objects in space, space itself appears unchangeable. Also, time seems to pass simply and uniformly, without being influenced by physical processes or technical instruments. Since gravity, according to Newton, acts instantaneously—independently of how far apart the masses are—the force need be formulated only for the case of two masses not at the same place, but at the same time.
Despite its plausible form and celebrated successes, Newton’s theory did have a flaw in its beauty. Like the beauty of the theory itself, this flaw, too, can be understood completely only with a sufficient amount of background knowledge. But even on the surface, it is a good example of the progress of theoretical physics. Newton himself had reportedly been uneasy about the “animalistic” tendencies of his law of gravitation: As an animal is attracted from far away by the expectation of food or companionship, a massive body appeared to move toward another one from a distance. This action at a distance, apparently without the more intuitive type of local interactions as realized for bodies pushing each other at close contact, was considered a serious conceptual weakness in spite of all concrete successes.
It is extremely difficult to correct this weak spot by constructing a theory only of local interactions that, of course, should otherwise remain compatible with the astronomical successes of Newton’s theory. To start with, one will have to consider the time dimension, too, for such a local interaction must take some time to propagate from one body to the other. As it turned out, a consistent reformulation is possible only by radically changing Newton’s—and our—intuitive conceptions of space and time. It requires much more highly sophisticated mathematical machineries and substantial efforts, but these efforts are rewarded by a theory