Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature

by Steven Weinberg

To understand this, you must look more closely at both Newton’s and Einstein’s theories. Newtonian physics did explain virtually all the observed motions of the solar system, but at the cost of introducing a set of somewhat arbitrary assumptions. For example, consider the law that says that the gravitational force produced by any body decreases like the inverse square of the distance from the body. In Newton’s theory there is nothing about an inverse-square law that is particularly compelling. Newton developed the idea of an inverse-square law in order to explain known facts about the solar system, like Kepler’s relation between the size of planetary orbits and the time it takes planets to go around the sun. Apart from these observational facts, in Newton’s theory one could have replaced the inverse-square law with an inverse-cube law or an inverse 2.01-power law without the slightest change in the conceptual framework of the theory. It would be changing a minor detail in the theory. Einstein’s theory was far less arbitrary, far more rigid. For slowly moving bodies in weak gravitational fields, for which one can legitimately speak of an ordinary gravitational force, general relativity requires that the force must fall off according to an inverse-square law. It is not possible in general relativity to adjust the theory to get anything but an inverse-square law without doing violence to the underlying assumptions of the theory.