The Broadest Laws of Physics

Abstract

There are in the history of physics many examples of developments that initially proceeded independently of each other and yet were later found to be intimately related. It can easily be seen that this is particularly true of the mathematical formulations of various theories. Thus, the wave equation (the partial differential equation that describes the propagation of a wave), which was first developed for acoustical waves, was carried over bodily, so to speak, to describe electromagnetic waves—that is, to describe the propagation of radiation. The potential theory, which was introduced to simplify gravitational problems, was applied, without change, to electrostatics and magnetostatics. Much later, Erwin Schrödinger applied the same classical wave equation to describe the wave characteristics of the motion of the electron. Another very interesting example is the successful application of the mathematics that describes the interference and diffraction patterns of a light wave passing through a series of slits in a screen to the distribution of the diffraction pattern of an electron passing through such slits. That similar mathematical schemes can be used to describe physical phenomena that appear to be unrelated does not, in general, mean that the phenomena are just different manifestations of the same basic reality.

The most important discoveries of the laws, methods and progress of Nature have nearly always sprung from the examination of the smallest objects which she contains.

—Jean Baptiste De Lamarck