Variational Principles

Abstract

The search for the ultimate principles of the physical universe was a popular field of contemplation throughout the ages. Even up to our own time we made no great progress in the question, whether we will forever stay on the surface of things and never come to grips with the “great ocean of truth”, as Newton called it, or gradually approach something that we could consider as basic to all physical phenomena. More often than not the human mind tried to read something into the workings of nature, as if nature attempted to achieve something, as if nature were imbued with a mathematical intelligence. Although the idea is of a metaphysical character and in apparent contradiction to the causal way of thinking, yet in all periods of history the concept had its fascination. The earliest example is undoubtedly the straight line as the shortest communication between two points. But Hero of Alexandria (first century A.D.) observed already that the laws of optical reflection could be obtained from the principle that light starting at A and reaching B via the mirror at C should reach its destination in the shortest possible time. Later, when the law of optical refraction was discovered, this law was again in full harmony with the same principle, which Fermat raised to a universal principle of optics.