When a change occurs in Nature, the quantity of action necessary for that change is as small as possible.The quantity of action is the product of the mass of the bodies times their speed and the distance they travel. When a body is transported from one place to another, the action is proportional to the mass of the body, to its speed and to the distance over which it is transported.
Fermat making use of the argument that Nature could not be wasteful, and was bound for this reason to cause the rays of light to travel between two points in the shortest time possible, was able to deduce from this proposition the laws of reflexion and refraction. Though we do not now attach any weight to the premise, we accept the conclusion.
Above all, the ominous clouds of those phenomena that we are with varying success seeking to explain by means of the quantum of action, are throwing their shadows over the sphere of physical knowledge, threatening no one knows what new revolution.
When the theory of relativity supplanted classical science, it was recognised that the classical equations of mechanics were only approximate, and it became necessary to reformulate the principle of action so as to render it compatible... This work was carried out by the pure mathematicians—by Klein and Hilbert in particular. It was then found that a principle of action differing but slightly from the classical one could be obtained.