By the last few decades of the nineteenth century, theoretical physics was entering a state of crisis. This crisis, which reached its culmination about the turn of the century, was due to several factors. New discoveries, some quite accidental (such as that of X-rays) made physicists aware of previously unimagined form of radiant energy.
In addition, the development of precise means of measurements allowed experimental confirmation to be sought even for extremely subtle effects, which previously would have remained in the domain of theory alone. For example, the luminiferous ether, through which light was supposed to move, was widely assumed to exist by nineteenth century physicists. Once its effects became measurable, experimentalists sought to identify them--and failed to find them, triggering a crisis resolved only with the development of Special Relativity in 1905. Apart entirely from crises brought on in one way or another by experimental findings, however, physics was by the late years of the century embroiled in a purely theoretical crisis. This crisis may be briefly characterized as the crisis of mechanics. To understand how it developed in the last years of the nineteenth century, it is necessary to look back a few decades to the second quarter of the century, when what is now called classical mechanics appeared to be both triumphant and secure.
As a theory explaining the behavior of large discrete bodies, classical mechanics had its roots in Newton's laws. By the end of the eighteenth century, application of these laws had solved all those problems of the behavior of the Solar System that were detectable with existing instruments (with one profound exception: the radiance of the Sun). By the mid-nineteenth century, with the discovery of Neptune in a position previously determined by Newtonian calculations, classical mechanics had achieved a profound predictive triumph as well.
In the eighteenth cen...