Before entering on a further discussion of this fact and of the difficulty to which it leads in the electrodynamical theory of heat radiation, it may be pointed out that exactly the same case and the same difficulty are met with in the mechanical theory of heat, especially in the kinetic theory of gases. For when, for example, in the case of a gas flowing out of an opening at the time
, the velocity, the density, and the temperature are given at every point, and the boundary conditions are completely known, we should expect, according to all experience, that these data would suffice for a unique determination of the way in which the process takes place in time.
This, however, from a purely mechanical point of view is not the case at all; for the positions and velocities of all the separate molecules are not at all given by the visible velocity, density, and temperature of the gas, and they would have to be known exactly, if the way in which the process takes place in time had to be completely calculated from the equations of motion.
In fact, it is easy to show that, with given initial values of the visible velocity, density, and temperature, an infinite number of entirely different processes is mechanically possible, some of which are in direct contradiction to the principles of thermodynamics, especially the second principle.