688 X. ON THE STRUCTURE OF 'MATTER'
for instance, that our x is neither 1 nor 2 nor 4, and cannot be larger than 4, the only solution is that our * must be 3.
These conditions, which are actually found in the atomic mechanics, represent an entirely new and unexpected structural state of affairs. The whole of the older quantum mechanics can be summarized in the statement, that its peculiarity consists in the fact that structurally characteristic discrete numbers make their appearance, and that the processes 'inside the atom' are to be described by discrete numbers.
The usual classical quantum mechanics demands that * be allowed to take all possible continuous values, but that the integral values of x represent the so-called stationary states through the quantum conditions. Under such conditions the intermediate fractional values had no meanings.
It is safe to say that, when in 1900 Planck formulated his quantum theory along the structural lines sketched here, it meant a complete and revolutionary structural and semantic departure from all accepted standards in life and science, for studying this world.
Planck has shown that it is impossible to explain the spectral distribution of the energy radiated by a black body under the older assumptions that energy can be divided indefinitely into smaller and smaller parts, but that it may be explained on the structural assumption that the energy exists in quanta of finite size hv, where v is the frequency of the radiation and A is a constant
These observations lead to the revolutionary structural conclusion that the emission of radiation occurs discontinuously, and so the characteristic discrete numbers make their appearance.
It seems natural that because of this peculiar appearance of whole numbers, periodic processes such as rotations or oscillations should be closely related structurally with the quantum theory. As a matter of fact the most important structural and semantic reconciliation of continuous differential equations of the older mechanics with the appearance of discontinuous whole numbers has been solved by the newer quantum mechanics on this basis as explained in the following chapter.
The kinetic theory of heat and the atomistic theory of electricity have shown an enormous productivity. It is quite natural that these theories (verbal structures) should be highly workable, considering the structure of our nervous systems, as explained in the foregoing chapters. It was this principle of individualization which helped so greatly. The quantum theory is a structural attempt to extend this method of individualization, or the atomistic principle, to processes themselves.
As in the older days we introduced units or elementary quanta of mass, and later, an elementary quantum of electric charge, so in our newer knowledge we have need for an elementary quantum of action. Action is defined as energy multiplied by 'time', or
Naturally such a product as energy multiplied by 'time' must play an extremely important structural and semantic role in this world of space-time,