Finally, we must comment on the general tactics of the quantum situation. It would seem that there have already been a sufficient number of unsuccessful attempts to formulate quantum behavior in terms of ordinary mechanics to justify the expectation that ultimately something quite different must evolve. The difficulties of an unmodified carrying over of ordinary mechanical notions to quantum phenomena may be illustrated by a simple example. Consider a particle of mass _m_ rotating in a frictionless circular track of radius _r_. Then according to quantum conditions it can move stably on this track only with certain definite velocities, such that ∫ pdq = mv 2πr = nh. Suppose now the particle rotating with one of the allowed velocities, and a tangential force applied. If the usual mechanical notions of force are still valid, the particle must respond by moving in its track with continually increasing velocity. After the velocity has been increased by a small amount, we remove the force. The motion is now no longer one of the allowed ones, and the particle must in some way change its velocity; it must either slow down or speed up. In the first case it must either radiate energy, which a system of the simple mechanical properties we have supposed is not capable of doing, or else the law of conservation of energy fails, and also Newton's first law of motion during the process of acquiring the steady condition. If, on the other hand, the particle speeds up, it must increase its energy from nowhere, and again ordinary mechanics does not apply. It seems then a mistake to attempt to formulate the quantum conditions in terms of the notions of ordinary mechanics (momentum, and position coördinates in either the ordinary or the generalized Lagrangean sense). It would seem, on the other hand, plausible to expect that mechanics is not a fundamental thing, but is in some way an effect produced by the aggregate action of a great many elementary quantum processes. Amplitude of radiational vibration, for example, may be such a statistical aspect of a great many processes, in some such way as on the ordinary level of experience temperature is a statistical aspect of the average kinetic energy of the atoms. One possibility of this kind has already been more explicitly indicated; in the elementary process of emission of radiation, frequency and energy are not two independently assignable variables, but are connected [E = hν]. That is, on the quantum level radiation has only a single property, which is properly neither energy or frequency. [We are now neglecting the polarization aspect of radiation.] On a higher level, that of ordinary radiation, the single elementary property has expanded itself into two (energy and frequency) through the additional variable of the number of elementary quantum processes in the complex radiation.