THE NEWER 'MATTER'
represented structurally by a trigonometrical Fourier series; in the new, it is represented by a two-dimensional table of values; that is, by a matrix giving the frequencies and the intensities of radiations.
An important and interesting structural issue now appears. It is that the Heisenberg theory gives a new formulation for the hamiltonian equations of motion, whereby their form is preserved, yet they are made applicable both to periodic and to non-periodic motion. It becomes possible to fuse the classical mechanics with the quantum mechanics. The distinction between 'quantised' and 'unquantised' motion loses all meaning, and a fundamental equation,
is formulated which is valid for all motion.
The Heisenberg theory is also characterized by its thoroughly behaviour-istic, actional, functional, and operational character. The number of unjustifiable assumptions is the lowest in existence and most of the identifications are eliminated. According to Heisenberg, electrons and atoms do not have the 'same' kind of 'reality' as ordinary objects of lower order abstractions. This conclusion, which underlies his whole work, is of particular importance structurally. As we know, differences in character separate different orders of abstraction and since the quantum phenomena belong to a higher order of abstraction they must differ from objects which belong to a lower order of abstraction. In this theory the feelings of 'space' and 'time' are no longer applicable to the 'inside' of the atomas might be expected.
The distinction between 'inner' and 'outer' electrons in an atom becomes meaningless, since it is impossible to recognize a particular entity among a series of similar entities. In accordance with the new 'space-time' outlook we gain a physical basis for the absolute individuality of some eventual unit.
Because of its structure, the Heisenberg theory is a very fundamental one and there is little doubt that the Heisenberg methods will be elaborated further and will be kept as a permanent checking method in physics. A theory which is thoroughly behaviouristic, with a minimum of assumptions, will probably remain both a most important instrument of research and an inspiration to physicists and mathematicians.
The Heisenberg theory, again, because of its structure and method, does not lend itself easily to visualization. This is not against the theory. The pictorial representations of lower order abstractions are not to be relied upon. Besides, visualization depends on the lower centres and therefore must be represented by a macroscopic representation of a continuous (rather than a discrete) character, such as waves , .
\i we were to try to describe the Heisenberg theory pictorially, which is obviously difficult to do, we would have to give a negative description. We should have to say that what we observe must be considered only as radiations from the location which the atom was supposed to occupy.8
There remains but to mention some more characteristics of the Heisenberg theory which seem to have very far-reaching structural and semantic bearings