12 THE PRINCIPLE OF SUPERPOSITION §4
the conditions could be imposed by a suitable preparation of the
system, consisting perhaps in passing it through various kinds of
sorting apparatus, such as slits and polarimeters, the system being
left undisturbed after the preparation. The word state may be
used to mean either the state at one particular time (after the
preparation), or the state throughout the whole of time after the
preparation. To distinguish these two meanings, the latter win be
called a state of motion when there is liable to be ambiguity.
The general principle of superposition of quantum mechanics
applies to the states, with either of the above meanings, of any one
dynamical system. It requires us to assume that between these
states there exist peculiar relationships such that whenever the
system is definitely in one state we can consider it as being partly
in each of two or more other states. The original state must be
regarded as the result of a kind of superposition of the two or more
new states, in a way that cannot be conceived on classical ideas. Any
state may be considered as the result of a superposition of two or
more other states, and indeed in an infinite number of ways. Con-
Conversely any two or more states may be superposed to give a new
state. The procedure of expressing a state as the result of super-
superposition of a number of other states is a mathematical procedure
that is always permissible, independent of any reference to physical
conditions, like the procedure of resolving a wave into Fourier com-
components. Whether it is useful in any particular case, though, depends
on the special physical conditions of the problem under consideration.
In the two preceding sections examples were given of the super-
superposition principle applied to a system consisting of a single photon.
§ 2 dealt with states differing only with regard to the polarization and
§ 3 with states differing only with regard to the motion of the photon
as a whole.
The nature of the relationships which the superposition principle
requires to exist between the states of any system is of a kind that
cannot be explained in terms of familiar physical concepts. One
cannot in the classical sense picture a system being partly in each of
two states and see the equivalence of this to the system being com-
completely in some other state. There is an entirely new idea involved,
to which one must get accustomed and in terms of which one must
proceed to build up an exact mathematical theory, without having
any detailed classical picture.