A picturesque illustration of the same dilemma is afforded if we imagine ourselves trying to see one of the electrons in an atom. For such finicking work it is no use employing ordinary light to see with; it is far too gross, its wave-length being greater than the whole atom. We must use fine-grained illumination and train our eyes to see with radiation of short wave-length—with X-rays in fact. It is well to remember that X-rays have a rather disastrous effect on atoms, so we had better use them sparingly. The least amount we can use is one quantum. Now, if we are ready, will you watch, whilst I flash one quantum of X-rays on to the atom? I may not hit the electron the first time; in that case, of course, you will not see it. Try again; this time my quantum has hit the electron. Look sharp, and notice where it is. Isn’t it there? Bother! I must have blown the electron out of the atom. This is not a casual difficulty; it is a cunningly arranged plot—a plot to prevent you from seeing something that does not exist, viz. the locality of the electron within the atom. If I use longer waves which do no harm, they will not define the electron sharply enough for you to see where it is. In shortening the wave-length, just as the light becomes fine enough its quantum becomes too rough and knocks the [Pg 225] electron out of the atom. Other examples of the reciprocal uncertainty have been given, and there seems to be no doubt that it is entirely general. The suggestion is that an association of exact position with exact momentum can never be discovered by us because there is no such thing in Nature. This is not inconceivable. Schrödinger’s model of the particle as a wave-group gives a good illustration of how it can happen. We have seen (p. 217) that as the position of a wave-group becomes more defined the energy (frequency) becomes more indeterminate, and vice versa. I think that that is the essential value of Schrödinger’s theory; it refrains from attributing to a particle a kind of determinacy which does not correspond to anything in Nature. But I would not regard the principle of indeterminacy as a result to be deduced from Schrödinger’s theory; it is the other way about. The principle of indeterminacy, like the principle of relativity, represents the abandonment of a mistaken assumption which we never had sufficient reason for making. Just as we were misled into untenable ideas of the aether through trusting to an analogy with the material ocean, so we have been misled into untenable ideas of the attributes of the microscopic elements of world-structure through trusting to analogy with gross particles.