Another conspicuous failure of classical mechanics was with one aspect of the problem of radiation. ...Imagine a crowd of steel balls rolling about o… - James Hopwood Jeans

...a detailed mathematical discussion shows that whatever kind of wave-packet we select to represent the electron, the product of the two uncertainties of position and momentum can never be less than h, which is precisely what Heisenberg found...

Heisenberg finds that facts of observation lead uniquely and inevitably to the theoretical structure known as matrix mechanics. This shows that the total radiation in any region of empty space can change only by a single complete quantum at a time. Thus not only in the photo-electric phenomenon, but in all other transfers of energy through space, energy is always transferred by complete quanta; fractions of a quantum can never occur. This brings atomicity into our picture of radiation just as definitely as the discovery of the electron and its standard charge brought atomicity into our picture of matter and of electricity.

It would, however, be wrong to think of an electron as a bullet-like structure with tentacles sticking out from its surface. We can calculate the mass of the bullet, and also the mass of the tentacles. The two masses are found to be identical, each agreeing with the known mass of the electron. Thus we cannot take the electron to be bullet plus tentacles... The two pictures do not depict two different parts of the electron, but two different aspects of the electron. They are not additive but alternative; as one comes into play, the other must disappear.