To begin, I will try to show that the appearance of paradox cannot be dismissed as an artefact of quantum theory, nor as merely a matter of indeterminism. Before we look at quantum theory, I shall describe such strange phenomena, and show that they cannot possibly be fitted into traditional ('causal') models. 1 I shall also discuss the extent to which actual experiments indicate or establish that such phenomena indeed exist. The two philosophically significant points are (a) that the world can harbour such phenomena; and (b) that, if it does, then physical theory must provide us with models which are not deterministic, or 'causal' in a certain wider sense, and which also cannot be embedded in ones that are. In that case, in other words, the phenomena themselves demand the main peculiarities of the new theory.
Radioactive decay and the photoelectric effect were studied and recognized at the beginning of our century. The models proposed were ones in which matter is particulate and energy transmitted only in quanta. Let us begin by looking at the threat immediately posed by them for determinism. How conservative could a theory remain, while confronting that threat?
The most familiar law of radioactive decay is just this: the half-life of radium is 1600 years. 2 Roughly: a sample of radium, left alone for 1600 years, will have partially decayed into radon, with exactly half the amount of radium remaining. Now you can see at once that this so-called law must, strictly speaking, be false. For what if the sample consists of an odd number of radium atoms?