I am a very ordinary art teacher, one who breaks into a rash at the merest
Hi Keith. A perfectly good question. The short answer is that any such assumption is, to put it mildly, controversial. There are respectable ways of thinking about quantum theory that look at it in more or less the way you suggest. Those ways, however, come at a price: they require us to assume that there are influences on the particile that propogate faster than light. They also go beyond what the theory itself has to say, and add some extra physical/interpretive machinery.
That's not a criticism of such views; it's just a remark. Quantum theory, alas, is a topic that leaves us in a peculiar lurch. As physics, it's fantastically well-confirmed and scientists and engineers make use of it in a vast number of ways that give us things like cell phones, laptop computers, MRI machines and a good deal else. But there are weird things about the math of the theory (I'll spare you any equations) that make it quite different from "classical" theories in ways that are still enormously controversial. Just to mention one important sort of issue: probability is built into quantum theory at the very foundation. But how to understand the probabilities is quite another matter. If we treat them as merely reflecting incomplete description or incomplete knowledge, we run into one set of problems; if we treat them as deeply random behavior in nature itself, we run into other problems. And on it goes.
It's hard to talk about the puzzles of quantum theory with no math at all. One book that at least makes an attempt is the latter part of Peter Kosso's Appearance and Reality. (Actually, there are some simple equations, but not the kind you need to solve. They're just abbreviations.) You might have a look there.