The primary solecism of quantum theory

Last night, the BBC's popular science series, Horizon, once again featured the popular comedian Alan Davies, in a programme entitled How long is a piece of string? Like virtually every other popular science book or programme, it is also reiterated the following interpretation of quantum theory:

A particle can be in two different places, A & B, at the same time.

This is a claim repeated not just by many science journalists and popularisers, but also by many working physicists, yet it is completely wrong. Instead, the weirdness of quantum theory arises from the fact that either-or statements of the following form,

Either particle x is at position A or particle x is at position B,

can be true, even though quantum theory doesn't represent either of the constituent disjuncts to be true:

Particle x is at position A.

Particle x is at position B.

Thus, a disjunction can be true in quantum theory without either of the disjuncts being true. In technical terms, the logic of quantum theory is said to be non-distributive. This is the problem which any successful interpretation of quantum theory must deal with, and, in particular, this is why one of the possible approaches is the so-called hidden variables interpretation, which claims that quantum theory provides an incomplete specification of the actual state of a physical system.

For an excellent summary of the issues involved, one could do worse than this excellent review from Oxford philosopher of physics, David Wallace: The quantum measurement problem: state of play.

Paradoxes, however, are good press, and physicists are trying to sell their products to an increasingly ill-educated public, so don't expect the solecisms to abate.