To the layman, the philosopher, or the classical physicist, a statement of the form "this particle doesn't have a well-defined position" (or momentum, or x-component of spin angular momentum, or whatever) sounds vague, incompetent, or (worst of all) profound. It is none of these. But its precise meaning is, I think, almost impossible to convey to anyone who has not studied quantum mechanics in some depth.
I haven't studied quantum mechanics in any depth at all. The meaning I, as a layman, derive from this statement is: in the formal QM system a particle has no property labelled "position". There is perhaps an emergent property called position, but it is not fundamental and is not always well defined, just like there are no ice-cream atoms. Is this wrong?
Another month has passed and here is a new rationality quotes thread. The usual rules are: