Halliday & Matthiessen (2004: 450-1):
In the environment of ‘mental’ projection, the contrast between statement and question is not concerned with the speech functional orientation of giving vs demanding information but rather with the status of the validity of the information. In a statement, it is fixed with respect to the polarity and the elements of transitivity (realised by an indirect declarative clause optionally introduced by that), but in a question, it is open with respect [to] the polarity (realised by an indirect yes/no interrogative clause introduced by whether or if) or one (or more) of the elements of transitivity (realised by an indirect wh- interrogative clause introduced by who, which, when, where, etc). Consequently, mental clauses representing an ‘undecided’ state of mind are used to project indirect questions. These include clauses of wondering and doubting, finding out and checking, and contemplating, which tend to be characterised by special lexical verbs such as wonder, ascertain …