The Hartle-Hawking model fails to give us any reason to believe that the universe did not have a beginning; furthermore“… the use of imaginary quantities for time is an inherent feature of all quantum gravity models. This precludes their being construed realistically as accounts of the origin of the space-time universe in a timelessly existing four-space” (Copan and Craig, 2004, p.237)
It is not at all clear that the Hartle-Hawking model gives a intelligible physical description of the early universe. The difficulty lies in giving the concept of ‘imaginary time’ a realistic interpretation. Copan and Craig ask “[w]hat would it mean to speak of a lapse of an imaginary second or of a physical object’s enduring through two imaginary minutes?” (2004, p.236). And Hawking himself states:
Imaginary numbers can be thought of as a new kind of number at right angles to ordinary real numbers. Because they are a mathematical construct, they don’t need a physical realisation; one can’t have an imaginary number of oranges or an imaginary credit card bill. One might think this means that imaginary numbers are just a mathematical game having nothing to do with the real world (Hawking, 2001, p.59).
Furthermore, imaginary time obscures the difference between past, present and future. Time is metaphysically distinct from space: we should be able to order its moments into “earlier than” and “later than” relations. However, Holder (2004, p.60) and Copan and Craig (2004, p.236) note that these problems can be avoided if we do not interpret the Hartle-Hawking model realistically.