Some of these questions are answered by string/M-theory in its current state; some of these questions were approximately answered even by QFT tools before string theory; some of these questions remain open.

For example, the Wheeler-DeWitt equation (together with its various solutions such as the Hartle-Hawking state) mostly belongs to the third category (the things not yet established). It’s the equation HΨ=0, expressing the idea that the Hamiltonian constraint in GR actually encodes the full evolution in time, something that is possible due to the ambiguous meaning of the word “time” in diffeomorphism-symmetric theories. To solve it, one must first define his own time, by linking it to some coordinate-independent evolving quantity, and so on.

— answered Oct 25 ’11 at 6:50

— Lubos Motl

2012.07.31 Tuesday ACHK