I am reading a book called "Philosophy and Physics Meet at the Planck Scale" that lists several definitions of time that come from General Relativity: local time, proper time, Weyl time and one other that I forget. The latter two depend on the configuration of matter. I do not claim to understand what they are talking about, except that time is more complicated than simply being another coordinate. They claim that the concept of time is a fundamental difficulty in determining a combined GR and QM theory.

By the way, the fact that 6 dimensions curl up is not a fact. It cannot be derived from string theory. It's just that string theory requires 9, or mostly 10, or sometimes 11 or 12 dimensions to formulate a fermionic theory, or 26 dimensions to formulate a bosonic theory (that contains particles that are faster than light). The string theorists are just guessing that the extra dimensions curl up as our experience is only of 3 space and perhaps one time dimension. How they curl up cannot be derived from string theory, at least not in its present form.

I am not bothered by particles that travel fasterm than light. Virtual particles have this property and such accurate theories as QED are full of them. In addition, QED requires particles to travel backwards in time, at least in the Feymann formulation that summs all possible particle histories, forwards and backwards.

So since QED works without satisfying our common experience of nature- one-way time- I find the need to curl up dimensions to satisfy our common experience of nature rather suspect. It seems that a 26-d universe is just as likely curlicules and 2 way time. I am not a member of the Hawking fan club.