From the diagrams in the Penrose paper, he seems to be saying that time and the spacial dimensions existed before the "Big Bang"(always existed). That'll cause some to cough and wheeze.
His theory also states "... all particles will lose their mass towards the end of the universe". Wonder if he means that all particles will become photons whizzing around at the speed of light?
It would seem so. I recently read that photons cannot decay; in relativity theory their clocks are stopped from the point of view of every frame of reference.