I’m still reading “On Space and Time” that I started reviewing last week. I just finished the chapter by Roger Penrose entitled “Causality, Quantum Theory and Cosmology.” Like Majid’s article, this one is a pleasure to read.
Penrose has always and still motivates me to learn GR much much much better. His article addresses his idea for the Big Bang and cosmology. He’s a proponent of it but is honest about its short comings. It’s called Conformal Cyclic Cosmology, or CCC for short. This is the second “Conformal – awesome theory” that I’ve come across in the past few months (the other being conformal quantum field theories). The idea seems to be to conformally map the Big Bang singularity onto a 3-surface that joins our spacetime (up until the big bang) to another 4-manifold. This can be done either as a mathematical trick for some ease in calculations, or taken seriously as Penrose suggests.
Penrose is concerned about the arrow of time and the very low entropy (and phase space volume of the universe) at the Big Bang and he’s trying to find it a way to reconcile this with the remote future. He has some unorthodox views, but again he’s honest about them, concerning information loss in black holes and quantum measurement. He suggests that information is indeed lost in a black hole and so once it’s evaporated, in the remote future, that this information is truly gone. This, as I understand, is contrary to the current view after the long standing debate between Hawking and Susskind (and others?).
This works for CCC which posits that our spacetime is sandwiched between 3-surfaces, one of them being the big bang and the other being the remote future. Won’t the future go on forever? Here’s where it gets really interesting. He suggests that eventually there’ll be no massive particles left. Once everything has been sucked into black holes and those black holes are colliding with one another and evaporating we’re left with a universe of pure electromagnetic and gravitational radiation. The representative particles do not experience time and a clock in such a future could not exist. Penrose suggests that at such a time the universe is purely conformal (all the matters is casual structure not the rate of time passage). He notes (and I want to check this eventually) that out of the metric tensors 10 components, 9 are conformal and only 1 sets the scale for the passage of time.
The remote future is then thought of as a 3-surface along with some scalar field (not sure of this part, it generates dark matter or something?) that initiates a new aeon (a new big bang). These surfaces are not identified, there’s no toroidal universe, it’s a steady progression of Bang, followed by expansion, followed by black holes and evaporation, followed by another aeon.
The link between conformal invariance and time is something I’d never considered. He notes that EM is entirely conformally invariant since photons don’t carry clocks (or at least those clocks don’t tick) which is very neat. All that EM (and gravitational radiation) cares about is causality, the light cone structure of space which is conformal. This is really neat!
Another neat bit is that he really gets his mileage out of the Weyl tensor that I have no familiarity with other than in name. It motivates me to spend some time with it and I wonder if this article and Penrose’s ideas would be a nice way to illustrate the point and utility of the Weyl tensor?
Onto Connes’ essay, his stuff is always a doozy.