Continuing his series of posts on space and time, Shahn Majid examines some of coauthor Roger Penrose’s revolutionary ideas.

Could we, today, see remnants of a previous universe?

Past lives and life after death are paltry matters compared to Roger Penrose’s latest ideas about the origin and fate of the Universe itself. In his chapter of the multi-authored volume On Space and Time, Penrose argues that certain types of information could be carried over from a previous Universe through the ‘big bang’ into the present Universe, and likewise information could proceed to the infinite cold dark future of our Universe to be carried over into the next.

This is bold stuff and in this week’s post I’d like to give some idea of what is involved. Roger would be able to do it far better himself of course.

The first ingredient is one that many popular science readers will be familiar with — the idea of time dilation. You may know that if you travel in a train at high velocity then you actually experience time more slowly relative to a person on the ground. This is not too noticeable on the Eurostar train, as you have to be close to the speed of light for the effect to be significant (I make it about 0.2 nanoseconds less time experienced on the trip London to Paris).

But, as Penrose observes, for a photon of light itself, time is so stretched that it experiences no time at all! So it is that a photon could traverse the 10 billion year history of the Universe and quite easily carry information to its infinite future and, according to Penrose, beyond it.

Next, many readers will also know that these days gravity is expressed as the curvature of spacetime. The usual way to visualise this is to think of an ant moving about on a two-dimensional surface, which could be bent this way or that. Some of what you see is an artefact of the visualisation but some of it is intrinsic to the surface and determines such things as the shortest path between two points and the length of that path. It’s an analogy for our 4-dimensional spacetime where we don’t have the luxury of being able to `step outside it’ as we do when we look down on the ant.

Now, suppose spacetime were to be stretched or distorted in such a way that relative angles and shapes were preserved, even if distances were not. The thing that Penrose observes is that light and other massless particles are necessarily insensitive to such ‘conformal rescalings’. If the world was only made up of such things, there would be no way to detect such a rescaling!

So what?

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