Introduction

I have been asked to debate Alan Guth on the question ‘Did time begin?’. We have both chosen to do so within the context of inflation, a theory of the very early universe, developed by Alan and others in the 1980’s.Inflation is the best theory we currently have of the origin of the cosmic expansion, of the apparent flatness of the Universe and of the primordial density inhomogeneities which gave rise to galaxies, stars and planets. So it must be taken seriously. It is also a good theoretical ‘playground’ in which to attempt to discuss even deeper questions such as the beginning of time. But we should make clear at the start that inflation is still a ‘scenario’, and isn’t yet on the same footing as those parts of theoretical physics we now accept as ‘proven’: electrodynamics, quantum mechanics or general relativity. For one thing, inflation lacks a final theoretical formulation. There are many different models and no clear criterion to choose between them. And the observational tests, whilst rapidly improving, are still rather limited.

Alan changed the title of his talk from Eternal Inflation to semi-Eternal Inflation in the run-up to this meeting. He concedes that inflation could probably not be infinite in the negative as well as positive time directions: it had to begin at some time. That means he has already conceded the debate: so I should begin by claiming victory!

But it would be a hollow victory if his main claim were true. For what he is saying is that inflation, once begun, is eternal to the future.And second, he is implicitly arguing that we are most likely to exist at an epoch infinitely far to the future of the beginning of inflation. Since the universe by now may be infinitely large, the information regarding the beginning would be infinitely dispersed, and any theory of the beginning would be untestable in any conceivable, even ‘Gedanken’, experiment. This is a convenient argument for inflationary theorists such as Alan, who would like inflation to be a complete theory which does not rest on a more fundamental theory of what came before inflation. But the argument has always seemed deeply unsatisfactory to me in the sense that whilst admitting a theory of initial conditions is needed, one is denying that it would have any consequences. In fact, I think the argument is wrong and I shall endeavour to explain why.

Before doing so, it would be appropriate to explain to the audience that both Alan and I both regard these questions as ones which we hope to settle in the manner traditional in theoretical physics - namely by careful definitions, by mathematically precise formulations and calculations, by demonstrating that counter-arguments are nonsensical or violate some physical principle established through other means. There are of course philosophical assumptions underlying this type of work, which may be regarded as simplistic or reductionist by outsiders, but they are to a very large extent shared by practitioners. We have no profound objections to trying to construct a mathematical theory of how time and the Universe began, and believe the litmus tests should be mathematical consistency, and observational realism. These are extremely powerful criteria, so powerful that none of our current theories fully satisfy them.

Contributed by: Dr. Neil Turok