Big Bang to Big Crunch

John Leslie

The Nature of Space and Time contains six lectures-three by Stephen Hawking, three by Roger Penrose – and a closing Hawking-Penrose debate. As Penrose indicates, it might be viewed as continuing the famous Bohr-Einstein exchange of some seventy years ago. Against the background of new cosmological theories, Hawking defends Bohr’s thesis that quantum theory has no radical incompleteness. Those who think it incomplete are wrongly treating its formulas as describing reality, rather than as predictive tools. Like Einstein, Penrose disagrees. Things then get somewhat tense. Hawking uses terms like ‘magic’ in dismissing theories which Penrose brought to the general public in The Emperor’s New Mind. Penrose throws some courteous cold water on the universe-creating mechanism made famous by Hawking’s A Brief History of Time.

The book contains a few cartoons: a full-bearded God throwing dice towards a black hole, for example. Also some jokes: miniature black holes gobbling up ‘all those odd socks’, four-dimensional slide projector screens becoming unavailable through ‘government cuts’. A three-part companion videotape can be had. Still, when the Foreword by Michael Atiyah remarks that ‘some of the presentation requires a technical understanding of the mathematics and physics’ this can seem a grave understatement. Very little of the volume will be intelligible to the ‘broader audience’ to which Atiyah commends it for its ‘argument at a higher (or deeper) level’: the philosophical level. So what might Atiyah have had in mind?

In the Sixties Hawking and Penrose joined in constructing ‘singularity theorems’. These seemed to show that everything now visible to us must have originated from a single point, or from something much like one: some ‘singularity’ where gravitationally induced curvature was indefinitely high, and at which particle histories had their first moments. Hawking’s opening lecture (Chapter I: ‘Classical Theory’) tells us that ‘this led to the abandonment of attempts to argue that there was a previous contracting phase and a nonsingular bounce into expansion. Instead, almost everyone now believes that the universe, and time itself, had a beginning at the big bang. This is a discovery far more important than a few miscellaneous unstable particles, but not one that has been so well recognised by Nobel prizes.’

The Nobel prizes may be delayed for a while because the ‘discovery’ is far from secure. For a start, some have argued that String Theory, currently popular as a Theory of Everything, would ‘smear out’ any singularity. (Hawking notes this, but has a distaste for String Theory: ‘so far, its performance has been pretty pathetic’.) Again, the Hawking-Penrose singularity theorems assumed that gravity never acted repulsively. A cosmological constant – Einstein called it his ‘greatest blunder’, yet it’s taken seriously nowadays – could change matters, however. Penrose explains in his first lecture (Chapter 2: ‘Structure of Spacetime Singularities’) that such a constant could make ‘naked singularities’ respectable, these being singularities into which material can enter from the past, then exit to the future. Moreover, a central theme of Hawking’s third lecture (Chapter 5: ‘Quantum Cosmology’) is that a ‘singular’ beginning of things could be disastrous to science. Its consequence would be that ‘the laws of physics could break down anywhere’ so that ‘predictability would disappear completely’: something of an exaggeration, one might think, yet perhaps containing enough truth to make singularity theorems unpopular with prize-givers. In any case, Hawking himself avoids a singular beginning of things when making the ‘noboundary proposal’, which Chapter 5 defends.

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