Arrow-minded views

The Nature of Space and Time
March 15, 1996

Time is of the essence. This slogan is common to estate agents and to quantum gravity theorists. After reading The Nature of Space and Time by renowned general relativists Stephen Hawking and Roger Penrose, I am inclined to adopt the former perspective. At least in this case, one is, literally, on solid ground and is psychologically well equipped to cope with the direction of time. Compare this with Hawking's advocacy of imaginary time as a panacea for everything we fail to comprehend about the origins of space and time. I expect that only a mere handful of the ten million odd readers of A Brief History of Time could cope with imaginary time.

A debate between Hawking and Penrose on such issues raises the reader's expectations of a lively interaction, and this is fully borne out in the transcribed discussion. The level of the lectures, however, leaves much to be desired. An imaginary real estate agent, with an advanced degree in quantum gravity, would plough through this slender book with ease. Most others, however, will be frustrated by the technicalities that are presented with little or no explanation.

Hawking's effervescent sense of humour frequently enlivens the text. Cats feature significantly. Is the quantised cat dead or alive, or possibly in some indeterminate state that only exists when observed? I sympathise with the alleged reaction of Herman Goering (or was it Goebbels?) whenever he was confronted with the paradox of Schrodinger's cat (or was it culture: Hawking takes liberties with the historical record, but perhaps he was joking?): he was irresistibly tempted to reach for his gun. Whether he would aim the gun at the cat or the authors we can only imagine.

No doubt most readers would develop a similar reaction when confronted with imaginary time. Any self-respecting quantum gravity theorist is as comfortable with imaginary time as with its real world conjugate. Imaginary time is a mathematical device for euclideanising in four dimensions the space and time that we arbitrarily separate into time and three space dimensions that are nearly euclidean, a procedure that conceptually is fine for the fourth dimension as long as we are not too concerned with its direction. In a four-dimensional universe, there would seem to be no distinction between time running forwards or backwards. Yet common sense tells us that time has an arrow. This is where either physics (Hawking) or metaphysics in the guise of initial conditions (Penrose) enters, enshrined in the second law of thermodynamics. Disorder increases, and chaos reigns, on a sufficiently long time-scale. We age, and the cosmos approaches its heat death. The information content of the universe decreases, just as our memories ultimately fail, or our computers eventually run amok as programs become more and more complex.

Black holes seemingly violate the second law of thermodynamics. As black holes absorb thermal radiation, the chaotic component of the universe decreases. Hawking solved this dilemma when he showed that black holes are not forever: they radiate, and the smallest holes evaporate. Complex stuff enters and only thermal radiation emerges: information decreases, and the second law survives. Black hole evaporation is a quantum phenomenon. If the universe began as a motley collection of black holes and their counterparts, white holes in the era of quantum gravity, the outcome is wholly unpredictable.

A naturally corollary is that at the beginning of time, the universe contained an amalgam of black holes. There is energy enough to make vast quantities of black holes; indeed black holes may be the dominant form of matter. It is tempting and even logical, to regard the quantum beginning as a chaotic foam of evaporating and forming black holes. Information comes and goes: there is a precarious balance.

Yet time implies an arrow: there must be a net flow of information. To comprehend time, we need more than the second law, we need the universe. To understand its present state, we must understand how the universe began. There are an infinity of possible beginnings, and an infinite of outcomes. Yet our universe is rather special. There are galaxies, and stars, and life around at least one star.

When the Big Bang occurred, the universe was so dense and hot that quantum gravity supplanted Einstein's gravity and Bohr's quantum. Sadly, we lack a theory of quantum gravity, although to hear Hawking and Penrose one might be deceived. How then did the cosmos avoid this dilemma? Hawking and Penrose provide distinct alternatives for the initial state. We have two hypotheses for the universe at an age of 10-43 second.

Penrose builds in predictability. He argues that the arrow of time is established by having a universe initially free of white holes. A white hole is the time reverse of a black hole, and is fatal to the second law of thermodynamics. Information is generated, and anything may emerge. Penrose appeals to higher powers or possibly yet undiscovered theories to establish the initial lack of white holes. Black holes swallow information, and the arrow of time is established. Hawking, on the other hand, mixes quantum black and white holes indiscriminately. There is no net gain or loss of information. All is symmetric. What then established the arrow of time?

Here is where Hawking plays his trump card. He states by fiat that the space-time of the universe began as a random fluctuation that was constrained to be in a space that was compact but unbounded, as is the surface of the sphere. The compactness ensures predictability, and the no-boundary condition is claimed to predict the spontaneous creation of an exponentially expanding universe. From infinitesimally small beginnings, our present universe emerged. Its vastness and its near, but not complete smoothness, are naturally explained, or as Hawking would have it, predicted. Prediction is actually an overstatement: the occurrence of inflation is the key to understanding the universe around us, and one does not need the no-boundary condition to set the stage for inflation. Inflation may have happened anywhere, and must have happened somewhere via a chance quantum fluctuation. Nevertheless, we are left with the persuasive argument for compactness to allow predictability, and thereby ensure the forward flow of time.

If Hawking is correct, the arrow of time requires the universe to be closed, destined to terminate in a fiery big crunch. If Penrose's view prevails, the arrow of time is determined by the inexorable expansion of the universe, and the accompanying growth of irregularity and chaos: the universe expands forever into a bleak and desolate heat death. These are glorious predictions, and it is by no means beyond hope that astronomers will learn the answer within the next decade.

Joseph Silk is professor of astronomy and physics, University of California, Berkeley.

The Nature of Space and Time

Author - Stephen Hawking and Roger Penrose
ISBN - 0 691 03791 4
Publisher - Princeton University Press
Price - £16.95
Pages - 141

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