September 4, 2010 12:21 am

The Grand Design

The Grand Design, by Stephen Hawking and Leonard Mlodinow, Bantam Press RRP£18.99, 208 pages

 

In The Grand Design, Stephen Hawking gives his perspectives on physical reality and expectations for future fundamental physics, ably assisted by the fine science writer Leonard Mlodinow. These issues are made accessible to general readers via apposite analogies. Nonetheless, I doubt that adequate understandings can arise in this way. This applies particularly to “M-theory”, a popular (but fundamentally incomplete) development of string theory, regarded by the authors as most promising for future physics, and illustrating Hawking’s strange-sounding philosophical standpoint of theory-dependent realism put forward here.

Concerning the latter, which I shall try to explain shortly, it may be illuminating to recall a dinner party in California in the early 1970s. Earlier, Stephen Hawking and I had apparently shared similar views on the nature of physical reality, but afterwards our viewpoints took very different turns. Sitting at the head of my table, seeming intent on getting a rise out of those present, Hawking made three remarkable assertions. The first, “baryon number is not conserved”, while unorthodox, did not particularly trouble me. Baryon conservation is what prevents atomic nuclei from decaying away. Hawking’s proposal entailed an unobservably slow decay rate, not disturbing to my world-view.

So he tried again with the far more radical “A pure state can evolve into a density matrix”, asserting a fundamental change in the very rules of quantum mechanics. Far from displeasing me, this was appealing, as I already had other reasons for believing quantum mechanics must someday require profound modification. I was rather glad to have Hawking’s new line of reasoning which, like baryon decay, came from his deep considerations of black holes and his revolutionary prediction that they ultimately disappear through quantum effects, after an absurdly long time. Again I nodded my acceptance and exclaimed approval.

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I fear that this was far from the reaction that Hawking wanted, so he launched into “Black holes and white holes are the same thing!” That did it, for me. A hypothetical “white hole” would be like a black hole, but with opposite temporal behaviour, so that it would disappear by expelling matter, in contrast to a black hole’s appearance through swallowing matter. Hawking’s conclusion was that these two processes must become identical when quantum modifications of space-time geometry are effected. I appreciated a relevance to minuscule holes but could not accept this at the vast scales of collapsing stars. Hawking’s resolution was to regard space-time geometry as a profoundly subjective, ie “observer-dependent”, concept, even at the level of huge black holes. My own resolution was quite different, as I believed (and still believe) that the standard rules of quantum mechanics cannot survive without some serious change, when gravitational effects become involved.

This difference in attitudes to quantum mechanics has remained central to our divergent viewpoints, where Hawking has more recently retreated from the second of his bold assertions recounted above, appearing now to believe that quantum theory must hold at all levels without change. Among Einstein’s difficulties with current quantum mechanics was its leading to subjective pictures of physical reality – as abhorrent to him as to me. The viewpoint of “theory-dependent realism” being espoused in this book appears to be a kind of half-way house, objective reality being not fully abandoned, but taking different forms depending upon the particular theoretical perspective it is viewed from, enabling the possibility of equivalence between black and white holes.

An illustrative example the authors provide involves goldfish trying to formulate a theory of the physical space outside their spherical goldfish bowl. The external room appears to them to have curved walls, despite being regarded as rectilinear by its human inhabitants. Yet the goldfish’s and human’s viewpoints are equally consistent, providing identical predictions for those physical actions accessible to both life forms at once. Neither viewpoint is more real than the other, being equivalent for making predictions.

I do not see what is new or “theory-dependent” about this perspective on reality. Einstein’s general theory of relativity already deals with such situations in a completely satisfactory way, in which different observers may choose to use different co-ordinate systems for local descriptions of the geometry of the single fixed over-reaching objective space-time. There is a degree of subtlety and sophistication in the mathematics, going significantly beyond what is present in Euclid’s ancient geometry of space. But the mathematical “space-time”, whereby the theory describes the world, has complete objectivity.

It is nevertheless true that current quantum theory presents threats to this objectivity of classical physics (including general relativity) and has not yet provided an accepted universally objective picture of reality. In my opinion, this reflects an incompleteness in current quantum theory, as was also Einstein’s view. It is likely that any “completion” of quantum theory to an objective picture of reality would require new mathematical ideas of subtlety and sophistication beyond even that of Einstein’s general-relativistic space-time, but this challenge is addressed to future theorists’ ingenuity and does not, in my view, represent any real threat to the existence of an objective universe. The same might apply to M-theory, but unlike quantum mechanics, M-theory enjoys no observational support whatever.

Roger Penrose is Emeritus Rouse Ball Professor of Mathematics at the University of Oxford

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