Reviewed by Ian Lipke
When Roger Penrose set out to write this remarkable tome he confessed that most of his comments would be of a general nature and relatively insensitive to issues of great technicality. His argument was that if only insiders are considered competent to make critical comments about the subject then the criticisms are likely to be limited to technical issues and some of the broader aspects of criticism significantly neglected. However, he warned that he was taking no prisoners. Yet to make significant improvement upon what has been achieved up until now, any new theory must be based on some clear mathematical scheme i.e. it ought to make mathematical sense i.e. it ought to be mathematically consistent.
Penrose further defines his boundaries by arguing that many physical theories are not physically self-consistent. Physicists tend not to be overly worried by detailed matters of mathematical or ontological inconsistency if the theory, when applied with appropriate judgment and careful calculation, continues to provide answers that are in excellent agreement with the results of observation through delicate and precise measurement.
The situation with string theory is different. There appear to be no results that provide it with experimental support. It has been argued that string theory is largely a quantum gravity theory, fundamentally concerned with the Planck scale of very tiny distances (10 to the minus sixteen) and hence with energies some 10 to the sixteen times larger, than those that are accessible to current experimentation. While modern string theories attempt to apply the principles of quantum mechanics to gravitational phenomena, Penrose warns that the importance of aesthetic judgment should not be overlooked. (e.g. Paul Dirac 1963 was very explicit about this in his discovery of the equation for the electron and again in his predictions of anti-particles).
But elements of fashion can often assume unreasonable proportions when it comes to aesthetic judgments. Any theoretical scheme which departs too radically from the general consensus, which is out of step with current research, may find itself starved of funds and support.
Some fashionable physics of the past have been the ancient Greek idea of Platonic solids, the Ptolemaic model of planetary motion, and, among others, the phlogiston theory of combustion. Current theories that are fashionable and, to a certain degree accepted by the author, are quantum field theory and string theory, the former described remarkably clearly. However it is the latter that leads Penrose into very difficult terrain for the non-specialist but intelligent reader. The discussion on multidimensionality is more than interesting, it is fascinating. Although the mathematics gets pretty ‘hairy’ to use a non-expert’s judgment, the direction of the argument is clear providing the reader does not let the difficulty of the mathematical constructs throw him off his stride. Although Penrose gets carried away with the science – and what a scientist this man is – he does tie his abstract discussion into his thesis “fashion in the new physics”.
As reviewer I find myself at odds with myself as student. Penrose has a great deal more to say and I want to remain with him, but my review must look at the other two strands that make up this amazing book. I’ll leave this section with Penrose taking aim at string theorists who follow the following line: “String theory is so obviously finite that if anyone were to present a mathematical proof of this, then I wouldn’t be interested in reading it” (attributed to Nobel laureate David Gross). According to the data presented on page 85, string theory remains a very popular approach to quantum gravity research. This is gratifying enough to a string theorist of many years standing, and it was humbling to read Penrose’s admission that the popularity of string theory research has resulted in its gaining a stranglehold on theoretical research in many universities in the USA.
I have said that Penrose presents lucid arguments accompanied by some difficult, but comprehensible, mathematics. All that is required, I indicated, was stamina. I have to confess myself beaten by the argument on pages 110 and 111. This is rugged terrain and I draw attention to it but make no attempt to comment further. It is a weak spot in the book from the point of view of the non-specialist reader.
The dictionary might define faith as belief founded on authority. Our cultures condition us to accept the beliefs of authorities without question, but science expects that our beliefs should be tested against the realities of the world. For this to happen, we call on reason, judgment, objectivity, and common sense. All this is fine until we come to the quantum superposition principle that shows a particle can exist in two positions at the same time. There are so many instances of quantum theory at work (many listed on page 123) that we must accept that “it provides a compelling description of physical reality that goes greatly beyond the classical pictures that had been held to so firmly” (23). There is no puzzle in the fact that a profound faith has arisen among physicists that all the phenomena of nature must adhere to quantum mechanics theory. Of course Penrose then raises the spectre of a profound limit to our quantum faith (126). His evidence is detailed and supported by a drawing of The Little Mermaid representing the magic and mystery of quantum mechanics on page 139.
Penrose is making the point in this detailed dissertation that scientists have a faith in the principle that physics as a whole must be a unity, that individual issues may appear to operate outside that unity but may equally contribute importantly to the consistency of the picture as a whole. He acknowledges that quantum field theory has its difficulties with divergences (from which sprang early string theory formulations) and puts forward the view that there is “a clear need to break free of that frequently expressed total faith in the dogma of the standard quantum formalism” (145).
A mass of closely argued statements that cover a vast number of topics and include enough mathematics to keep the specialist happy follows and leads us to page 216 and the introduction of the fantasy section of this book.
The previous sections have shown fantastic behaviour at the sub-atomic level. A single material object can occupy several locations at the same time and can behave as a wave or a particle, its behaviour governed by mysterious numbers involving the ‘imaginary’ square root of -1. At the other end of the scale space-time distortional effects at their most extreme can lead to massive black holes, some so massive that they can swallow entire solar systems. At an even greater scale are the vast regions of invisible matter referred to as ‘dark matter’ or ‘dark energy’ that determine the overall structure of the known universe. Again, current cosmological evidence is driving us to the belief in the ‘Big Bang” theory. “There is much observational evidence to support the actuality of an incredibly dense and violently expanding very early stage of our universe, encompassing not merely the known universe’s total material content, but also the entire space-time within which all physical substance now plays out its existence, and which appears to extend indefinitely in all directions” (217). In subsequent pages Penrose raises the question why our Sun is where it is. It is a hot spot in an otherwise dark sky. This leads to an explanation of a process of gravitational clumping from an initially uniform distribution of gas and dark matter.
Perhaps the most fantastic finding of all relates to the likelihood of intelligent life, including human life, in the known universe. “Intelligent life on our own earth needs only a very tiny proportion of this volume of gravitational low-entropy…we see no limit to the broad similarity of the distant universe with the kind of conditions that we are familiar with in our local universe region, and this appears to hold true no matter how far out we look” (313). The writer continues to amaze with his discussion of such ideas as parallel universes and bubble-universe inflation and even more fantastic ways of describing and explaining the cosmos. Can there be anything more fantasy-like than that?
Well, yes there can. Part 4: A New Physics for the Universe introduces twistor theory (an alternative to strings) that introduces us to gluons, and what has become known as the googly problem with its seemingly insurmountable mathematics issues. There is much more.
This learned, extremely authoritative publication contributes an enormous amount to scientific understanding in the community. It is of inestimable worth.
By Roger Penrose
Princeton University Press