(Copyright © 2013 Piero Scaruffi | Legal restrictions )
This 1100-pages tome is a rather technical introduction (yes, only an introduction)
to the state of the art in physics. Penrose methodically introduces the concepts
that lie at the foundation of modern science, and, while trying to be as
understandable as possible, he can't help getting into a lot of technical
details. So if you want a book of popular science, this is not. But this should
be indispensable reading for everybody. You can't talk about anything unless
you master the ideas of Quantum and Relativity theories.
Penrose being a superb mathematician besides being a theoretical physicist,
the approach is rigorous but also demanding, demanding but also rigorous.
In fact, he makes a point of first introducing the mathematical concepts and
then showing how they are used to study reality. As our picture of the world
got more and more unusual, so did the math needed to describe it.
The book therefore begins with an explanation of imaginary numbers and
non-Euclidean geometries, of calculus (derivative and integration, and the
magical property that rate of change turns out to be the inverse
of areas of surfaces), of logic (Goedel, Turing and so on)
and for several of these Penrose has a unique interpretation.
For example, Goedel's theorem is widely assumed to express a limit to
human knowledge; whereas Penrose views it as a sort of gateway to a higher
Then Penrose begins to explain how physics got where it got: Lagrangian and Hamiltonian formalisms (and therefore configuration and phase spaces), quantum wavefunction, warped spacetime, etc. What Penrose emphasizes is the beauty of the math that describes these theories, and slowly he hints at one of the key points: scientists are often driven not by the search for truth but by the search for elegance, which in most cases means "some form of symmetry".
As the book progresses towards contemporary physics, Penrose also takes the reader behind the scenes to show the weaknesses of modern science. For example, Quantum Field Theory is de facto mathematically inconsistent and scientists: it creates infinities that would not be useful for any practical purpose. Then scientists need to use various tricks to remove those infinities ("renormalizations"). Ditto for cosmology: the inflationary model of the universe (the "big bang" model) has been tweaked to look "good" but in arbitrary manners. Penrose especially takes issues with physicists who are trying to unify Quantum and Relativity theories using the former as the starting point and bending the latter to fit in. Gravity behaves in a manner that is fundamentally different from the behavior of the other fields. Penrose feels that Relativity is actually more likely to be a complete theory and it is the former that needs to adapt. He repeatedly argues that a time-asymmetrical theory might be necessary here. After all, there is a fundamental asymmetry in the "collapse" of the wavefunction: there are many possibilities before one observes the system but the observation causes the system to pick only one (to "collapse") and you can't go back to the state of many possibilities. Last but not least, Penrose wants to remove the whole notion of the random collapse. His "objective state reduction" doesn't require an observer: wavefunctions collapse into a state that is not random thanks to properties of spacetime (i.e., something related to gravitation), properties that are time-asymmetrical. To be fair, the resulting state is neither deterministic nor random.
Penrose is clearly not convinced by string theory, the dominant theory in today's physics. That theory introduces extra dimensions, that Penrose feel are unwarranted. The whole "standard model" of particles and forces that contemporary physics presents to us is not a finite theory but a renormalized theory. This theory is still unable to explain masses and electrical charges. Furthermore, the same renormalization techniques do not work on Einstein's theory: a quantization of Relativity leads to a non-normalized theory, i.e. to more infinities. Penrose seems to lose his patience with the multitudes of scientists who refuse to admit that something got to be changed in Quantum Theory. The supersymmetry of the standard model is an elegant mathematical model that not only "rotates" the particles of each family among themselves (bosons with bosons and fermions with fermions) but also "rotates" bosons with fermions. Penrose finds it difficult to believe in such an abstraction that seems to be so far removed from reality. String theory employs both supersymmetry and extra dimensions. That's where the original sin comes to play: physicists have been driven by mathematical beauty to pick string theory (which then became superstring theory for similar reasons). The fact that Einstein's Relativity only admits the usual 3+1 dimensions did not stop quantum physicists from coming up with ever more exotic constructs (such as D-branes) to fix the theory.
Penrose shows more sympathy for Smolin's loop quantum gravity, that can be expressed in Penrose's own spin networks.
From Penrose's insider's account of the evolution of superstring theory, one gets the feeling that physics influenced mathematics, not the other way around: mathematicians were encouraged to study ever more exotic "symmetries", "groups", and assorted abstractions in order to provide physicists for ever more powerful tools to fix theories that were leaking all over the place.
The theory was further twisted to accommodate the simple fact that one needs to make measurements, and measurements are in real numbers. Quantum Theory, however, is based on complex numbers (an imaginary number plus a real number). Since the result of the calculations must be a real number, a complex amplitude gets converted into a probability.
Penrose feels that this is all in vain: changes are needed in the foundations of Quantum Theory or no fix will do. Physicists are on a wild goose chase and mathematicians are all too happy to appease them.
Penrose feels that, when all is said and done, we will find out that it is not the conscious observer that accounts for the collapse of the wavefunction but it is the collapse of the wavefunction that helps explain the nature of consciousness. And Penrose is the rare physicist who argues that no theory of nature can be considered complete unless it includes an explanation for human consciousness.
I made a point of spending one hour a day reading this book. In retrospect, it felt like an hour of ritual humiliation.
By the same author:
Penrose Roger: SHADOWS OF THE MIND (Oxford University Press, 1994)
Penrose, Roger: THE EMPEROR'S NEW MIND (Oxford Univ Press, 1989)