Amazing. While I can not exactly call Road to Reality a popularization of general relativity and quantum theory, it is a peerless introduction to and...moreAmazing. While I can not exactly call Road to Reality a popularization of general relativity and quantum theory, it is a peerless introduction to and review of those topics. I have a PhD in mathematics, and studied physics and math as an undergraduate, and there was plenty for me to learn from this book. There are very few people in the world who would not learn much from reading it.
Many years ago, I read Penrose's Emporer's New Mind which was good as far as it went, but earned my derision with doubtful, hand-waving arguments for quantum origins of consciousness. Knowing Penrose is no dummy, I permitted a friend to convince me his work deserved another chance.
I am very glad to have read RtR, even though the process took me most of 2010. I now have a far better understanding of mathematical physics than I could have achieved with any other reading list. I did not complete most of the exercises; I suspect that if I had, then (A) I would not have finished until 2012, and (B) the exercises would have been sufficient to bring me to a fairly professional level of competence. Kudos to Mr. Penrose for including them.
The book begins with quite a few chapters of mathematics, quickly progressing to advanced undergraduate topics such as calculus on manifolds. In some ways I liked Penrose's clear treatment and drawings better than, say, Michael Spivak's beautiful but sparse texts. In order to provide a foundation for his chapters on physics, more mathematics is interspersed where necessary.
Penrose introduces complex manifolds, continuous groups (Lie groups), and principal bundles. This machinery is all truly essential to the physics, and it was enlightening to see it collected in a single place, however briefly explained. It is especially useful because most graduate students in physics or math end up missing a formal introduction to one or more of these topics.
The grand themes in RtR are the two major 20th century discoveries of general relativity and quantum theory. Penrose is particularly interested in probing how the two may be made consistent. He covers some of the cosmological work that treats both (e.g. Hawking radiation from black holes), and then discusses theories that seem to join them, including various level of detail on spin foams, string theory and M-theory, loop quantum gravity and his own invention, twistors.
A great strength of this magnum opus is Penrose's ability and willingness to discuss philosophical and aesthetic issues of the physics. Four of these stand out. First, I quite like his perspective on the futility of obtaining unified theories by (more-or-less) trying to guess a tractable Lagrangian. Second, his detailed treatment of entropy, especially the universe's original low-entropy state with respect to gravity and the cosmological implications, was really fascinating.
Third, Penrose seriously considers the various interpretations available for (apparent) collapse of the quantum wavefunction. His bias is toward objective collapse (environmental collapse), rather than being spookily dependent on "observation" by a conscious observer, and I agree with him that far. He suggests that general relativity, being the only other physical theory we have of similar stature to quantum theory) may somehow provide the mechanism. This is not an assertion but merely a suspicion on his part, and personally I lend it little credence. I do agree with him that general relativity is likely to remain a permanent Newtonian-style large-scale limit of the physics, while quantum theory seems ripe for some kind of fundamental reinterpretation.
Finally, Penrose revels in the aesthetics of what he labels complex number magic. That is, he considers the interesting ways in which physical reality is so well described not just by mathematics but specifically by complex analytic structures, a simple example being the phases of quantum wavefunctions. His fascinating twistors are the coolest example of this, where he changes the physical perspective utterly. No longer are points in spacetime the essential quantities; rather the physics is on the manifold of (potential) light rays. A spacetime point is a confluence of rays, and the interesting part is how fundamentally a point can be represented by, and treated as, a Riemann sphere (a compactified 1-dimensional complex line). As an ex-complex-manifolds guy, this was wonderful stuff to me.
I will conclude by noting that Penrose even redeemed, somewhat, his handwaving arguments from New Mind. I now understand that he is essentially pointing out that our conscious observations of physical phenomena are (or appear to be) collapsing the wavefunction. Since there must be a mechanism for that collapse, Penrose is arguing that something fundamental about conscious minds (as opposed to highly sophisticated computers) is triggering it. I still don't agree, because I believe consciousness is computational and emergent from complex systems, but his point no longer seems so silly.(less)
This was one of clearest, most novel nonfiction books I have ever read. It's not technical at all, but gives the reader an understanding of (some aspe...moreThis was one of clearest, most novel nonfiction books I have ever read. It's not technical at all, but gives the reader an understanding of (some aspects of) music that are utterly transformative.(less)
For anyone who has ever done....things...to watch the Tour (de France, you philistines) or the Giro or Vuelta, this book is absolutely gripping. And I...moreFor anyone who has ever done....things...to watch the Tour (de France, you philistines) or the Giro or Vuelta, this book is absolutely gripping. And I learned a new moniker: "sweat-thief".(less)