Thu, 03 Jul 2008
Penrose, The road to reality
A summary of fundamental physics, with all the mathematics.
Hawking's Brief history of time attempted to give a short overview of fundamental physics without any mathematics. Penrose provides us with a very long overview with all the mathemetics.
The first third of this book is a survey of the mathematics required for the rest of the book. It is largely concerned with analysis (calculus) rather than algebra — the only algebra that he really covers is symmetry groups, with a brief introduction to knots later in the book — with a focus on complex analysis. Penrose starts from basics (he even explains fractions) and works up from there. He provides a series of exercises.
The second third of this book is the basic physical theory in which Penrose applies this mathematics to gravitation (relativity, Einstein) and quantum mechanics.
The last third of this book is Penrose's survey of current theories. He quickly makes it clear that he considers inflation and string theory to be speculative and lacking in experimental validation. Penrose also explains his preferred theories.
It's not possible to really address so large a text in a few lines, but I can say that Penrose has a gift for explaining quite advanced mathematics. His use of diagrams is particularly helpful. Althugh I understood only a small part, this did expand my knowledge of quite a few areas, and I think I could probably bluff my way through a few discussion now by confidently throwing around terms like 'collapse of the state vector'.
Discussions of the philosophy and religion of consciousness (the mind-body 'problem' and the like) often attract comments about 'recent' developments in physics — 'recent' seems to be about 1930 — so it is interesting to see Penrose's comments in this area. Penrose has covered this in more detail in other works, so it is not surprising that he adverts directly to this here. It is interesting to read that he does think quantum theory does have a part to play here, in particular in explaining consciousness [section 34.7].
Penrose, Roger. The road to reality: a complete guide to the laws of the universe. 2004, Jonathan Cape, London. hardback. 1094 pages.
ISBN 0-224-04447-8.
