Dave Langford, SF&F critic and reviewer, in his long-since defunct column for White Dwarf magazine, once said that, "There is a tendency to over-praise big books simply because one has got through them." I agree that this tendency exists but note that Langford gave no reason for it. I think the reason is more or less macho intellectual pride; look at me! I read this honking great saga! It must be great or I'd have to admit wasting my time! And I need to show off my intellectual credentials! Now imagine that the book is not only huge, but really difficult because, say, it's dense with obscure references (e.g. Ulysses) or full of mathematics and not kiddie maths, either...the temptation must be even worse.
Hence I'm going to start my review with a couple of gripes: This book, which is full of maths, much of which would make your average undergrad scientist grunt with the strain at the very least, as well as physics to post-grad level in places, has no glossary of technical terms. There is ample cross-referencing and an index but these are no substitute. When you want to know, Clifford Algebra, which one was that again? (Because you've met ordinary algebra, complex algebra, Clifford Algebras, Lie Algebras and Grassman Algebras...), going back and reading through an entire section again to find out, is a bit annoying - a list of definitions at the back would have helped enormously. Admittedly this would have made a big book even bigger but it would have made it much more user-friendly.
Gripe number two is in a similar vein; Penrose fails to supply a list of the upper and lower case Greek alphabet symbols and their names or a similar list for obscure mathematical symbols, such as del and scri. Given that nobody without training in Greek or in science is going to know these and such a list would only take up one page, its omission is egregious.
This leads neatly into a topic that has been dicussed quite a bit here on Goodreads - namely, who is this book aimed at? What is it's purpose? Firstly I would point out that the subtitle "A Complete Guide to the Laws of the Universe" is not really true: Classical Thermodynamics is barely seen as we rush straight into the statistical view of the Second Law. Of the other three Laws of Thermodynamics, Zero is never mentioned and the others barely name-checked. I doubt many physicists would consider that all the basic theories have been covered in such a circumstance. But I think this is a marketing problem; I don't believe Penrose ever intended to write such a "Complete Guide."
In the preface Penrose talks about wanting, with this book, to make cutting edge physics available to people who struggle to understand fractions. Now, this can only be taken as a joke, considering what one is up against only in chapter 2, but I would guess that Penrose genuinely wants to have the widest possible audience for his book whilst not compromising his aims.
What are those aims? In my view he wants to give his personal views on the state of cosmology and fundamental physics but to be able to do it at an advanced technical and mathematical level and additionally to give his own philosophies regarding the nature of thought, science, maths and...Nature! This means that he wanted to deliver Chapters 27 - 33 on the physics/cosmology, bracketed by Chapters 1 and 34 of philosophising. The entirety of the rest of the book is simply there in order to equip readers to understand what he says in those six technical chapters! This requires 15 Chapters of maths and ten Chapters of physics/cosmology...
Looked at this way, the book begins to reflect the genius and madness of the author: Many of the explanations in earlier stages of the book left me thinking, why do it that way? That's not the easiest way to understand this if you've never come across it before! He also goes straight to very general mathematical principles, missing out intermediate levels of abstraction that might make what comes later easier. He chooses to emphasise the geometrical/topological view of everything, which, it might surprise one to know, is not always the easiest way to understand things. Many of the choices of what to emphasise and what to ignore seem odd...that is until one gets to the late stages of the book.
Upon arrival at Chapters 27 - 33 (i.e. what I think Penrose really wants to talk about) one can see that everything that has gone before has been put together in order to provide the most efficient route to understanding - hardly a page has been wasted. All those strange choices of what to emphasise, all the peculiar, non-standard explanations when easier explanations exist, all the leaping to the most general mathematical ideas, all the things missed out, all these things are done so that the points he wants to discuss can be followed without wasting time or space in what is a 1000+p book as it stands. The necessary skill, thought and effort required to do this impress me enormously.
Inevitably this means that most of what is covered in the book of "standard" physics has been explained better (by which I mean more readily comprehensibly), even at a mathematical level, elsewhere - but not in one volume! The consequence of this is that Penrose's widest possible audience may not be all that wide: although he suggests one could read the book and ignore every equation in it, (something I often do when reading technical literature!) I suspect one would rapidly become bored and disenchanted. The unavoidable fact is that the greater your mathematical capabilities, the more you will get from this book and additionally, the more maths and physics you know before starting, the more you will gain from this book.
Further, the more you are willing to study the book the more you will gain. Manny approached it by reading 3 hours per night until done. I would suggest that the nearer to that approach you can get the better off you will be, even though I failed miserably to do so. There are numerous excercises scattered through-out, which I did not attempt, but I would suggest that if you are determined to attempt them, you should read the remainder of each chapter as soon as you hit a hard problem, then go back and look at the problems again. (And note the solutions web address given in the preface!)
So what did I gain from the unavoidable slog of this book?
The general philosophising of Chapters 1 and 34 struck me as a waste of time; I either thought what was being espoused was obviously clap-trap or obviously true - and for me the questions he raises mostly aren't interesting to me anymore. (They were back when I hadn't reached my own conclusions yet.) Others, may feel very differently, however - and many would not agree about which parts are claptrap! The remainder offered me quite a bit, however.
For instance, a frankly embarressing mis-understanding of the EPR paradox I was labouring under was corrected! (Something of a body-blow to me as it is undergrad physics!) On the other hand, Penrose makes an astounding mistake at one point, where he gets himself horribly messed up with basic (high school) probability theory and time-reversal. (Pretty good combination to the head from me!) This is a good reminder that there is no argument from authority in science: just 'cos Penrose says it, doesn't make it right! This wrong argument is then used to go on to explain a completely freaky (and I suspect wrong) prediction about basic quantum theory. I am not clear that the example, which is definitely wrong, invalidates his whole line of reasoning, though; it may be that other examples show the general argument to be correct.
Then Penrose delivers the knock-out punch: Conservation of energy/momentum/angular momentum in General Relativity is non-local! Not only that but it has only been proved to be true at all in a subset of cases! Seriously, how could I have never known this before?! (Non-physicists may well have no clue why I am so thunder-struck by this revelation, but it is not far short of learning that there's a whole continent you'd never heard of before.) It's completely gob-smacking. And I can't see how I didn't get told as an undergrad.
Further, Penrose's main purpose was achieved; I have a much better understanding of the main approaches to tackling the outstanding problems in cosmology/fundamental physics than I did before and along the way I gained some insights I previously lacked. Two examples are the Higgs boson explanation of the origin of mass and spinors. The Higgs boson theory is barely touched upon and is one of the rare examples of something being included that is not strictly necessary later. I wish there had been more about it, whilst recognising precisely why there is not. What material there is made the theory seem much less arbitrary than it had previously.
Spinors are a mathematical concept that feature heavily in the book, mainly because they feature extremely strongly in Penrose's Twistor Theory of quantum gravitation. Penrose gives an assessment of his own theory that I respect enormously and cannot praise highly enough; he expresses clearly what it it can acheive and equally clearly and forthrightly what it cannot. Every weakness and limitation is mentioned and explained. The only time I have previously come across a scientist giving such an honest and complete assessment of the weaknesses of his own theories in a popular account is when I read Charles Darwin's Origin of Species. I cannot express how much respect Penrose earns from me by doing this. Suffice to say that most popular science books will make out that the author's ideas are obviously and unassailably correct. Further, many technical papers fail to match this level of dispassionate critical assessment.
But back to the spinors; they feature in the now well established Dirac Equation for a relativistic electron but the (non-standard) way Penrose shows this and explains their connection with the left-handedness of the Weak nuclear force and how they link to the Higgs boson ideas are fascinating. However I am not clear about them in one (crucial) regard: are they real? Penrose says they are. I am not sure (because my understanding is still muddy) and I find (somewhat to my horror!) that even though I've read all 1050p of the main text, all of Chapters 2-17 twice and many individual sections several more times, I am still not done with this book!
Spinors and Spin
I re-read the material on the Dirac Equation: