My hard copy has just arrived, a respite from reading Gareth Stedman Jones' theory-and-history-dense biographical tome, "Karl Marx: Greatness and Illusion".
Here is how Peter Woit describes Penrose's book.
"Besides a mathematical appendix, the book is divided up into four parts:Update: I have just been reading the mathematical appendices and - just as with The Road to Reality - Penrose's concept of 'lay person' essentially equates to: reader trained in mathematics and physics to at least graduate level, but not a practising post-doctoral physicist!
"This is the section that deals with string theory, and Penrose’s central objection is to the use of extra spatial dimensions as a crucial part of the theory. When trying to use string theory as a unified theory, an assumption is made that one can take four space-time dimensions very large, and the rest very small, decoupling the large and small dimensions. Penrose argues that there is no reason to believe one can consistently do this, that there should be couplings between these degrees of freedom that cannot be ignored, leading to instability of the theory, rather than a stable ground state with large dimensions.
"In this section Penrose addresses the measurement problem of quantum mechanics, pointing out correctly that our standard story about quantum mechanics introduces an “ontological shift”, indicating that something more is going on than a well-understood consistent framework. He favors the idea that perhaps the introduction of gravity into the usual framework could resolve this problem, backing this up a dimensional analysis argument that a relevant effect could come from gravity, while being too small to be observable so far.
"Here Penrose describes in detail some basic problems in the theory of cosmology, and how they are supposedly resolved by the theory of inflation. He explains that characterizing this as “fantasy” is not meant to be purely critical, that “fantasizing” about the moment of the big bang is what theorists do in the absence of compelling evidence, and that he just has other fantasies he thinks worthwhile.
"A new physics for the universe?
"In a final section, Penrose describes some of his more positive ideas addressing the problems pointed out in the earlier sections. This begins with a wonderful summary of the theory of twistors, and I strongly suspect that he’s right that this very different way of thinking about space-time geometry will ultimately be part of any successful integration of our understanding of quantization and geometry. That this geometry is very specific to four space-time dimensions provides yet another reason for skepticism about the fashion of theories with more spatial dimensions."
You might also be interested in John Baez's blog, Azimuth, where he has four pieces published so far under the general title, "Struggles with the Continuum". Part one is here, and each part links to the next.
"Is spacetime really a continuum? That is, can points of spacetime really be described—at least locally—by lists of four real numbers (t,x,y,z)? Or is this description, though immensely successful so far, just an approximation that breaks down at short distances?Part one is devoted to Newtonian mechanics and considers point particles moving under gravity. Is this well-understood and well-behaved?
"Rather than trying to answer this hard question, let’s look back at the struggles with the continuum that mathematicians and physicists have had so far."
"Xia proved in 1992 that with 5 or more particles, there are solutions where particles shoot off to infinity in a finite amount of time!"The second part introduces the quantum mechanics of charged point-particles (deploying the uncertainty principle). This makes a difference, but things break down with more than three spatial dimensions.
Part three brings in special relativity, and part four quantum field theory.
There is at least one more part promised, and the level of analysis is not beyond that of a maths/physics graduate - at least to get the general idea.
Today, another one of "the last days of summer", found us at Lytes Cary Manor in the 28 degrees sunshine.
|Lytes Cary Manor, Somerset|
We had a picnic, swished off a wasp or two, took a walk around the woodland trail then sat in the gardens for a while, watching the Yeovilton helicopters training overhead. Then we came home.