Finally, I’ll draw these threads together more tightly by citing the following paper by Dowker, Henson, and Sorkin: In the case of string theory, there are much less subtle instability problems with extra dimensions than the ones you need Penrose’s singularity theorems to see. You already have a huge problem at the linearized level. I’m referring to the well-known problems fixing the moduli parameters that describe the size and shape of the extra dimensions. Unless you first solve that problem, worrying about more subtle problems seems to me a waste of time. The only “solution” to this problem I know of leads to the “Landscape” and a completely useless theory. The literature contains several derivations of Hawking radiation, each with strengths and weaknesses. … General points of philosophy and arguments of authority are just a matter of taste. The facts are that the question of linearized stability of KK spacetime, to the extent that it is a mathematically precise question, was settled long ago by precise calcualtions. I suggest that if Penrose had something concrete to say about it, he would publish a paper on the subject, which would then be subjected to the usual scrutiny. In the absence of that there is really nothing to agree or disagree with. Just relying on his authority is unfair to many talented and devoted people who actually worked on the subject. Similar words can be said about Hawking and the fiasco of the information paradox resolution. Here is a fundamental objection of mine (which I think is a fairly obvious one) to the main theme in many of your posts againsts string theory (I am not a string theorist, by the way):

The Road to Reality by Roger Penrose: 9780679776314

Penrose asks us to consider if the world of mathematics is in any sense real. He claims that objective truths are revealed through mathematics and that it is not a subjective matter of opinion. He uses Fermat's last theorem as a point to consider what it would mean for mathematical statements to be subjective. He shows that "the issue is the objectivity of the Fermat assertion itself, not whether anyone’s particular demonstration of it (or of its negation) might happen to be convincing to the mathematical community of any particular time". Penrose introduces a more complicated mathematical notion, the axiom of choice, which has been debated amongst mathematicians. He notes that "questions as to whether some particular proposal for a mathematical entity is or is not to be regarded as having objective existence can be delicate and sometimes technical". Finally he discusses the Mandelbrot set and claims that it exists in a place outside of time and space and was only uncovered by Mandelbrot. Any mathematical notion can be thought of as existing in that place. Penrose invites the reader to reconsider their notions of reality beyond the matter and stuff that makes up the physical world. I hope that this would serve as some kind of a signal also to Peter Woit, who has been continually censoring out my messages. This just to help the raise the level of discussion from what it is now.

I got the book on Saturday, it should be in every physicist’s library. It reminds me of Klein’s various “Vorlesungen”– lectures, literally “readings”. One thing Peter may not have mentioned is the clever prologue, which I assume takes place in Atlantis 🙂 This book appeals on many levels, including the very “tominess” of it! Maybe at a later time you will speak to this in more detail? This clarifies to me the essence of your resistance to other theoretical approaches and helps to point towards more information to be look at. This is good. Besides, please, have and show (!) some respect for Penrose: He did more in a lifetime than most of us combined and/or put together will ever do! Or are you telling me that if Newton were alive you’d walk all over his ass because he ‘was wrong’?!!! (Sorry, Peter, for the language; it’s just too soon in the morning to read gigantic loads of crap… add that to a bit of Napolitan blood and you have a recipe for a (flame-)war! >;-) Now, I should not have to tell you that if you had applied LINEAR analysis to this problem, you would have had never of found these CHAOTIC solutions!!!

The Road to Reality : A Complete Guide to the Laws of (PDF) The Road to Reality : A Complete Guide to the Laws of (PDF)

You should be trying to figure out how to use symmetries to gain control of the space-time degrees of freedom, not throwing out the gauge symmetry, creating a higher dimensional mess whose dynamics you don’t understand, then hoping to recover gauge symmetry as an effective low energy phenomenon. I’m certainly fond of true statements, In this case we have one of the world’s leading experts on singularity theorems in classical GR making a claim about them in print. I strongly suspect that he knows what he is talking about here and is making true statements, that’s why I reported on them. As for mathematically precise statements, they have their place, but in many contexts they’re either not possible, not appropriate or not worth the investment of time and energy needed to get them. I’m not convinced that his exposition of fourier analysis would be easily graspible for the beginner, but I sure as hell enjoyed it! The following might have been missed by the readers due to it having been posted a couple of days ago, but here it is (to humble ST people)As a general matter of philosophy though, I very much agree with Penrose’s point of view about Kaluza-Klein. You’ve got enough trouble dealing with the metric degrees of freedom of space-time. You’re just making things worse when you add in a dynamical metric for the fibers of your principal bundle or for some internal space. I dont know what Wilczek thinks or what he has said about extra dimensions. But here is something that could help round out the picture. Wilczek is evidently interested in quantum gravity and has just posted this paper with Sean Robinson To explore the process of pursuing mathematical truth, Penrose outlines a few proofs of the Pythagorean theorem. The theorem can be stated as such, "For any right-angled triangle, the squared length of the hypotenuse [math]\displaystyle{ c }[/math] is the sum of the squared lengths of the other two sides [math]\displaystyle{ a }[/math] and [math]\displaystyle{ b }[/math] or in mathematical notation [math]\displaystyle{ a Penrose essentially claims that his and Hawking’s singularity theorems also apply in this higher dimensional case. If you want the details, you have to take a look at the book, although Tony Smith just posted a relevant abstract. Just before a total eclipse of the Sun, the Moon is given a large velocity tangential to its orbit at mid-eclipse. Do the effects of relativity prevent the eclipse? Explain.