Twistor Theory
Sol - Dec 19, 2003 6:05 am
Edited Aug 4, 2004 2:57 pm
The motivation and one of the initial aims of twistor theory is to provide an adequate formalism for the union of quantum theory and general relativity. Twistors are essentially complex objects, like wavefunctions in quantum mechanics, as well as endowed with holomorphic and algebraic structure sufficient to encode space-time points. In this sense twistor space can be considered more primitive than the space-time itself and indeed provides a background against which space-time could be meaningfully quantised.
(6 previous messages)Sol
- Aug 4, 2004 9:55 pm (#7 of 11)
Light Source : So, is that everything then?
In his book, Penrose reviews the history of theories both elegant and ugly like a gourmet singling out hors d’oeuvres. His appetite is heroic, his knowledge encylopaedic, his modesty a reminder that not all physicists claim to be able to explain the world in 250 pages. True, its subtitle — A Complete Guide to the Laws of the Universe — implies that we might be in for another dose of the Mind of God-style science book so fashionable since Stephen Hawking’s A Brief History of Time.
Hawking was told that every equation he put in his book would lose him a thousand readers: if this is true, then Penrose is in minus numbers by about page 23. His book is packed with equations, as well as injunctions to the reader to work it all out for himself. Page 98, which happens to be about the geometry of logarithms, powers, and roots, has four footnotes, which reads as: “Why is this an allowable specification?” “Show why this works.” “Spell this out.” And, finally: “Show this.” Each request is accompanied by a little face, smiling if the proof is easy, frowning if it takes some thought, scratching its head if the task is not to be undertaken lightly. Penrose’s take on the epistemological crisis into which physics seems to be slipping is also refreshing to those tired of triumphalism.
— The Times, London
http://www.thestatesman.net/page.news.php?clid=24&theme=&usrsess=1&id=50300
Sol
- Aug 4, 2004 4:29 pm (#8 of 11)
THE ROAD TO REALITY , by Roger Penrose
WHEN Stephen Hawking was writing A Brief History Of Time in the 1980s, his editor told him every equation he included in the book would halve its sales. Hawking’s colleague and rival Roger Penrose clearly has no such fears. His new book, subtitled "a complete guide to the laws of the universe", is crammed with equations. And Hawking’s emphasis on brevity - followed more recently by Bill Bryson’s A Short History Of Nearly Everything - is also disregarded. Penrose’s ‘complete’ version is over a thousand pages long. Reading doesn’t get much heavier than this, unless it’s a phone directory.
Not only has the book industry lost its fear of writers with brains, it is actively pursuing them, offering lucrative contracts to anyone who can turn genes or atoms into readable prose. Publisher Jonathan Cape makes no bones about Penrose’s opus, which it dubs "the most important science book published this century". Hardly worth waiting around for the next 96 years, then.
I asked an industry insider if he could explain this feeding frenzy among publishers of popular science books. "They don’t understand what they’re publishing," was the wry response. In the case of The Road To Reality, that is hardly surprising - but at least Penrose is a safe bet, since he truly is one of the world’s leading mathematical physicists.
In the 1960s, he and Hawking proved that the ‘singularity’ of the Big Bang - when all space and matter were somehow shrunk to a point - was an unavoidable feature of general relativity. The only way round the problem was to ditch Einstein, hence physicists (Penrose included) have spent the following decades hunting for a theory of ‘quantum gravity’ that will make better sense of the universe’s origin. That great quest is the real subject of Penrose’s book - but before we get to the nitty gritty there are an awful lot of preliminaries to get out of the way.
Most popular guides start with a gentle introduction to mind-bending ideas like curved space and quantum waves, before gradually upping the learning curve to a point where non-specialist readers either fall off completely or else are lulled into uncomprehending acceptance.
There is no such pussy-footing for Penrose. By chapter two he is proving Pythagoras’ theorem from first principles and introducing non-Euclidean geometry. His initial approach, though, is seductive. An Escher woodcut graphically shows what life might be like in ‘hyperbolic space’, where objects change size and shape when moved around.
Linking art and science in this way is a great idea, but alas it is a rare foray. The next 300 or so pages are given over almost entirely to pure maths, making one wonder who exactly this book is aimed at. Penrose says he would like it to be accessible to people who struggled with fractions at school (in other words everyone). But I find it hard to square this with his subsequent exposition of quaternions, hyperfunctions and tensors, in which he neglects to define basic terms such as ‘natural logarithm’ for the benefit of any bewildered math-phobes still in the audience.
Another 300 pages do much the same for physics, making this book ideal for anyone needing to do last-minute revision for a degree exam. After that, if you can last the course, we hit the really interesting part, when Penrose airs some of his own theories and takes issue with those of his contemporaries.
http://news.scotsman.com/features.cfm?id=849142004
Sol
- Feb 29, 2004 6:01 am (#9 of 11)
Penroses Influence on Escher
During the later half of the 1950’s, Maurits Cornelius Escher received a letter from Lionel and Roger Penrose. This letter consisted of a report by the father and son team that focused on impossible figures. By this time, Escher had begun exploring impossible worlds. He had recently produced the lithograph Belvedere based on the “rib-cube,” an impossible cuboid named by Escher (Teuber 161). However, the letter by the Penroses, which would later appear in the British Journal of Psychology, enlightened Escher to two new impossible objects; the Penrose triangle and the Penrose stairs. With these figures, Escher went on to create further impossible worlds that break the laws of three-dimensional space, mystify one’s mind, and give a window to the artist heart.
In order to understand how Escher used impossible figures to create impossible worlds, impossible figures must be clearly defined. In his article Escher’s Impossible Figure Prints in a New Context, Ernst Bruno gives a thorough description of the thought process one goes through upon seeing an impossible figure. Bruno’s account can be summed up to produce a concise definition of an impossible figure; a definite figure with conflicting depth cues.
http://www2.bc.edu/~schiavop/escher.html
Sol
- Jul 31, 2004 1:37 pm (#10 of 11)
Edited Aug 4, 2004 3:11 pm
So who has last word?
Lubos said,
We have discussed these questions a lot on this board. If the number of
possibilities to create a Universe - including working cosmology - in the
correct theory *is* that huge, we will have to live with this fact. String
theorists don't agree yet whether the usage of the Anthropic Reasoning
will be necessary. Many of us hate it. But it is a logical possibility. At
any rate, as long as theoretical physics exists as a field, the scholars
in it will study something. Because they have no new experiments, they
must study more or less pure theory. String theory remains the most
promising game in town, perhaps the only game in town. This might
hypothetically change - but only if someone found something equally (or
more) interesting. It cannot change by political speaches without
scientific content, even if the speaker is as famous as Roger Penrose.
http://www.physicsforums.com/showthread.php?p=271882#post271882
So you can see, you have to be smarter then Edward Witten, and apparently you Marcus and Jeff are not. Cheez, that Lubos guy is sure not very nice. :rofl: He think's he's tuff guy 
(LM)Most string theorists are also too
nice - perhaps except for me- and therefore they won't comment on
declines of Roger Penrose although there would certainly be a lot of stuff
to discuss. 
I think the issue has become somewhat confusing when you think the universe came from a pea So where did the Pea come from?
And then he has the nerve to comment on the GRanium and Daisey's as Tulips! Not very original I think although they do belong to the class of the flower children. Maybe we can work the image of the tulip into Hawking's as a good visualization of the Instanton? Or even the lotus flower, as a symbol of the "emergent realites," deep from our subconscious level
String theory has had a kind of tulip-mania fad or craze and now seems to be in decline.
Well, we've heard such things since the middle 1980s at least. It is
certainly a longer-lasting fad than any other fad in the history of
humankind. ;-)LM
Let's heard from you now Lubos-the tuff guy. I know thorny Jeff(the rose) can give you a run for your money:smile:
So now being lead into this fantasy:
Sol said:Would twenty mattresses help Alice, and how complex can each mattress remove the thinking from the pea of concern?:)
http://superstringtheory.com/forum/dualboard/messages11/44.html
Fictional Alice was a deep thinker :) Mathematicians tire easily becoming lost in the abstract theoretical world, so often times like Lewis Carroll, they create this new found fantasy to help see the world in a different way? Break the bonds of abstractness, and loose themselves in this world of fantasy.
What you don't like Penroses tessellations or Escher's interconnecting lizards?
Sol
- Aug 4, 2004 10:13 pm (#11 of 11)
Posted by sol on December 24, 2002 at 10:32:49:
Kx21,
It was important to understand this evolution and roots, to have better understood the value of this historical progression. You will find the posts correspond quite nicely to the articles that I have moved this discussion through a sequence of events.
It began with Einstein, and today, we have a interesting question about photon splitting, the sum of its parts, and about, what information could have existed. How such distances, can have been removed to have least time principle at the heart of science today?
For me to understand this progression, it was necessary to understand this history, gives us a good understanding of that standard model, the force carriers and their role in how we might have understood this progression.
What does strings have to do with all this and Dickt summation on Dirac to Superstring theory, is a basis from which to work. There is a lot in between, that one must visit Einstein and the Reinmann sphere and what is of value in geometrical expression and the dimensional significance.
Penrose now raises a understanding about the value of spin we did not have before?
Superstring theory answers this value of Einstein, in simultameity, that the Bell Theorem now handles quite nicely. We have those who like the Aton Zielinger, with the Aspect experiments allowed us to speak to this, as well as Holt Shimony and Chuaser. I am sure I have missed many people that we have not understood this historical, necessary as well.
Sol
Twistor Theory