Talk:Twistor theory

complex spaces
Unless I am missing something, I thought complex spaces don't have metric signatures, unlike real spaces. Phys 06:28, 1 Dec 2004 (UTC)

I'm a physics student at UCLA, I've only read about Twistors but from what Roger Penrose describes it as it is "Higher dimensional spinors" (from his tome "Road to Reality"). So, rather than the conventional 2 dimensional complex vector space, there is instead a 4 dimensional complex vector space. This is, of course, from an undergrad's understanding, so I may have missed the boat completely!

Further the twistor depends on the spinor momentum $$\pi\,_{A'}$$ where it satisfies

$$ p^{ \alpha\, } = \bar{ \pi\,^{ A } }\pi\,^{ A' } $$

the noncontracted multiplication of it and its complex conjugate is equal to the four-momentum. These, however, are the last two coordinates of the Twistor.

The first two are related to the angular momentum, but can be calculated from the momentum components of the twistor.

Twistors are concerned, first of all, with incidence (in the geometric sense of the word). That is to say, with (say) a light cone, if an event lies within the light cone it is in incidence with the light cone. The coordinates of the event in incidence with the twistor is $$r^{ A A' }$$. That is

$$ r^{ A A' } = \begin{bmatrix} t+z & x-iy \\ x+iy & t-z \end{bmatrix} $$

in spinor form. The relation of the angular momentum components $$\omega\,^{ A }$$ to the linear momentum components $$\pi\,_{A'}$$ are

$$ \omega\,^{ A } = i r^{ A A' } \pi\,_{A'} $$

Thus a spinor $$Z^{\alpha \,} = (\omega \,^{A}, \pi \,^{A'} )$$. The norm of the twistor has a unique relation to the helicity of the particle in question with the equation

$$ s = \frac{ 1 }{ 2 } \bar{Z_{ \alpha }}Z^{ \alpha }\,$$

where $$ s $$ is helicity. That's the primer. Cheers! - Pablo.

sentence
Can someone tell me why this is "For some time there was hope that the twistor theory may be the right approach towards solving quantum gravity, but this is now considered unlikely."?

Thanks

Alan ( alan_stafford@btinternet.com )


 * Originates from the first edit of this page by the User:Tracian on 4 July 2003. http://en.wikipedia.org/w/index.php?title=Twistor_theory&oldid=1111051


 * I think he means why is twistor theory no longer perceived as a great hope for approaching quantum gravity...not why that section is in the text. Well, for one it works primarily with special relativity rather than general relativity...twistors could be seen more as a quantization of the light cone rather than a quantization of gravity itself. It does, nonetheless, give insight into making events "fuzzy" rather than null vectors (the paths light takes). I recall reading from a monograph from the late 80s or early 90s that Christopher Isham thought Twistors would be more of a "last resort" rather than a "frontal assault" for quantum gravity, so "when all else fails" we can still fall back on it! The reason for his stance, I think, was the promise of Ashtekar variables in the canonical approach to quantum gravity appeared to be superior to the promise of the twistor programme. That is not to say however that twistors are useless, they are actually rather interesting things...it's just that there are other approaches which appear to be superior at the moment.

User:Tracian on 4 July 2003 is obviously an idiot. —Preceding unsigned comment added by 81.98.169.252 (talk) 06:34, 13 August 2009 (UTC)

music
How does the link "Music based on twistor theory" have anything to do with Twistor theory - besides the band's founder (Mr. Hogan) studying Twistor Theory at a university and adopting the name "TWISTOR" for his DJing business? There may be some valid relationship between Twistor Theory and Mr. Hogan, but there seems to be no basis in Twistor theory within the music itself. Davidl9999 19:38, 29 October 2007 (UTC)

Too short, too technical, insufficient motivation
This entry is too short, given the importance of its topic, and too technical for Wikipedia. There should be more historical and motivational material. The technical parts should be written at the level of The Road to Reality.

Just where does twistor theory propose to take fundamental theoretical physics? Is it a candidate theory of everything? Can it integrate general relativity and quantum theory? More should be said on why Mr String Theory Incarnate, Ed Witten decided to draw on twistor theory early this decade. Andrew Hodges's website conveys a lot of recent excitement about twistor theory. Could some bits of the info underlying Hodges's enthusiasm be added to this entry? Peter Woit and Lee Smolin have written recent books arguing that string theory is not living up to its former promise. What do they think of twistor theory?123.255.26.213 (talk) 22:59, 8 April 2009 (UTC)

Comment
add the definition of a null ray (not transformers of course) which is given by Juan Martín Maldacena — Preceding unsigned comment added by 2a02:587:410a:c500:8d92:8418:8856:6cf1 (talk) 20:44, 2 December 2016 (UTC)

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Utterly (and deliberately?) useless article
The “overview” is literally useless for understanding what this is. Which is, you know, the whole point of the article. Only someone who alteady onows better than even the article author himself, can decode the way those lines of code words are carefully put together to maximize the stumpedness, for the purpose of making the author feel big and smart. I noticed, this is a common pattern in Wikipedia’s mathematics and physics articles. But at this point, this is actually more harmful than not having the article at all. As it leads people away from actual explanations and makes them think this is too hard for them. (It certainly is not! It is just badly explained. Richard Feynman, 3blue1brown, ScienceClic, Sabine Hossenfelder or Harald Lesch could explain it to laypeople just fine.)

What can we do, to fix this situation? Clearly, Wikipedia is broken here. INobody intended this. It needs a change at Wikipedia’s core.

— 2A02:3035:60F:BB77:6E29:63C:7557:1A1F (talk) 20:49, 27 May 2024 (UTC)