Talk:Twistor theory

	Mathematics portal This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics articles
Low	This article has been rated as Low-priority on the project's priority scale.

Physics: Relativity Mid‑importance

	Physics portal This article is within the scope of WikiProject Physics, a collaborative effort to improve the coverage of Physics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.PhysicsWikipedia:WikiProject PhysicsTemplate:WikiProject Physicsphysics articles
Mid	This article has been rated as Mid-importance on the project's importance scale.
	This article is supported by the relativity task force.

complex spaces[edit]

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 $r^{AA'}$ . That is

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

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

$\omega \,^{A}=ir^{AA'}\pi \,_{A'}$

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[edit]

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)[reply]

music[edit]

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)[reply]

Too short, too technical, insufficient motivation[edit]

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)[reply]

Comment[edit]

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)[reply]

External links modified (January 2018)[edit]

Hello fellow Wikipedians,

I have just modified one external link on Twistor theory. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:

Added archive https://archive.is/20130112095407/http://link.aip.org/link/JMAPAQ/v8/i2/p345/s1 to http://link.aip.org/link/JMAPAQ/v8/i2/p345/s1

When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.

This message was posted before February 2018. After February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot. No special action is required regarding these talk page notices, other than regular verification using the archive tool instructions below. Editors have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the RfC before doing mass systematic removals. This message is updated dynamically through the template {{source check}} (last update: 18 January 2022).

If you have discovered URLs which were erroneously considered dead by the bot, you can report them with this tool.
If you found an error with any archives or the URLs themselves, you can fix them with this tool.

Cheers.—InternetArchiveBot (Report bug) 01:06, 22 January 2018 (UTC)[reply]