Exploring the Progress and Challenges of Twistor Theory in Quantum Gravity

In summary: In summary, there is some progress being made with twistor theory, although the original ideas by Penrose are still being explored.
  • #1
tom.stoer
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Are there any news regarding twistor theory?

The original ideas by Penrose to replace spacetime by its "dual lightcones" always fascinated me, but it seems the whole program is stuck. What are the reasons? Is there any progress and relation to recent progress in other QG approaches?

Tom
 
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  • #2
There are works in progress... although I don't know much about the details, but take a look at
http://www.twistordiagrams.org.uk/

See also the talk by Nima Arkani-Hamed.

http://streamer.perimeterinstitute.ca/mediasite/viewer/NoPopupRedirector.aspx?peid=ff8f97a4-2848-4b93-98d9-1218de2070af&shouldResize=False [Broken]
 
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  • #3
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  • #4
All these papers focus on scattering amplitudes; is twistor theory as of today "only" a calculational tool, or is there some fundamental light-cone structure replacing spacetime? Has Penrose's original program suceeded or failed?
 
  • #5
tom.stoer said:
All these papers focus on scattering amplitudes; is twistor theory as of today "only" a calculational tool, or is there some fundamental light-cone structure replacing spacetime? Has Penrose's original program suceeded or failed?

I don't think that's known. The hope is that it is the "magic" underlying AdS/CFT and points to more general non-perturbative formulation of string theory. But perhaps it is just a very neat trick for a very specific set of QFTs.
 
  • #6
I was really interested in the core twistor program.
 
  • #7
tom.stoer said:
I was really interested in the core twistor program.

So was I. I worked on the "original" twistor programme, but left to join industry in 1984 and haven't really kept up to date, and my memory's a little hazy. The two main classes of problem I was aware of then were:

1 Twistor theory was good at modelling self-dual or anti self-dual solutions of various physical systems. So, for example, there was a natural way to get, say, anti self-dual solutions from holomorphic functions on twistor space, but no natural way to get the self-dual solutions from holomorphic functions (the "googly problem").

2 It was good for modelling conformally invariant systems, but not for field equations containing mass terms.
 
  • #8
tom.stoer said:
I was really interested in the core twistor program.


lets see if this could be interresting to you. I am sure you know why I think twister will be the ultimate theory.



http://arxiv.org/PS_cache/arxiv/pdf/0902/0902.0274v2.pdf




This is an elementary and self–contained review of twistor theory as a geometric tool for solving non-linear differential equations...

and ultimately to Einstein–Weyl curved geometries generalising the flat Minkowski space.
 
  • #9
You might want to check out

http://arxiv.org/abs/1006.0199

and references therein. It's about the relation of twistor geometry to the classical phase space of loop gravity.
 

1. What is twistor theory and how does it work?

Twistor theory is a mathematical framework that was developed by physicist Roger Penrose in the 1960s to describe the geometry of spacetime. It uses complex numbers and spinors to represent the physical properties of particles and their interactions. Twistor theory is based on the idea that the fundamental building blocks of the universe are not particles, but rather geometric objects called "twistors" that encode the information about the particles. It provides a new perspective on the fundamental laws of physics and has the potential to unify quantum mechanics and general relativity.

2. What are the applications of twistor theory?

Twistor theory has been primarily used in theoretical physics to study the fundamental laws of the universe, but it has also found applications in other fields such as mathematics, engineering, and computer science. Some potential applications of twistor theory include improving our understanding of quantum gravity, developing new methods for solving complex differential equations, and creating new technologies based on the principles of spinors and complex numbers.

3. What recent developments have been made in twistor theory?

In recent years, there have been several exciting developments in twistor theory. One of the most significant breakthroughs was the discovery of the twistor string theory, which combines twistor theory with string theory to provide a new framework for understanding the fundamental laws of physics. Other developments include the use of twistor methods to solve complex problems in mathematics and the application of twistor theory to study the behavior of black holes.

4. How does twistor theory relate to other theories in physics?

Twistor theory has been compared to other theories in physics, such as string theory and loop quantum gravity. While it shares some similarities with these theories, twistor theory offers a distinct approach to understanding the fundamental laws of the universe. It provides a more geometric and intuitive perspective on quantum mechanics and general relativity, and has the potential to bridge the gap between these two theories.

5. What are some challenges and criticisms of twistor theory?

As with any scientific theory, twistor theory has faced its share of challenges and criticisms. Some critics argue that it lacks experimental evidence and is therefore not testable. Others point out that it does not fully explain all aspects of the universe and may need to be combined with other theories. Additionally, the mathematical complexity of twistor theory makes it difficult for non-experts to understand and apply. However, ongoing research and advancements in the field continue to address these challenges and explore the potential of twistor theory.

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