Which do you think are the most promising alternatives?
Didn't think SUGRA was a theory of quantum gravity.
LQG, spin foams in particular, has been reformulated in terms of twistors, so when you say "twistor theory" that is what immediately comes to mind.
Some of the Loop researchers involved with the Twistor formulation of Loop are:
Laurent Freidel, Etera Livine, Simone Speziale, Wolfgang Wieland. I'll get some links to their papers.
It's hard for me to imagine what "twistor theory" could be as a ALTERNATIVE to LQG. Maybe you can clarify what the current twistor theory direction is that is distinct from what's going on in Loop.
I guess there could be several parallel (eventually intertwining?) lines of development...
As far as I'm concerned, the Amplituhedron is based on twistor theory. Are you suggesting, then, that LQG is related anyway with the Amplituhedron?
YIKES! No! Because I don't know enough about that to say anything sensible about a relationship
My problem is that I don't know the OTHER current applications of twistors to quantum gravity et al.
So to enable me to respond to your poll, you'd probably have to give a thumbnail sketch of what the current research is, under the heading of twistor theory. Sort of define the term.
Maybe this could help both of us. Wieland gave some twistor references in his "future directions--including matter" section at the end of his thesis. I was just about to begin to explore a little, unpack the links and take a look at the articles he mentioned:
== http://tel.archives-ouvertes.fr/docs/00/95/24/98/PDF/diss.pdf pages 136-137==
Inclusion of matter
To aim at a phenomenology of loop quantum gravity [201–203], …
(iv) The recent understanding of loop quantum gravity in terms of twistors is mirrored [205–209] by similar developments in the study of scattering amplitudes of e.g. N = 4 super Yang–Mills theory . It is tempting to say these results all point towards the same direction eventually yielding a twistorial framework for all interactions.
I quoted that earlier, now I'll unpack some of the references cited:
 T. Adamo, M. Bullimore, L. Mason, and D. Skinner, “Scattering amplitudes and Wilson loops in twistor space,” J. Phys. A: Math. Theor. 44 (2011) 454008,
 J. J. Heckman and H. Verlinde, “Instantons, Twistors, and Emergent Gravity,”
 J. J. Heckman and H. Verlinde, “Gravity Amplitudes from a Gaussian Matrix Model,”
 F. Cachazo, L. Mason, and D. Skinner, “Gravity in Twistor Space and its Grassmannian Formulation.”
I followed the links and had a look at these and some other similar papers. I get the impression that we are dealing more with a LANGUAGE or formalism than with a specific theory of nature. It may be an especially useful framework in which to formulate theories of geometry-and-matter, so people pursuing different lines of investigation are all trying to cast their theories in those terms. Or I may be overstating, or have gotten the wrong impression--anyway it's interesting. Thanks for broaching this and related topics of discussion!
in first place, please note that twistors existed before finding applications to lqg. In second place, note that twistors are an independent approach to the quantum gravity problem, though conections to other fields of research have been suggested and explored, and that it was born BEFORE strings and lqg and other approaches. So if a researcher has no idea about the loop/spinfoam programe, he still can do a lot of things in twistor theory.
And third, let's clarify an issue: though twistors and lqg were found to be related, you should also be aware of twistor string theory, discovered in 2003 by leading physicist Edward Witten. This is more than a vague and remote suggestion; the amplituhedron is based, after all, in twistor string theory.
And when I say ALTERNATIVE, I REALLY mean that. (e.g.: twistor theory doesn't predict discreetness of spacetime, as lqg does).
So does Twistor Theory include all manner of quantum theories of gravity and matter that are formulated using twistors?
The amplituhedron http://arxiv.org/abs/1312.2007 is about a CFT, so if it's related to gravity, presumably it would be through AdS/CFT. Freidel, Krasnov and Livine say in http://arxiv.org/abs/0905.3627 that there is a formula that bizarrely appears in LQG and the AdS/CFT of string theory!
Freidel and Livine, as marcus pointed out above, are investigating twistory stuff in LQG. If you look at Witten's prehistoric paper http://arxiv.org/abs/hep-th/0312171 that had some part in kicking off the current twistory stuff in strings that indirectly led to the amplituhedron, you'll find Krasnov's http://arxiv.org/abs/hep-th/0311162 cited.
Rovelli reviews alternatives here:
loop quantum gravity,
discrete quantum gravity (Regge calculus, dynamical triangulations and simplicial models),
Euclidean quantum gravity,
perturbative quantum gravity,
quantum field theory on curved spacetime,
topological quantum field theories and
spin foam models
I can't find a more up to date review, but there have been other propositions since then.
See http://www.twistordiagrams.org.uk/ for a disscusion about the quantum side of twistors and their relation to strings.
That's apples and oranges.
LQG is about quantizing gravity, string theory is about unifying all forces of nature - including gravity. So it's like asking about alternatives to bikes and mobility.
Regarding string theory I don't see any alternative.
Regarding quantum gravity I would certainly include
- causal dynamical triangulation
- the asymptotic safety program
in a list of promising alternative approaches.
It would save face for theoretical physics if someone could now append, to Rovelli's list, any experiments or observations --- as predicted by these subjects --- which have confirmed or ruled any of them out. Or does the list still stand naked, after 17 years?
Note that transitive relations are not the only kind of relations:
Good point! So far "twistor theory" has not been defined in this discussion, so talking about it as if it were a physical theory of nature verges on nonsense. However twistor FORMALISM, the mathematical language of twistors, is well defined.
It's analogous to the complex numbers x+iy. Many different physics theories can use the language of complex numbers. In and of themselves, the complex numbers are not a physical theory
The relation we are talking about is "uses the language of".
Some LQG research now uses the language of twistors
The amplituhedral business also uses the language of twistors
AFAIK since the formalism is pretty general and you can do a lot of different physics with it, this does not imply any useful connection betw. LQG and amplituhedral business.
Quite different stuff can use the same formalism.
I would say the key fact here is that the relation is not SYMMETRIC.
The fact that physics theory X uses the language of twistors does not imply that the language twistors uses the physics theory X. Thanks for pointing out the ludicrousness, Demy.
Please note that, though refuting an argument is fine (in fact, I didn't argue that the Amplituhedron and LQG are related, but asked if you were suggesting that), refering to it as ludicrous isn't. We're here to discuss about physics and enrich our understanding of it, not to discriminate others' arguments, simply by saying they are ludicrous :shy:. I wish that in the future we will debate respectfully, without hurting the feelings of other members of the furum.:thumbs:
No one suggested YOU said anything ludicrous, Twistor. NEITHER OF US IMPLIED a connection between LQG and Ampli'dron. Demy simply pointed out, in what I thought was a witty way, the absurdity of connecting the two theories merely because they both used the language of twistor "numbers".
I was not offended (since I hadn't implied it) and certainly YOU shouldn't be either, for the same reason :-). Live long and prosper! Isn't that what Vulcans say? or is it Klingons?
BTW I'm still wondering, as I have from the start of this thread, what "Twistor Theory" is.
I know some actual theories that USE twistor language but I don't recall hearing about a twistor theory "per se". Maybe you can explain.
Twistor theory uses, of course, twistor formalism. The Amplituhedron also uses the twistor formalism, and also some versions of string theory use it. The twistor formalism, as you said, was shown to be an adequate formalism to describe lqg. But twistor theory goes beyond that. As pointed out before, twistor theory was born long before string theory and loop quantum gravity. Twistor theory didn't add new physics, so in that sense, as you said, it's not an alternative. Nevertheless, it's aim was to unite GR and QM, not to modify them, as, for example, string theory
did (e. g.: susy, branes, strings, etc.). The point of twistor theory was to rewrite GR and QM by using the same formalism (it would change the formalism, not the physics). The twistor research program has split into two parts: the GR program and the QM program. For the last one, see twistordiagrams, a web page by Andrew hodges. See also "the twistor programe (R. Penrose)" and the chapter MORE RADICAL APPROACHES: TWISTOR THEORY", a chapter in The Road to Reality.
twistor theory. also Ed Witten found a relationship between twistor geometry and string theory. https://arxiv.org/abs/hep-th/0312171 Nathan Berkovitz is best researchers in this field.
Separate names with a comma.