What is the physical/philosophical motivation for twistors?

[MTd2]

When I look for it, the best I can come up with are things related to making calculations simpler. But I would like something deeper. The best thing I could find is this:

In the (translated) words of Jacques Hadamard: "the shortest path between two truths in the real domain passes through the complex domain."

http://en.wikipedia.org/wiki/Twistor_space

So, it looks like that a shorter then shortest path can be found by making an analytic continuation to complex numbers. Given that Penrose like the Plato's allegory of the cave, I suppose that the shortest path is not in the cave, but in the space from where the projection comes from. Or the true shapes are not in the shadows but behind it.

I am not sure of these things. What do you people think?

 

[sheaf]

Well I think part of it was that, in the quest for some sort of union of quantum mechanics and GR, Roger Penrose considered that the causal structure of spacetime had some special status. Since the causal structure was encoded in the light rays, it was natural to consider the space of light rays (which is "projective null twistor space"). In the flat space picture, the natural completion of this space had an interpretation in terms of a complexification of Minkowski space. The space of null twistors divided the full twistor space into two halves which played a part in the description of positive and negative frequency fields on spacetime.

The "Penrose Transform" allows a very nice mapping between zero rest mass fields on spacetime and equivalence classes of functions on twistor space (strictly elements of various sheaf cohomology groups).

 

[MTd2]

You are giving me an idea of what the mathematical definition looks like. But I know the definition. What I cannot understand was what motivated that definition. Why not something else? Also, saying space of light rays is a bit vague given that a light ray is just a null cone on minkowski space, and not including some weird kind of transformation.

 

[martinbn]

You are probably aware of this and it is not what you are looking for, but just in case here it is

http://users.ox.ac.uk/~tweb/00001/

 

[MTd2]

Yes, that's the first thing I met. But it involves reading papers which I do not have access.t seems that a lot is missing, if one just reads that text.

 

[atyy]

Krasnov gave an interpretation in http://arxiv.org/abs/hep-th/0311162

Andrew Hodges has a motivational talk at http://online.kitp.ucsb.edu/online/qcdscat11/hodges2/

Penrose has some amazing slides at http://people.maths.ox.ac.uk/lmason/Tws/Penrose1.pdf & http://people.maths.ox.ac.uk/lmason/Tws/Penrose2.pdf

It seems he somehow wanted quantum gravity to be about fuzzy points, not fuzzy light cones. So he made the spacetime point into a Riemann sphere, and light rays became points.