# What is the physical/philosophical motivation for twistors?

#### MTd2

Gold Member
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?

Related Beyond the Standard Model News on Phys.org

#### 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

Gold Member
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.

#### MTd2

Gold Member
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

Last edited by a moderator:

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving