My head is spinning from Penrose's treatment of twistors. Isn't it essentially a special sort of spinor?

 

[math]Z^{/alpha} = (\omega^{A}, \pi_{A'})[/math] where Z is a twistor.

 

Also, why is the linear and angular momentum used? Can't I use, say, something else that satisfies: [math] \omega^{A} = i r^{AA'}\pi_{A'}[/math];

[math]\frac{\omega^{A}}{\pi_{A'}} = ir^{AA'}[/math] or am I on the wrong track totally?

Are you reading this from his "Road to Reality" or the second volume of his and Rindler's book on spinors/twistors?

I first came upon them in Three Roads to Quantum Gravity by Lee Smolin, then I dug them up in the internet.

 

I have read his book Road to Reality and from his description, it's just a more complex spinor. Rather than working with two axes, one works with four? Is that it? Or am I way off?