# 3 space and 1 time

by K S Mallesh
Tags: space, time
 P: 410 There is a relationship between spacetime and spinors, but it isn't the one that you think (although I will ponder upon it). You can assign to every 4-vector satisfying $$v^2 = 1$$ a 2x2 special unitary matrix satisfying $$\det u = 1$$, etc. Now SU(2) matrices transform as two copies of SU(2), whereas spinors transform as one copy. So it is often said that spinors are "square roots" of vectors. There's a related construction for null vectors and this goes by the name of twistors.