Light Cone Coordinates Explained

[JonnyMaddox]

Hi guys, I'm trying to understand light cone coordinates for which I uploaded this picture. The light cone coordinates are given by
$x^{+}= \frac{1}{\sqrt{2}} (x^{0}+x^{1})$
$x^{-}= \frac{1}{\sqrt{2}} (x^{0}-x^{1})$

Now how should I think of this? I guess the space curves do only life in the space that is spanned by the $x^{0}$ and [itex]x^{1}[/latex] axes. But what does it mean that a light curve is zero in this coordinate system?

 

[Nugatory]

It means that a flash of light emitted at the origin travels along the two axes (because we chose them that way - that's what makes these coordinates "light-cone" coordinates). One axis is described by the equation $x^{+}=0$ and the other by $x^{-}=0$, just as in Cartesian coordinates the y-axis is described by $x=0$ and the x-axis by $y=0$.