The light-cone coordinates are defined as
$$x^{\pm} ~=~\frac{x^0 \pm x^3}{\sqrt{2}}.$$
Then in the light cone coordinates the position 4-vector becomes: $(x^+, x^-, x^1, x^2)$ .
Zwiebach, in his A First Course in String Theory [Second Edition,page-25], says that: There is no Lorentz transformation that takes the coordinates $(x^0, x^1 , x^2 , x^3)$ into coordinates $(x^+, x^-, x^1, x^2)$.
Why? What is the reason behind this?