relativity - Degrees of freedom in the infinite momentum frame

Lenny Susskind explains in this video at about 40min, as an extended object (for example a relativistic string) is boosted to the infinite momentum frame (sometimes called light cone frame), it has no non-relativistic degrees of freedom in the boost direction. Instead, these degrees of freedom are completely determined by the (non-relativistic) motions in the plane perpendicular to the boost direction.

I dont see why this is, so can somebody explain to me how the degrees of freedom are described in this infinite momentum frame?

Answer

Without seeing the quote/context I can only imagine that it means something like: if you take, say, a cube moving at close to c in the z direction, then (in the frame in which it's moving) its z extent gets Lorentz contracted to virtually zero, so it is effectively now a square in the xy plane and has only the degrees of freedom that a square in the xy plane has.