Null spacetime directions
Null directions
The set of all null directions in (1,N) spacetime are projected on ND as the projection of the light cone.
Figure 1.3.1: Null directions in (1,1) spacetime and their projections in 1d space
Figure 1.3.2: Null multivector directions in (1,2) spacetime (2d projections)
Dynamic app 1.3.1: Null bivectors in (1,2) spacetime and 2d projection plane
Caption for dynamic app 1.3.1: Null bivectors in (1,2) spacetime and 2d projection plane.
Left: 2d projection plane, Right: (1,2) spacetime
Drag the green slider L around the circular projection of the Future
(blue) light cone.
The null plane is shown in red color, and the bivector direction is a
red diametral circumference (intersection between the null plane and the
unit sphere)
The projection of this null bivector is the red circumference (left)
which crosses the unit circumference diametrally, being tangent to the
Future light cone (blue) and the Past cone (violet color). Its center
lies on the unit circumference.
Figure 1.3.3: Null multivector directions in (1,3) spacetime (3d projections)
Dynamic app 1.3.2: Null trivector
Null trivector in 3d projection space (caption for dynamic app 1.3.2)
Drag the green slider C (the centre of the projected null trivector sphere) around the grey unit sphere.
The null trivector is projected as a red sphere which intersects the grey unit sphere at a diametral circumference (dc).
The null trivector is tangent to the inner blue sphere (projection of the Future light cone) in FL, and the opposite point LP is tangent at the violet sphere corresponding to the projection of the Past light cone, which is only shown as a small violet circle tangent to it.