This relates to the post here.
There are three dimensions of motion with two measures of the extent of motion, which makes a total of six metric dimensions of motion. But these six metric dimensions collapse into two structures of one and three dimensions as the conversion factor approaches infinity.
With the pace of light, k, the invariant proper length, dσ, is:
dσ² = dr² – dt²/k² = dr1² + dr2² + dr3² – dt²/k² = dr² – dt1²/k² – dt2²/k² – dt3²/k² = dr1² + dr2² + dr3² – dt1²/k² – dt2²/k² – dt3²/k².
As the pace of light approaches infinity this becomes
dσ² = dr² = dr1² + dr2² + dr3².
That is, the time coordinates separate from the invariant length, which becomes the Euclidean distance of three dimensional space. Time is left as an invariant scalar called the time.
Similarly, with the speed of light c, the invariant proper time, dτ, is:
dτ² = dσ²/c² = dr²/c² – dt² = (dr1² + dr2² + dr3²)/c² – dt² = dr²/c² – dt1² – dt2² – dt3² = (dr1² + dr2² + dr3²)/c² – dt1² – dt2² – dt3².
As the speed of light approaches infinity this becomes
dτ² = – dt² = – dt² = – dt1² – dt2² – dt3².
That is, the length coordinates separate from the invariant time, which becomes the Euclidean distime of three dimensional time. Space is left as an invariant scalar called the stance.
The result is that six dimensional spacetime collapses into 3D space with scalar time or 3D time with scalar space.