Causal Order of Limits: Timelike, Spacelike, or Lightlike (1/2)

1. Start with the differential element:
   


2. Rescale to the Lorentz invariant interval :
   :
   


3. If the rescaled differential element's 3-vector goes to zero first, velocity approaches zero.
   The interval between the differential elements is timelike.
   Classical mechanics applies.