Spacetime Maps

Previous section: Defining Spacetime.

Next section: Particle History and Proper Velocity.


Spacetime maps are essential for physical interpretation of GA equations in relativity theory.

X 3 X 2 X 1 X 0 Spacelike lines through Xo (red) Lightlike lines through Xo (blue) Timelike lines through Xo (green) Forward light cone Backward light cone Absolute Past Absolute Present Absolute Future


This is a spacetime map showing the lightcone for an event X0 . Events Xk (k = 1, 2, 3) lie on straight lines passing through X0. Displacements ∆Xk = Xk − X0 are said to be timelike, lightlike, or spacelike, respectively, as they lie inside, on, or outside the invariant lightcone.

X 1 Spacelike lines through Xo (red) Lightlike lines through Xo (blue) Timelike lines through Xo (green) Absolute Past Absolute Present Absolute Future X 2 = X X 0 = 0 → x → x ct cτ


This is a spacetime map of events in a timelike plane showing the position vector x = X2 − X1 for the event X = ct + x with respect to a given inertial system.


A differentiable curve in spacetime is said to be timelike, lightlike, or spacelike if its tangent is proportional to, respectively, a timelike, lightlike, or spacelike displacement.




Previous section: Defining Spacetime.

Next section: Particle History and Proper Velocity.


© David Hestenes 2005, 2014