Minkowski Spacetime: The Geometry of Special Relativity
These diagrams help us picture relativity paradoxes
Visualizing 4th-dimensional relativistic spacetime on a 2-dimensional diagram may seem like a tall order. Hermann Minkowski, a teacher of Albert Einstein, developed a way to do just that. These spacetime diagrams can help us see the geometry behind special relativity. Here’s how they work.
You may be familiar with a similar diagram from high school physics. We plot time on the horizontal axis and displacement on the vertical axis.
In Figure 1, a car moves forward at a constant speed. It stops. It reverses at constant speed past the starting point. It stops.
This diagram takes the motion of the car in one dimension and maps it to two dimensions, plotting its position against time.
A Minkowski diagram is similar. However, we plot time on the vertical axis. In the theory, all of 3-D space is compressed into the horizontal axis. However, here we will consider motion in only one dimension. The path taken by a body is its worldline.
We’ll use a scale such that the motion of a photon follows a worldline at 45⁰ to the horizontal (dotted line, Figure 2). We include two reference frames in the one diagram. They share a single worldline for the…
