What Is Minkowski Diagram?

This section provides an introduction of Minkowski diagram, which represents the Lorentz Transformation overlaying a moving frame into a stationary frame.

What Is Minkowski Diagram? Minkowski diagram is a spacetime diagram that overlays a moving frame into a stationary frame to represent Lorentz Transformation in a geometric model.

Using the same thought experiment in the previous section as an example, the Minkowski diagram from Bob's point of view can constructed as below:

• Draw an orthogonal coordinate system of (x,ct) to represent Bob's frame.
• Draw the ct' axis of Amy's frame along the worldline of Amy's location.
• Draw the x' axis of Amy's frame by flipping ct' axis against the light cone line.
• Scale ct' as (sqrt(1+(v/c)**2)/sqrt(1-(v/c)**2))*ct.
• Scale x' as (sqrt(1+(v/c)**2)/sqrt(1-(v/c)**2))*x.

For a given event E=(X,cT), the (X',cT') coordinates calculated by the Lorentz Transformation can be read from the Minkowski diagram geometrically:

• Draw a point E at (X,cT) in Bob's frame.
• Read X' value on x' axis by projecting E along ct' to x'
• Read cT' value on ct' axis by projecting E along x' to ct'

For example, assuming the train is moving at the speed of 0.6*c, an event E at (X,cT)=(5.5,6.5) on Bob's light cone would be observed by Bob in Amy's frame as (X',cT')=(2,4) based on Lorentz transformation.

The following picture shows a Minkowski diagram of the above example produced by the interactive Minkowski diagram tool at http://www.trell.org/div/minkowski.html: