File:Time dilation spacetime diagram03.gif

English: This image represents a space-time diagram of Minkowski space-time continuum with one dimension of space and the dimension of time. In this diagram 1 unit of space is the distance that light travels in 1 unit of time.

For an object moving from point O in space-time to point A in space-time t3 units of proper time will elapse.
The line ${\displaystyle {\sqrt {(}}t^{2}-x^{2})=3}$ connects all the points in space-time that have in common that for an object moving from point O in space-time to any point on that line, 3 units of proper time elapse.
In Minkowski space-time, the proper time is a measure of the amount of separation between points in space-time. The line ${\displaystyle {\sqrt {(}}t^{2}-x^{2})=3}$ is a collection of all the points that are 3 units of proper time away from point O.

This image is designed to be used together with
Image:time_dilation_spacetime_diagram02.gif
Image:time_dilation_spacetime_diagram04.gif
Image:time_dilation_spacetime_diagram05.gif

Image:time_dilation_spacetime_diagram06.gif