Spacetime diagrams

Spacetime diagrams are graphical representations of spacetime events as seen by an observer.
They combine the dimensions of space and time into a single diagram, often using two spatial dimensions and one time dimension.
Representations of events in spacetime diagrams are commonly known as worldlines.

Understanding Spacetime Diagrams

Space is usually represented on the x-axis and time on the y-axis. The units of measure are often light-years for distance and years for time.
Each point on the diagram represents an event in spacetime.
The path that an object takes through spacetime is called its worldline.
On Earth, we all move slowly compared to the speed of light, so our worldlines are nearly vertical.
The worldline of a beam of light is a 45-degree line on a spacetime diagram.

The slope of a worldline on a spacetime diagram shows the object’s velocity, with steeper lines indicating slower speeds and shallower lines indicating faster speeds.
The spacetime diagram illustrates how observers moving at different relative speeds will perceive time and space differently. This is known as time dilation and length contraction.
A worldline can also bend or curve if an object is accelerating.

Light Cones: These are regions on a spacetime diagram that show all possible directions for light emanating from a point. The future light cone includes all possible locations for light to reach in the future, and the past light cone includes all possible locations light could have come from in the past.
Simultaneity: It’s important to remember that two events being simultaneous in one frame of reference may not be simultaneous in another frame. This is clearly shown on spacetime diagrams and is a direct consequence of special relativity.
Invariance of Light Speed: One of the key postulates of special relativity – that the speed of light in a vacuum is the same for all observers – is clearly visible on spacetime diagrams.

Spacetime diagrams provide a useful visual representation of how special relativity works.
They help to grasp significant concepts such as time dilation, length contraction, and the relativity of simultaneity.
They are key tools in theoretical physics, especially in understanding relativistic effects.