The Interactive Space Time Diagram is an interactive space time diagram that allows you to visualize the concepts of Einstein's Theory of Special Relativity without needing to know any of the math. The tool does the calculations, Lorentz transforms, for you. This helps you to focus on understanding the motion of objects relative to each in other in space and time.

How it works

The diagram's vertical axis shows time, where each mark represents one tick of the object's clock, to keep it simple one can assume that each tick equals 1 second.

The horizontal axis shows the distance traveled by light during a tick of the object's clock. Given our 1 second assumption, each mark represents 1 light second or 299,792,458 meters.

The vertical neon green line on the diagram is the world line of the reference object. Each circle represents an event (not a location). A world line shows the link between events over time. The line is vertical because the object is not moving.

The orange diagonals represent the speed of light, more specifically the world lines of two photons each traveling from the origin at the speed of light in opposite directions. The area beneath the orange lines is greyed out. To reach this area an object would need to travel faster than the speed of light, which is not possible.

Add an object

To add an object to the diagram, begin by clicking the “Add” button with the “+” emoji. This will point you to the "Add new object" input form. Fill in the form following these steps:

  • select an emoji to identify the object on the diagram;
  • enter the object's velocity as percentage of the speed of light;
  • optionally you can enter a starting position, by default a new object will begin at the origin;
  • press blue "Add" button.

The new object's world line will then appear on the diagram. The circles with the emojis represent events that occurred at each tick of the reference object's clock (1 second intervals based on our assumption from above). These points do not represent a x,y position as one would see in a Cartesian coordinate system. You will notice that as you switch to another object's perspective these points will change relative to each other. They will either be squeezed closer together or stretched further apart.

Boost to change perspective

To change perspective, click on the new object's button. This will perform a Lorentz transform or “boost” the world lines and show the diagram from the new object's perspective. The new object's world line will now be in the vertical position, and the circles will be squeezed closer together. That is the events that appeared to occur at 1 second intervals from the reference object's perspective, occur at shorter intervals when viewed from the new object's perspective. This is what is referred to as time dilation.

Hyperbolae the spacetime intervals

It may appear that the emoji circles, are squeezed or stretched arbitrarily. This isn't the case. You will notice that for each object there is a set of nested hyperbolic curves shown. These curves are the space-time intervals. These curves remain fixed, that is, they do not move when viewed from different perspectives. When the perspective changes then the events move but always remains on it's respective curve.

Add more

You can add up to six objects to the diagram and switch between each object's perspective. You can also customize the chart title, add a description of what is shown, then save and share a link to your diagram with your friends, who can then leave comments.

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Space Time Diagram

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🌐 Space(x) Time(ct)

Object World Lines

Click on the "Add" button to add a new object world line or click on an object button to "boost" to its perspective.

Object 1

Viewing from this object's perspective

Add new object

Diagram Description:

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Space Time Diagram