Illustration 5: Understanding Spacetime Diagrams

Animation 1 Animation 2 Animation 3

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One of the most useful ways to visualize moving objects in special relativity is with spacetime diagrams.  Restart.  Consider the animation of a woman walking (position given in meters and time is given in seconds).  The motion of the woman in Animation 1 is rather ordinary and is plotted on a position versus time graph as well as in a data table.  Notice, as in kinematics, that the speed of the woman can be determined by the slope of the position versus time graph (in this case 1 m/s). 

Now consider what is being represented in Animation 2.  In this animation, time is plotted versus position.  The graph is the same as Animation 1 with the axes flipped.  This way to represent the motion of the woman is almost what physicists would call a spacetime diagram.  Two things are missing: we want to treat the time on the same footing (as far as units) as the position and we need to take into account the universal speed limit, c.

Animation 3 puts time on equal footing with position.  What has been done is to multiply time by the speed of the woman.  Therefore, velocity*time is plotted versus position.  This converts the unit of time into meters.

v / c =  

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Finally, we need to take into account the universal speed limit of the speed of light.  Restart.  In Animation 3 it made some sense to multiply the time by the speed of the woman.  For a true spacetime diagram, we multiply the time by the speed of light.  The unit of the y axis now becomes the amount of time it takes for light to travel one meter or 3.33 X 10-9 seconds.  Select  v / c to be zero and then press the set value and play button.  Notice that the woman does not move in space but moves in time.  Now try a v / c of 0.9.  What does her "trajectory" or "worldline" on the spacetime diagram look like now?  As v / c gets bigger (approaches 1) the trajectory of the woman on the spacetime diagram approaches the line of v = c.  This is the 45 degree line of slope 1 that appears on the graph.  Now try a v / c of -0.9.  Since nothing can travel faster than the speed of light, an object that begins at the origin is forced to have a worldline between the two lines on the graph.  The only object that can have a worldline on either of those lines is light.  If we let the woman move in two dimensions her motion would be constrained to move within a cone which is called the lightcone.  The one's boundaries mark the possible worldlines that light can have if it starts at the origin at t = 0 m.



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