World Science Scholars
26.8 Coordinates of Events in Stationary and Moving Frames
demonstration

The previous demonstrations provide practice with setting up the moving frame’s coordinate system. Now we use that understanding to determine the spacetime coordinates of an event in both the stationary and moving frames. Use the first two sliders to choose an event, described by its coordinates in the stationary $(t,x)$ coordinate system. Use the third slider to choose the velocity of the moving frame. The key thing is to note how the coordinates of the chosen event are determined: For the stationary frame, drop lines from the event that are parallel to the $x$ and $t$ axes. The intersection of these lines with the $x$ and $t$ axes give the $x$ and $t$ coordinates of the event. In the diagram, these lines are blue. For the moving frame, follow the same procedure. Drop lines from the event that are parallel to the $x^\prime$ and $t^\prime$ axes. The intersection of these lines with the $x^\prime$ and $t^\prime$ axes give the $x^\prime$ and $t^\prime$ coordinates of the event. In the diagram, these lines are pink. (Recall: The $x^\prime$ axis is the line $t^\prime=0$ and is marked as such; the $t^\prime$ axis is the line $x^\prime=0$, and is marked as such.)

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