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History1
History2
β
Animate
 
 

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Boost Histories

Look for the toothpaste effect: events are stretched apart in some cases, and squeezed together in others.

Different inertial grids have different coordinates for events. Here, two grids, Grid 1 and Grid 2, differ by a boost, in which Grid 2 is moving along the x-axis of Grid 1, at a speed β, with -1<β<1. The sign of β indicates if Grid 2 moves in the +x direction, or the -x direction.

Given the coordinates of an event as measured in Grid 1, you use the boost transformation to find the coordinates for the same event, as measured in Grid 2.

The form lets you input multiple events for each of the two separate histories. For example, this input for a history:

-100,-150,100,175
generates these two events:
(x,ct)=(-100,-150)

(x,ct)=(100,175)
These events are joined by a line to make a history. If you entered 3 events, then they would be joined to form a single history as well, and so on. Black dots represent the ticks of a wristwatch. The tick marks stretch out as Γ increases.

The units used in this chart aren't specified. It shows values only within a certain range, about +/- 225 or so.