Unformatted text preview: igid, the rest of the pole takes time to stop,
and hence compresses. In the runner’s frame, the back comes to rest inside the
barn after the door has closed.
(f) As you can see in the above spacetime diagram, in the friend’s frame, the pole
front hits the barn door after the back door closes (t, x) = (0, 0), while in the
runners frame it hits the front before (0, 0). The fronts of the pole and barn are
indicated in blue. The t axis coincides with the back of the pole. The dotted red
line indicates the best case speed of light signal that the front of the pole sends to
the back at the pole to “stop”.
3. Consider two events located at two spacetime points X1 and X2 ; now deﬁne the vector
∆X = X1 − X2 . Note all of these things are four-vectors; so in a general (primed)
coordinate system I have ∆X = (∆t, ∆x). I am calling this the primed coordinate
system because I am about to transform to one that I want to call unprimed: consider
rotating my (spatial) coordinate system so that ∆x points entirely in the x direct...
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