Online Course Support | Understanding Einstein: The Special Theory of Relativity

Bob is moving to the right (positive x direction) in his spaceship at a velocity v, and Alice is observing him. If we want to draw Bob’s world line on Alice’s spacetime diagram, how do we figure out where it goes?

ByAdmin July 28, 2021July 29, 2021

Because Bob is moving to the right, the Lorentz equations show that his world line will be at a 45 degree angle to Alice’s time axis.

Bob’s world line in his frame of reference is the line where x_B equals 0, so substitute that into the appropriate Lorentz transformation to find a relationship involving x_A and t_A, which can be plotted on Alice’s diagram.

Bob’s world line is the line where t_B equals 0, so substitute that into the appropriate Lorentz transformation to find a relationship involving x_A and t_A, which can be plotted on Alice’s diagram.

Bob’s world line will be identical in both his spacetime diagram and Alice’s spacetime diagram, so there’s no need to figure anything out.

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Online Course Support | Understanding Einstein: The Special Theory of Relativity

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