# Drawing spacetime diagrams with Alice and Bob

Following our standard conventions for drawing spacetime diagrams, draw four diagrams, with all the named points, hyperplanes, and individuals labeled on all four diagrams. Use graph paper.

The first two diagrams represent a situation in Galilean spacetime, described below. Follow our standard conventions for drawing Galilean spacetime diagrams.

a. The first diagram should be associated with Alice’s and Bob’s pre-acceleration inertial reference frame. (The pre-acceleration portions of their worldliness should be vertical.)

b. The second diagram should be associated with Alice’s and Bob’s post- acceleration point of view. (The post-acceleration portions of their worldlines should be vertical.)

The story of Alice and Bob. Alice and Bob are floating together inertially in outer space. Alice is to the left of Bob. They are mutually at rest. Relative to their shared rest frame, they are 50 feet apart. They synchronize their watches and, simultaneously (relative to their pre-acceleration frame), they both accelerate to the left. These accelerations are for all practical purposes instantaneous, and thereafter Alice and Bob are inertial, and mutually at rest, once again. The point on Alice’s worldline at which she accelerates is pa1, and the point on Bob’s worldline at which he accelerates is pb1. The hyperplane-in- their-pre-acceleration-rest-frame that passes through these points is h1.

After their accelerations, Alice and Bob drift inertially for a while. Then, at the same moment relative to their new post-acceleration rest frame, they both suddenly pop out of existence. The final point on Alice’s worldline is pa2, and the final point on Bob’s worldline is pb2. The hyperplane-in-their-post-acceleration-rest-framethat passes through these points is h2.

The next two diagrams represent the same situation aside from the fact that it is now set in Minkowski spacetime, and it includes the following additional component:

Additional component (for Minkowski spacetime only). At pa1, Alice sends out aray of light toward Bob. It hits him and reflects back toward Alice, and hits her. It continues bouncing back and forth between them throughout the rest of the scenario.

c. The third diagram should be associated with Alice’s and Bob’s pre-acceleration point of view. (The pre-acceleration portions of their worldliness should be vertical.)

d. The fourth diagram should be associated with their post-acceleration point of view. (The post-acceleration portions of their worldlines should be vertical.)

When drawing Minkowski diagrams, be sure that lines representing the trajectories of all light rays intersect horizontal lines across the page at a 45 degree angle. Draw these lines in yellow, by hand [do as I say on this point, not as I do].

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