Answer to Question #98253 in Mechanics | Relativity for AbdulRehman

Question

For this problem, consider three inertial observers: You, Alice, and Bob.
All three of you meet at one event where your watches all read zero. Alice
recedes from you at 1
2
c on your left and Bob recedes from you at 1
2
c on
your right. Draw this situation on a spacetime diagram in your frame of
reference. Also draw in a light cone from the event where you all meet.
Recall that you measure distances using your own lines of simultaneity,
and note that you find each of the others to be ‘halfway between you and
the light cone’ along any of your lines of simultaneity.
Now, use the above observation to draw this situation on a spacetime
diagram in Alice’s frame of reference. Use this second diagram to estimate
the speed at which Alice finds Bob to be receding from her. What happens
if you draw in another observer (again meeting all of you at t = 0) and
traveling away from Bob on the right at 1
2
c as measured in Bob’s frame of
reference??

Answer 1

The first situation is shown below:

Bob's space-time diagram is green. Alice's is red, yours is blue.

In Alice's frame of reference you move toward her right at 1/2c, Bob moves away from toward her right as well with speed close to c:

Bob's lines are very close to the cone of light. If we add an observer which moves away from Bob at 1/2c, in Alice's red frame of reference the t- and x- lines will be indistinguishable.