Saturday, 17 March 2018

Exercise 1.03 Events ABC

The question was; Three events, A, B, C, are seen by observer O to occur in the order A B C. Another observer, O', sees the events to occur in the order C B A. Is it possible that a third observer O'' sees the events in the order A C B? Support your conclusion by drawing a spacetime diagram.

I couldn't see how to do this without a space time diagram, moreover to make life easier I created excel charts for them so that I could easily compare temporal orders.

I started with a diagram like this

It shows the x, t coordinates that B must have to get the sequence ABC in O and CBA in O'. B must be inside the yellow parallelogram. The boost is 0.6.

Next we have a boost of  0.16.
For the temporal order ABC in O and ACB in O'', B must be in the green triangle. (Actually it is a an open sided parallelogram with the lower side at t = ta.)

To fulfil both the conditions, B must be in the overlap of the yellow parallelogram and the green triangle, which is a small triangle, shown here:
By this time I had moved A to (0,0) to make life easier.

It then became possible to draw a fateful triangle for various boosts. Here are a few samples.

To see all the workings read the pdf here.

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