Why Are the Angles in a Minkowski Diagram Equal for Different Observers?

[Powergade]

1. Homework Statement

In a diagram where I have two observers (one still (A) and one moving with a "v" velocity (B)), where the two parts disagre in the simultaneity of events, how can I prove that the angles of the B person axis that are put in the A person axis are equal. (/alpha=/beta , in the image U'.)

Homework Equations

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The Attempt at a Solution

I tried to show that the angles /alpha and /beta follow the same rate of change because the velocity of the B person is constant. Is it because the speed of light goes in a 45° angle? Do I need to calculate something?

 

[Andrew Mason]

Welcome to PF Powergade!

Forget what I said in my earlier post about trying to find the angle of the axes to the line x = ct using the Lorentz transformations. It is much simpler.

Use the Lorentz transformation find the equation for the t' and x' axes in terms of x and t (hint: the x' axis is defined by t' = 0). Then find the slopes of each of those axes (dx/dt) and compare them.

AM