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

AI Thread Summary
The discussion centers on understanding why the angles in a Minkowski diagram are equal for different observers, specifically between a stationary observer (A) and a moving observer (B). The key point is that the angles, denoted as /alpha and /beta, are equal due to the constant velocity of observer B and the properties of the Lorentz transformation. The participants suggest using the Lorentz transformation to derive the equations for the t' and x' axes, which simplifies the process of finding the slopes of these axes. The relationship between the angles is tied to the invariant speed of light, which is represented at a 45° angle in the diagram. Overall, the discussion emphasizes the mathematical approach to proving the equality of angles in the context of special relativity.
Powergade
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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'.)
241px-MinkScale.svg.png

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?
 
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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
 
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