Answer to Question #101454 in Mechanics | Relativity for Kishu

Question

Use tiur knowledge of geometry to show that the angle alpha between the worldline of an inertial observer and the light cone(draw in intertial frame using units in which light rays travel at 45 degees) is the same as the angle B between that observer line of simultaneity.

Answer 1

Draw the situation:

If the observer moves to the right, his or her worldline tilts to the right. To meet this worldline, the line of simultaneity also tilts up for the same angle. And since the lightcone is at 45° angle from both the horizontal and vertical axes, the angles α and β will be the same: they are equal 45° minus the angle between the time and the worldline, or the horizontal and the line of simultaneity. The same situation occurs if the observer moves to the left.