Computer-based Activity to Understand Proper Acceleration Using the Rindler Observer

The absence of classroom activities dealing with concepts of instantaneously comoving inertial frames and proper acceleration has guided us to design a hands-on experiment using elementary knowledge of special relativity. We begin by posing the questions (1) what would be the worldline of an observer ℛ which has a constant spacetime interval from an inertial observer A ? and (2) what would be the speed and acceleration measurements of ℛ made by another inertial observer B moving relative to A ? We show that any inertial observer B with an arbitrary speed u_ B is associated with a unique event E along the worldline of Rindler observer ℛ. The inertial observer B records the velocity of ℛ to be non-zero at every instant except at this unique E where it is co-moving with ℛ. At this event, B records a minimised distance to ℛ and a maximised acceleration of ℛ along its worldline. Students grasp the concept of proper acceleration when they realise that though an inertial observer measures variable local acceleration, this maxima is the same for all inertial observers. Instructors can make good use of it to illustrate the concept of ‘proper’ acceleration not available in textbooks. The Python code is supplemented.