Computer based activity to understand proper acceleration using the Rindler observer

TL;DR

This paper presents a computational classroom experiment using Excel and Python to help students understand proper acceleration and the behavior of Rindler observers in special relativity.

Contribution

It introduces an educational method that visualizes proper acceleration and time dilation for Rindler observers, enhancing conceptual understanding.

Findings

Students grasp proper acceleration through visualization.

The experiment demonstrates variable local velocity and time dilation.

All inertial observers measure the same maximum proper acceleration.

Abstract

Using elementary knowledge of Special Relativity, we design a computational classroom experiment in excel and python. Here, we show that any inertial observer $\mathcal{B}$ with an arbitrary speed $u_\mathcal{B}$ is associated with a unique event ${E}$ along the worldline of Rindler observer $\mathcal{R}$. The inertial observer $\mathcal{B}$ records the velocity of $\mathcal{R}$ to be non-zero at every instant except at this unique ${E}$ where it is co-moving with $\mathcal{R}$. At this event, $\mathcal{B}$ records a minimized distance to $\mathcal{R}$ and a maximized acceleration of $\mathcal{R}$ along its worldline. Students grasp the concept of proper acceleration when they realise that though an inertial observer measures variable local acceleration but this maxima is the same for all inertial observers. Since the Rindler observer is associated with variable local velocity the time dilation factors are different. Parameterising the Rindler velocity by proper time we graphically present the concept of time dilation. We assume $\mathcal{B}$ to be moving with respect to an inertial observer $\mathcal{A}$ which is at rest and their clocks synchronize to zero when they meet.