Special Relativity Visualizer – AP Physics 2

Learning Objectives

Understand proper time ($\Delta t_0$) vs dilated time

Observe length contraction ($L = L_0/\gamma$) along the axis of motion

Compute the Lorentz factor ($\gamma$) as $v \to c$

Trace the diagonal path of a light clock in a moving frame

Key Equations

$ \gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} $

$ \Delta t = \gamma \Delta t_0 $ (Time Dilation)

$ L = \frac{L_0}{\gamma} $ (Length Contraction)

Why It Matters

At relativistic velocities, time and space are not absolute. The speed of light $c$ is constant for all observers, meaning coordinates must transform according to the Lorentz transformations. This underlies modern astrophysics, GPS satellite calibration, and quantum electrodynamics.