W3-03 Derivation of Time Dilation

This video is a physics lecture on the derivation of time dilation in special relativity. The instructor begins by reviewing a light clock constructed in a previous session, consisting of two mirrors separated by half a light-second. He then considers two inertial frames, S and S’, with S’ moving at velocity v relative to S. Each frame has an identical light clock. Observers in each frame see the other’s clock running slow due to the longer path light must travel in the moving frame. The concept of proper time interval is introduced: the time interval between two events that occur at the same spatial location in a given frame. The proper time is denoted Δτ, and the improper time interval (measured in a frame where events are separated in space) is related by the time dilation formula: Δt = Δτ / sqrt(1 - v^2/c^2). The instructor then derives this formula using the Lorentz transformation equations, showing that the time interval in the moving frame is larger than the proper time. The video concludes by emphasizing that time dilation is a fundamental consequence of relativity, independent of the clock’s construction.