W4-01 Examples of Time Dilation

This physics lecture focuses on solving two examples of time dilation from special relativity. The instructor begins by reviewing the time dilation formula, emphasizing the distinction between proper time (measured in the frame where events occur at the same location) and improper time (measured in a moving frame). The first example involves a person traveling on a bullet train at 180 km/h, measuring 5 hours between two stations with his wristwatch. The problem asks for the time interval as measured by station clocks. The solution calculates the Lorentz factor using the binomial approximation, yielding a negligible difference of 2.5×10^-10 seconds, illustrating why relativistic effects are imperceptible at everyday speeds. The second example considers a traveler moving at 5/13 the speed of light. The problem asks how often the traveler’s friend on Earth celebrates birthdays according to the traveler, and vice versa. The solution shows that the traveler observes the friend’s birthdays every 13 months, while the friend observes the traveler’s birthdays every 13 months as well, demonstrating the symmetry of time dilation. The lecture concludes by noting that at relativistic speeds, time dilation becomes significant, as in particle accelerators like the LHC.