Physics · Modern physics. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
Einstein built special relativity on two postulates. First, the laws of physics are the same in all inertial frames. Second, the speed of light in vacuum is the same for all inertial observers, whatever the motion of the source or the observer. The Michelson–Morley null result agrees with this.
The results follow. A moving clock runs slow (time dilation), a moving rod is shorter along its direction of motion (length contraction), and events simultaneous in one frame need not be simultaneous in another. Each effect is governed by the Lorentz factor γ, which is 1 at rest and grows without limit as v approaches c.
Mass and energy are equivalent, and no body with rest mass can reach c because its energy would become infinite.
Applying γ the wrong way round. The proper time is the shortest time and the proper length is the longest length; every other observer measures a longer time and a shorter length.
Answer: 72 m; 3.0 × 10−7 s (0.30 μs).
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