Time dilation means that the time interval between two events depends on the observer’s inertial reference frame. Calculate it using , where is the and is the .
Time dilation means that the time interval between two events depends on the observer’s inertial reference frame. Calculate it using , where is the and is the .
This is an Additional Higher Level concept in A.5 Galilean and special relativity (HL only). It follows from the postulate that the speed of light in a vacuum has the same value for every inertial observer.
One way to understand the mechanism is a light clock. A light pulse travels between two mirrors. In the clock’s rest frame, it follows the shortest path. An observer who sees the clock moving sees a longer diagonal path. Since both observers measure the same , that longer path must take more time.
As approaches , the denominator in decreases and increases, so time dilation becomes significant. At ordinary speeds, is approximately one.
The Lorentz factor is
where is the relative speed between the clock and observer, and .
The proper time is measured in the frame in which the two events occur at the same position. It is always the shortest measured interval. An observer who sees that clock moving measures the longer interval .
For example, a spacecraft travels at . A clock on the spacecraft measures between two events occurring inside it. Therefore,
An Earth observer therefore measures , while the spacecraft clock measures the proper time of .
A common misconception is that time dilation results from a faulty or mechanically slowed clock. It does not: all physical processes, including clock operation and particle decay, follow the same relativistic timing.
Exam technique: First identify which frame measures both events at the same location; that interval is . Then calculate , substitute into the data-booklet equation, and check that . For a Show question, include every algebraic and substitution step.