Let \(\mathcal I_1\) and \(\mathcal I_2\) be two inertial frames of reference moving relatively to each other with the constant speed \(v\) obeying the inequation \(0\le v < c\), where \(c\) denotes the constant speed of light1. If an observer inside the reference frame \(\mathcal I_1\) measures the time \(t_1\) elapsed in \(\mathcal I_1\) and compares it to the time \(t_2\) elapsed he observes in the inertial frame of reference \(\mathcal I_2\), then both times elapsed will show a difference called time dilation, which is given by the formula
\[t_1=t_2\cdot \gamma.\]
The factor \[\gamma:=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}},\quad\quad (0\le v < c)\]
is called the Lorentz factor2.
Explanations: 1
If both inertial frames of reference are in a vacuum, this speed equals \(c=299\,792\,458~m/s.\) ↩
Named so after Hendrik Antoon Lorentz (1853 - 1928). ↩
