Relativity Basics
Einstein’s special relativity redefines time and space, showing they depend on relative motion.
Time Dilation
Time slows for an object moving relative to an observer:
\[ t = \frac{t_0}{\sqrt{1 - \frac{v^2}{c^2}}} \]
Where \(t_0\) is proper time, \(v\) is velocity, and \(c = 3 \times 10^8 \, \text{m/s}\) (speed of light).
Example
A spaceship travels at \(0.8c\) for 10 seconds (\(t_0\)):
\[ t = \frac{10}{\sqrt{1 - \frac{(0.8c)^2}{c^2}}} = \frac{10}{\sqrt{1 - 0.64}} = \frac{10}{0.6} \approx 16.67 \, \text{s} \]
Applications
Relativity corrects GPS timing and is tested in particle accelerators.