Principle of Special Theory of Relativity
Simple Explanation
Einstein's special relativity is built on two principles: the laws of physics are the same for all observers moving at constant velocity, and the speed of light in a vacuum is the same for every observer, regardless of their own motion. One striking consequence is time dilation: a moving clock runs slower, delta t=gamma times delta t_0.
Why Do We Need It?
Special relativity fundamentally changed our understanding of space and time — and its effects are not just theoretical: GPS satellites must correct for relativistic time dilation to remain accurate.
See It
A curve starting near 1 at low speed and rising steeply, approaching infinity as the speed ratio v/c approaches 1
Formula
Time Dilation
delta t = gamma times delta t_0, where gamma = 1 / sqrt(1 minus v squared over c squared)
A clock moving at high speed relative to an observer runs slower, from that observer's point of view — time itself passes at a different rate depending on relative motion.
- delta t
- — the time interval measured by a stationary observer, in seconds (s)
- delta t_0
- — the "proper time" — the time interval measured by an observer moving WITH the clock, in seconds (s)
- gamma
- — the Lorentz factor (dimensionless), always greater than or equal to 1
- v
- — the relative speed between the two observers, in metres per second (m/s)
- c
- — the speed of light, 3 times 10 to the power 8 m/s
When to use it: Whenever comparing how much time passes for two observers in relative motion at a significant fraction of the speed of light.
Worked Example
Find the time dilation for a fast-moving spaceship
A spaceship travels at 0.8c. If 10 years pass on board the ship (proper time), find how much time passes for an observer on Earth.
Why Does This Work?
Because the speed of light must be measured as the same value by every observer, an observer watching a clock moving at high speed must conclude that clock is ticking more slowly — otherwise, the two observers would disagree about how fast light itself travels, which special relativity's second postulate forbids.
Real-Life Example
GPS satellites correcting for time dilation
GPS satellites orbit Earth at high speed and must keep extremely precise time to give accurate positions.
Their motion causes a small but real time dilation effect — without correcting for it using exactly this kind of relativistic calculation, GPS positions would drift by several kilometres per day.
Practice
A spaceship travels at 0.6c. If 5 years pass on board (proper time), find how much time passes on Earth.
HardCommon mistake
Assuming time dilation only matters at truly extreme speeds — while the effect is tiny at everyday speeds, it is never exactly zero, and becomes significant (as shown here) once speed becomes a substantial fraction of the speed of light.
Quick Review
- delta t = gamma times delta t_0, with gamma = 1/sqrt(1 minus v squared over c squared).
- A moving clock runs slower, from a stationary observer's point of view.
- Confirmed by real-world systems like GPS satellites.