The equation that allows us to calculate stuff in special relativity!
Take two observers with identical rules and stopwatch, and aligned axes, but one is on a car moving at towards the direction at speed .
When both observe an event, if we denote:
It is of course arbitrary who is standing and who is moving, we will just use the term "standing" for the one without primes.
- the observation of the standing observer
- the observation of the ending observer on a car
Note that if tends towards zero, then this reduces to the usual Galilean transformations which our intuition expects:
This explains why we don't observe special relativity in our daily lives: macroscopic objects move too slowly compared to light, and is almost zero.