Time dilation
In special relativity, the time dilation that will be experienced can be expressed with the formula:
where is the "proper" time experienced by the moving object.
is the relative velocity the ovject is moving to the observer.
is the speed of light; it can be simply expressed as 1, but then the velocity will have to be given in terms of .
is the time the events appear to occur, with the time dilation added.
This formula can be derived using a simple example. If there was a light clock that consisted of two mirrors with a light beam bouncing between them, the distance between the mirrors would be . If, the clock was inside a moving vehicle, than the distance the clock travels would equal . Finally, to an observer of the light clock, the light beam, instead of bouncing up and down, would move diagonally. The distance it appears to travel is . This forms a triangle, and using the Pythagorean theorem, it would obtain:
Subtracting by yields
Dividing by yields
Dividing by yields
Finding the root of both sides finally yields