Saturday, June 13, 2009

Everyone is running space-time at the speed of light!

Everyone knows the famous equation E=m of Einstein, because of its simplicity and it does not require advances Maths.
However, Einstein derived other equations, that I think are more
stunning and extraordinary.
In particular, he derived the following:
c²(∂τ/∂t)² + (∂x/∂t)² = c² where

τ : time in your clock
t : time in the framework of reference
(∂τ/∂t) : the velocity of your clock
(∂x/∂t) : your spatial velocity

It just says that, in reality, you have 2 velocities: the velocity of your clock (how fast it ticks) and your spatial velocity (the speed familiar to everyone, e.g. I am walking at 20km/h).

And we unify them by defining a velocity in space-time, v defined as the following:
v²=c²(∂τ/∂t)² + (∂x/∂t)²

The point is of course to note, that according to Einstein equation above in purple, always equals .
Beautiful isn't it?
In other words, every system in the universe, from a small particle to human beings, has the speed of light in space-time!

In particular, in the case of a photon,
(∂x/∂t)²=c² so (∂τ/∂t)²=0 , so we find that the clock of a photon is frozen! Time is stopped for a photon;

For systems like human beings or planet Earth,
(∂x/∂t)²~0 so (∂τ/∂t)²~1 (~ means close to) , which explains that time seems absolute and all the same for everyone of us.