Einstein's velocity additon formula in Space?how come the sum is always less then relative velocity?

Answer 1

When Einstein illustrated the relativity example of the ship and the sailor dropping the stone from the top of the mast,the sailor saw it drop straight down the mast,the observer on the dock,saw it drop at an angle,the hypotenuse of the mast height and the distance the ship traveled/
. He extended the mast height to one light second and said the rock would still land at the base of the mast,which seemed wrong,
He thought about it that night,next day he said,change one side of the equation and leave light at a constant,the rock will land at the base of the mast.
It still traveled the hypotenuse which was clearly greater than the mast height [One light second] and the distance the ship traveled.
If the ship traveled 1 and the height of the mast was 2 the hypotenuse had to be the square root of one squared plus two squared which equals The square root of five which is 2.2.
At the speed of light the rock could not have landed at the base of the mast without violating the speed of light,which is clearly impossible.

Answer 2

In laymens terms its because at sufficient velocities, and if the observer is in motion as well, the value used in the equation becomes negative.

Suppose ship A is moving at .9c and ship B is moving at .8 c and they are coming straight at each other. Now how fast does ship A see ship B moving? Here is the equation:

u' = v_b - v_a / 1 - ((v_b x v_a)/c^2)

where v_a = .9c and v_b = .8c
and u' = the speed of B as seen by A

So the acutal answer when you do the math is

-0.35714285714285715 c

thats right its a negative number because from A's point of view B is moving away. It ISNT intuitive, thats the point and thats why its difficult.

Because of the combined relativistic effects and the fact that velocities have to transform according to Lorentz transformations, this is the way it works.

I know that might not be satisfactory, but it works because it works. Einsteins equations on special relativity have held up for 102 years, and general relativity for 90 or so years. And dont think experiments and other people havent tried to discredit the equations, it just hasnt worked!