Surpassing the speed of light?

[mrcross555]

Lets say we manage to build a spaceship 30miles wide and long that is capable of reaching to 99.99% the speed of light. Now inside this massive spaceship we have a particle accelerator. The spaceship is now traveling just a fraction under the speed of light when we decide to fire up the particle accelerator inside. The path of these particles going in a loop at one point travel the same direction as the spaceship. If these particles inside the spaceship also reach 99.99% the speed of light (as if the spaceship were at a standstill) Would they not, in reality, be going much faster then the speed of light? Or would time slow so dramatically on the actual spacecraft to allow these particles not break the light speed?

 

[Pengwuino]

Or would time slow so dramatically on the actual spacecraft to allow these particles not break the light speed?

In a sense, yes, relative to someone watching the spacecraft zoom by at 99.99% the speed of light. It's a simple special relativistic velocity addition problem that will yield something less than the speed of light. Check out the FAQs.

 

[HallsofIvy]

If your spaceship is moving at speed u relative to some frame of reference and your particles are moving at speed v relative to your space ship, then the speed of the particles relative to the frame is
$$\frac{u+ v}{1+ \frac{uv}{c^2}}$$
As long as u and v are less than c, that will be less than c.