How to travel faster than light - why wont this work?

[Erazman]

what if the size of our main spaceship was unlimited.
Let's say our spaceship is the size of our solar system.
Reach the highest speed possible without breaking any laws of physics.
Lets say -- 90% the speed of light.


Now fly a smaller spaceship INSIDE the main ship as fast as you can (lets say -- 90% the speed of light).

You are now traveling 180% the speed of light through space.

 

[Pengwuino]

The spaceship doesn't have to have an unlimited mass (which is also impossible) for this scenario. One of the basic rules of special relativity is that velocities don't add up like they do in normal Newtonian mechanics.

 

[JesseM]

See How Do You Add Velocities in Special Relativity? If the large ship is moving at 0.9c relative to me, and the small ship is moving at 0.9c in the same direction relative to the large ship, then according to the formula for velocity addition the velocity of the small ship relative to me will be (0.9c + 0.9c)/(1 + 0.9*0.9) = 1.8c/1.81 = 0.994475c. Basically, the reason velocities don't add the same way in relativity as in Newtonian mechanics is because each observer uses rulers and clocks at rest with respect to himself, with the clocks synchronized in his rest frame, to measure distances and times (and each observer defines velocity in his frame in terms of distance/time according to his own measurements). Since each observer sees rulers shrink when they move relative to him, and clocks slow down, and each rest frame has a different definition of what it means for clocks to be "synchronized" (this is known as 'the relativity of simultaneity'), this should give you a rough idea of why you can't just add velocities the normal way.