Imagine a stationary person (with respect to a spaceship) floating in space and looks at a clock on the spaceship going 0.5c and sees it's clock ticking slower than his own, and concludes that it is moving closer to the speed of light than himself...
I learned recently that people on the spaceship will actually see the 'stationary' person's clock ticking not faster, but slower also, with respect to the spaceship's clock, which would make the spaceship person conclude that his spaceship was stationary and the floating man was moving the opposite direction at 0.5c.
My question is this... when physics says we can't move at the speed of light, I ask, with respect to who? The floating man calculates that he is moving at 0c and can accelerate all the way to 1c. But the person on the spaceship is moving, but concludes that he is stationary, so he calculates that his speed is 0c and he can accelerate all the way to 1c. If the man in the spaceship accelerates all the way to 0.99c with respect to his own reference frame, then the stationary person would see him accelerating from 0.5c to 1.499c, faster than light.