There is a spaceship, moving at a speed close to the speed of light.
The control room of the spaceship is in the front and the sleeping quarters are at the back.
One of the astronauts, Joe, decides to take a nap and floats back to his sleeping bag.
Will he be able to return to his post in the control room?
When he is sleeping, he is at rest with respect to the spaceship. However, to move to the control room, he must accelerate first, heading to the front, adding to his huge speed with respect to a "stationary" observer. But the spaceship is already going close to the speed of light, and there is this notion from a "stationary" observer's point of view that you must exert ever bigger forces to accelerate, the closer you already have got to the speed of light.
According to a "stationary" observer, Joe is close to the speed of light, and still accelerating by pushing the spaceship backwards. For the purpose of acceleration, he weights millions of billions of tons. Can his muscles keep up?
I understand that with respect to the spaceship, nothing strange happens, they are not accelerating, it is just like being on ISS. I don't understand, how to match this up with what an external observer moving slower can see?