Two astronauts in space compress a lightweight spring. After using it to fling themselves apart, they measure and agree their relative speed. Using special relativity, each astronaut calculates that the other's mass has increased by a millionth. But the rest mass of one was twice that of the other, so he gained twice the energy. How do they agree how much energy they put into the spring?

Observers remaining at rest would measure two relative speeds, not one, and would disagree even with the sum of the astronauts' estimates (special relativity's mass equation being non-linear).

Here is a slightly shorter paradox:

www.freephysics.uk/Strobe-paradox-01.pdf