A rocket is drifting in gravity-free space and is observed by an external observer who is also drifting at an unchanging location using an arbitrary coordinate system. The rocket accelerates at a fixed rate using a massless photon engine that results in a negligible change in the mass of the vehicle. The propellant has energy-mass, but for now, assume it's negligible. An observer within the rocket sees an instant and constant acceleration (A) on his accelerometer. The rocket uses energy at a fixed rate of R. He can start and stop the engine and run it for any length of time, and he always sees the same acceleration A being used at the rate R. His total energy consumption (E) is then E = R * T. In other words, total energy usage is proportional to time. The external observer see the rocket begin to accelerate. He notes that the rocket has mass and assigns a value of 1 to this mass. He uses his own clock (t) and sees that rocket's measured velocity (v) is t * the observed acceleration (a). Thus, v is proportional to t. Thus, the astronaut sees total energy (E) is proportional to T. The external observers, using the kinetic energy formula ek = mv2 / 2, sees that total ek is proportional to t2 / 2. Since the kinetic energy has to come from the energy produced on the rocket, how can both be right? Thanks!