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This answer gives a pretty unintuitive result. Apparently, acelerating at a constant rate without a speed limit takes longer (from the frame of reference of the traveler) than accelerating with one. I think it's unintuitive partly because it seems like accelerating for a shorter time would require less energy, and therefore should not be able propel you a given distance faster. But, while the power required to sustain constant acceleration in a Newtonian model is constant, that's not the case for a relatavistic model correct?

Obviously, despite my intuition, it's not valid to compare enegy requirements across different models, but I still think it's an interesting question. In which model, newtonian or relativistic, would it take more energy, $E$, to travel a distance, $d$ (from a frame of reference at rest), while accelerating with constant acceleration, $a$ (from the frame of reference of the traveler), starting from rest?

Vaelus
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  • "the power required to sustain constant acceleration in a Newtonian model is constant, that's not the case for a relativistic model correct?" Well, in both cases, the rocket's mass reduces over time as you burn fuel & eject reaction mass. But the amount of fuel you need to burn per kilo of the current rocket mass per second remains constant if you want the crew to feel constant acceleration. What the observers in inertial frames see is another story. You may like to take a look at my answer here. – PM 2Ring Jun 15 '19 at 19:56
  • Also see http://math.ucr.edu/home/baez/physics/Relativity/SR/Rocket/rocket.html – PM 2Ring Jun 15 '19 at 19:58

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