I have a fog in my brain as I am trying to wrap my head around a problem and I am not sure how to word it so I will do my best. If object A is moving near the speed of light but without acceleration then it could be said to be at rest. Measuring a beam of light that passes its position would come up with the expected answer of C. So object A decides to accelerate to achieve the speed of C (or near). We know this will take infinite mass-energy. So firing a rocket in this frame will accelerate the object, it will take energy, and it will increase speed. But I am trying to wrap my head around the image since the object A is already near the speed of light. (from the perspective of Z) It seems to me that this could all be taken as slices. That each frame of reference is taken individually and almost like its own little universe. A is near the speed of light, but only relative to another frame. (Z) When A measures a beam of light, the frame of reference switches to its frame, therefore all measurements are now changed (or recalibrated, or?) At this point its calculations of mass, energy etc are relative to itself so even though it is taking more energy the calculations work for it..... Hmmm seems to make more sense as i write it... almost like all frames of reference are warped bubbles and as you move from one frame to another the warping affect keeps all equations in line. The acceleration, from A's point, is moving from rest, firing a rocket and picking up speed. They are using, at first, zero energy and then burning energy to accelerate to the speed of light in their frame From Z's perspective A is already moving near the speed of light. No acceleration (energy already used to reach that speed) and then they expend more energy to accelerate. While A thinks they are moving at much greater velocity. Z's reference point might only see a small percentage change is speed and acceleration, BUT still below C (speed of light) My original thought got me confused because it occurred to me that the earth could be moving near the speed of light right now and we would not even know it. Then we fire a rocket to accelerate and it tries to reach the speed of light. Then it cuts its engines but continues without acceleration. It launches a ship and it accelerates to near the speed of light and so on... It was just an interesting thought to think the earth could already be moving near C from some point of view, but all our measurements are from our frame. I am starting to see the relationship between mass and energy now (even as I write) It will be relative to the frame you are in. We would measure a lot more energy in our current frame than an outside observer of our frame would. If that outside observer viewed us at a faster speed.