You have two trains sitting on the equator (one on each side of the equator so they don't collide -.-). Train one is moving East with the rotation of the earth, train two in moving west against it. both trains accelerate to a speed close to the speed of light, using the same amount of energy. So train one is moving near the speed of light plus the energy of the spin of the earth, train two is moving near the speed of light minus the energy of the spin of the earth. my question is would an outside observer on earth be able to measure a difference in the total speed of the two trains, and would an observer who is not on earth be able to measure a difference? My understand of this would state that an observe on earth would not be able to notice a difference and the two trains would cross at the same points, one for each side of the earth. But somebody who was not on earth would observe train one as moving faster than train two and would observe them as crossing at different points which has me.... thinking I need to understand this concept better.