Is there a speed/time relation? In other words, if I were were moving at half the speed of light, how much time (or "negative" time when moving into the past by traveling faster than light)would pass on Earth?
Can you put that into a graph or formula? Example graph:
1/2 C per minute = ? (time on earth)
Full C per minute = ? (time on earth)
+ 1/2 C per minute = ? (time on earth - or "negative" time)
1/2 C per minute = 100 years on Earth
So, Full C per minute = 200 years on Earth
You ask about traveling half the speed of light. Note that this must be defined with respect to the earth. If there were another object also moving at half the speed of light away from the earth in the same direction, the two objects would measure no time dilation with respect to each other, but both would measure it for the earth. Given the principle of relativity, the effect of such a time dilation would be 2/Sqrt (3) times the rest frame time. So people on earth see the people on the rocket move that much slower. However, people on the rocket observe people on the earth moving that much slower as well, by relativity. The only time you can find out who aged more is if you turn one around. Otherwise earth sees the rocket as being time dilated slower, and the rocket sees the earth getting time dilated slower in the same way. If the rocket turns around, then there's an acceleration (not just a frame change) that causes the discrepancy in age (people on the rocket age slower). However, if instead we accelerated the earth towards the rocket to catch back up to it, then it's the people on the earth that will age slower than the people on the rocket!
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