If one person was able to leave earth at one half the speed of light, at the end of the day when he looks at Earth, how many revolutions would it have made. At the speed of light, how many revolutions. Time and travel are linked only by 2 points in space and a unit of time measurement.
You will need to phrase this question in a different way, as it stands the only answer, is at the "end of the day" it will be 1 revolution. A
Assuming you wish to know what the person can see based on the time dilation effect applied to einsteins theory, the effect would be to double the number of days at half light speed(approximately)but interestingly the number of days at light speed would be infinite. Just does not make much sense does it.
You may find it easier to understand if you assume that the only difference is that the person ages at half as fast and stops ageing at light speed but actually experiences time (sic) the same as everyone else. This is of course not he accepted view but if you ask yourself what is time you will find no answer which gives you a physical quantity to measure.
Based on that,saying the Earth is a constant , the time traveler would see the earth slowing down until the earth stands still at the speed/o/light. Light waves are bouncing off the Earth and traveling toward him.The faster he travels the slower the light waves reach his eyes. Based that the Earth clock " the number of rev' are a given day" his days have stopped at the SOL. Of course that is not my belief. Every time line must have a point of origin. It does tickle our imagination. LOL
Even more interesting I have had some thoughts on all of this and I can no longer believe in time. At the best it is only a small part of the energy Sum for each and every atom. ie. There is no such thing as a quanta of time or any sort of temporal unit. It exists only as an interesting and unfortunate way of measuring a physical process which is part of matter. This is unfortunately rather inaccurate.
Consequently your original questions answer must conclude that the travellers experience of time is only relative to his own location, assuming that and if he were able to view his starting point without any intervening space/distance, he would experience and see the passage of events exactly as if they were proceeding at the correct pace. The only actual difference would be that his 'state' would be slowed and he would not be ageing as fast. So long as his speed did not preclude the electro chemical processes within his own body.
by the way the journey to this idea is long and confronting but does also point the way to a UFT and other far more dangerous things. I am worried.