Long long ago, there was a story that four spaceships were sent out from the earth to fly in different directions. Their relative speed to the earth was 0.9c. According to the calculation of "special relativity", their time became slower. It's only 0.435 * the time of the earth. t' = t*sqrt*(1-v^2/C^2)
But one day the earth exploded, there was no residue left, so the four spacecraft lost their original reference. They could only make reference to each other, and found that there was a relative speed between them, so they were surprised to find that the time between them was different.
God, without the earth, the time on the spaceship will be different. With the earth, it will be the same again.
Who can explain it?
Thanks very much.
As long as the spaceships never meet up again, they will all disagree as to how much time has passed for each other. Every ship will claim that the other ships are aging slower. So if ship A and ship B are heading in opposite directions as they leave the Earth, then they will measure their relative speed as being 0.9945c, and each will say that the other ship's clock is ticking 0.105 the rate of his own. This is true even when Earth is in the scenario. In fact, every ship will also say that the Earth is the one aging slower than they are by a factor of 0.435 If the ships all stop, turn around and meet back up back where they started, they
then will all say that they aged the same amount upon return, and less than a clock that had been left behind.
The existence or non-existence of the Earth does not come into play at all. Their speeds aren't being measured with respect to the Earth itself, but the inertial frame that the Earth is at rest with respect to. That inertial frame is still valid even if there were no earth at all.
I think the problem here is that you only have a very superficial grasp of Special Relativity. You gave the time dilation formula, but don't actually understand what it really means, how to properly apply it, or the fundamental reasoning behind it. For example, your claim that the ships would all agree on their respective times, as long as the Earth is present.
In truth, after 1 year by his clock, ship A will say that ship B has aged only some 38 days, while ship B will say that after 1 year by his clock, Ship A has only aged 38 days. As measured from the Earth, (or the inertial frame the Earth is at rest with respect to), both ships A and B's clocks read 1 year, at the same time and when the Earth clock reads 2.3 yrs. ( Again, there doesn't actually have to be an Earth there, nor does this clock have to be located at the point where the ships started together, it only has to be at rest with respect to this inertial frame.)
Thus while anyone at rest to the initial reference frame will say that the clocks on ships A and B always read the same, Anyone at rest with respect to either of the ships will say that the ship clocks don't read the same time. This is the relativity of simultaneity in play. And until you come to terms with it, Special Relativity will continue to elude you.
