asdff529 said:
My teacher gives me an explanation about this:
A moving clock(observer B) runs slower actually means it is slower comparing to two stationary clocks at different locations.
That's a useful way to think of it.
asdff529 said:
Does it have something to do with relativity of simultaneity?
Absolutely! One way to set up an example of "observing" time dilation is as follows. You, on the ground, set up clocks at points A and B, far apart. Now let that moving clock (in a rocket, say) move along, passing your A clock and then your B clock. You set things up so that when the rocket passes next to each clock, some mechanism at each clock records the time showing on the moving clock and the time showing on your clocks.
So some imaginary data might be as follows. When the rocket passes clock A, both the rocket clock and clock A show a reading of 1 pm. When the rocket clock passes clock B, the rocket clock shows 1:20 pm and clock B shows 1:30 pm. So, using this data, you calculate that the moving clock must be running slow, since it only shows 20 minutes having passed when you have clearly measured 30 minutes by your clocks. (As ghwellsjr explained, you don't directly "see" the time dilation, there are calculations and assumptions involved. That's why I put "see" in quotes.)
So what does the guy in the rocket say about all this? Well, relativity works for him too, so his observations must allow him to conclude that
as measured by his clocks it is
your clocks that are running slowly. That's where the relativity of simultaneity comes in. Whereas you have arranged things so that the clock at A and the clock at B are synchronized according to you, the rocket observer would measure that clock B is set ahead of clock A. So,
according to the rocket observer, when clock A shows 1 pm, clock B already shows 1:17 pm. (I'm just making up data here, but it would be something like that.) So, when the rocket measures the time to get from A to B, he gets 20 minutes, but he would say that clock B only went from 1:17 to 1:30 during his trip, so a time of only 13 minutes elapsed on your clocks. That leads him to conclude that
your clocks are running slow, when compared to his.
asdff529 said:
I also heard of Hafele-Keating experiment.And it comes out one clock is actually slower than the other clock.
Doesn't it contradict that both "see" the other's clock as running slowly?
No. As others have noted, that's a bit more complicated than simple time dilation. So stick to the simple case first.
