Relativity?

Question

Suppose that you are in the vacuum very far from everything, so gravity doesn't affects you so much. You are with a friend, and both of you has a digital clock. Both of you decide to coordinate the clocks. Then both of you decide to "travel" with a constant velocity and then come back to were you were, to compare the clocks. In your point of view, your friend's cloks is late compared to yours, and your friend has the same feeling, in his case it's your clock that is late. So when you come back to see the clocks, which is really late?

Answer 1

Mistress Bekki is correct.

Everyone remembers that "moving clocks run slow" but forgets the key to solving these "paradoxes" is that from the perspective of the accelerated observer, the readouts on the clocks when you return are affected most not by the rate at which the clocks tick, but by the shift in simultaneity when you turn around.

What you consider to be "now" in a distant location very sensitively depends on your speed. When you change that speed by accelerating and turning around, the event you consider to be "now" back at the starting point is much farther ahead in time than it was before you turned around. This shift completely corrects for any slowness of the other clock when you meet back up again.

bw022 is incorrect. Each person sees the other's clock as running slow because in each case it's the other clock that is in motion and moving clocks run slow. The two observers will NOT agree that when one's clock reads 12 PM, the other's reads 1 PM, until they arrive back at the starting point, where they must agree on each other's readouts, which will be the same if they traveled at equal speeds.

Answer 2

Nobody is late. If you both traveled at the same speeds for the same amount of time, and came back to the starting frame of reference, you will agree on the time.

The tricky part is that to get back to the same reference frame, you both have to accelerate. When you do that, your view of what "now" at another location changes. This is what allows you to compare watches and be the same.

The same issue arises in the twin paradox where one twin stays the same and the other goes off. Naively, you might think it's a paradox, because both twins should think the other's time is dillated. But clearly, only the traveling twin comes back younger at the end of the day in the original reference frame.

Answer 3

Relativity won't have that effect.

If he was moving faster than you, his clock will be moving slower than yours or yours is moving faster than his. However, both of you will agree that his clock is behind yours.

Depending upon your velocities, he might say that "1 hour" has passed and you will say that "2 hours" have passed. However, you won't disagree what the other's clock is actually reading. If you left at 2pm. His clock will read 3pm and your 4pm. There will be no disagreement on what each other's clock says. If you look at his clock is will read 3pm (to both of you) and your clock will read 4pm (to both of you).

Your friend won't have the same 'feeling' as you. You will have the opposite feeling towards each other's clocks. If you feel that his clock is running slowly, he will feel that your clock is running fast.

Answer 4

Both clocks will read the same, there was no difference in your speeds.

Answer 5

My girlfriend and I once syncronized our clocks in cafeteria and agreed to meet agian at 8pm sharp. When I arrived her clock showed 8:10 already and we had bitter argument about me being always late. My girlfriend, unfortunately, did not know about time dilation, and relativity, and stuff, and dumped me.