Time Dilation and relative velocity, 2 girls, 3 atomic clocks?

Question

Right, Time dilation due to velocity has been experimentally demonstrated when a airline took an atomic clock up traveled at speed and then came back down again comparing the atomic clock with one on the ground it was measurably behind the control clock.

So... Girl 1 takes her atomic clock on one plane and girl 2 takes hers on another and the control clock stays on the ground. The two planes travel away from each other at the same velocity so to the control clock both plane-bound clocks should fall behind by the same amount but to girl 1 who accepts her position as reference zero girl 2 is traveling at a greater velocity and to girl 2 who accepts her position as reference zero girl 1 is traveling at a greater velocity. Both girls should expect that when they meet to compare clocks that the other girls is behind by an amount.

when they do meet how can they both see the others clock as being behind and will a ground observer see both as being equally behind the control.

Informed answers only please I will call you an idiot if you fail to understand the question.

Lola F · Accepted Answer

Time dilation is not the only effect of Relativity. Failure of Simultaneity is another, and the one that everyone always forgets about.

While they are traveling at constant speeds, each girl observes the other's clock to run slow, just as each girl observes the Earth's clock to run slow. However, when they turn back towards the Earth, each changes her reference frame to a new frame with a different definition of which events are happening "now." 

It's the same as the resolution of the original twin paradox. Just before the twin turns around, she's in a frame in which her clock reading 1 hour is simultaneous with (for instance) the Earth's clock reading only 1 minute. After she turns around, she's in a new reference frame where her 1-hour clock is simultaneous with the Earth's clock reading many days. Aside from that turnaround, she always observes Earth's clocks running slow, and yet when she returns Earth's clock is far ahead of hers: because of the shift in simultaneity when she accelerates.

The same is true in your example. Each girl observes the other's clock to run slow, except when she jumps reference frames when she turns around. At that point, she shifts into a reference frame in which her twin's clock reads much farther ahead than it did just before the turnaround--- exactly enough so that, when they return to Earth, even though she observes the other's clock to run slow all the time (except at the turnaround), their clocks will read the same amount when they meet again.

billrussell42 · Answer

This can be understood better if you consider two girls traveling via spaceships in opposite directions. The travel a round trip, and after 2 years, return home, with both aging only 1 year. (case 1)

If you take one of the girls as reference, then you could say the other picked up 2 years in time while the reference didn't. (case 2) But this is not true to the facts, as they can compare their ages.

The difference between the two cases is acceleration, both girls underwent extended accelerations, while the earth didn't. That means the earth is the correct reference (case 1) since, while speed is relative, acceleration is not.

Apply this to your example...

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Anonymous · Answer

Ok, this can best be demonstrated when the two girls go in the opposite direction and return back after one year

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Time Dilation and relative velocity, 2 girls, 3 atomic clocks?

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