Time dilation

[Duncan]

Hello Joe,
Sorry but I don't follow you, the animation shows Zoe"s and Jasper's view of the pulse, heading in different directions
Duncan.

[joe]

True. The relative direction changes in a different frame. A crosswind when you are stationary at the lights becomes a cross-headwind as soon as you start pedalling. (The vector addition is more complicated for light, of course, but the principle is the same.)

But the pulses hit the same mirror, which is stationary in one frame but moving in the other (hence the different direction).

Joe

[Duncan]

G'day Joe,
Don't understand your answer, doesn't the animation show the observers view of the pulse, going in different directions?
Duncan.

[joe]

Yes. True. The relative direction changes in a different frame.

But the pulses hit the same mirrors for both observers, because for one observer the mirrors are moving.

Joe

[Duncan]

Hi Joe,
A different question. Convert Zoe's and Jasper's transportation to Collins Class, and run the experiment underwater. Reduce Zoe's speed in proportion to the reduced underwater light speed. What will the amount of time dilation be relative to the dry version?
Cheers,
Duncan.

[joe]

In the first case, the dilation factor is 1/sqrt(1-v1^2/c^2)
In the second case, because you impose the condition v2 = v1/n,
the new dilation factor is 1/sqrt(1-v2^2/c^2) = 1/sqrt(1-v1^2/n^2c^2)
so the ratio is sqrt((1-v1^2/c^2)/(1-v1^2/n^2c^2)

Joe