Time Dilation & Contraction: Conflicting Clocks

[intervoxel]

The ship leaves the station carrying two mirror clocks. One aligned with the motion. The other, orthogonal to the first. One suffers length contraction but the other does not. I suppose time dilation acts on both. So we have a contradiction here. What is happenning in fact?

 

[Naty1]

(a)What do you think the observer on the ship sees regarding her local clocks?

(b) Now try to write down [explain] excatly what you think is a 'contradication' and post it here.

(c) Hint: What is the 'contradiction here: Observers in relative motion each see the other's clock as ticking slower than their own.

 

[intervoxel]

I forgot to say that the observer remains at the station.

 

[PAllen]

The one aligned orthogonal suffers no length contraction. But, from the station observer, light is following a zigzag path between the mirrors. Thus, the station observer sees the train clock 'tick' slower because of the longer light path. The longer light path is sqrt(L^2 + (vt)^2), L being distance between mirrors. This must equal distance light travels, so we have ct = sqrt(L^2 + (vt)^2) . Solving for t, we get tick of train clock as seen from station: (L/c)/sqrt(1-(v/c)^2).

Now, for horizontal clock, we have contracted length L' = L sqrt(1-(v/c)^2). Here the train clicks are asymmetric, seen from the station; the station observer sees the train observer treat the sum of the asymmetric clicks as two even clicks. For the station observer, for the click with light moving the same direction as the train, t0 = L'/(c-v); for the other click, t1 = L'/(c+v). If you work this out, you see that t0+t1 = 2(L/c)/sqrt(1-(v/c)^2), consistent with the clock rate for the orthogonal clock.

 

[bahamagreen]

The one aligned with the direction of motion (light goes forward and backward between the mirrors) will appear to the station observer that the light going forward will take longer to travel the distance, shorter time to travel the backwards distance. This distance is the same for both directions and contracted.

The other one will have equal travel times, both clocks will "tick" the same rate (meaning a round trip light bounce will be the same time for both), and both tick slower than the observer's clock at the station.

An observer on the ship will see both ship clocks act and tick identically, and will see the station observer's clock to be slow, and the station contracted.

 

[intervoxel]

Thank you all. Things are clear now.