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The wikipedia article on Time Dilation (http://en.wikipedia.org/wiki/Time_dilation) has an explanation involving the following two diagrams:

At rest Moving

I have some problems with these diagrams. In the second one the bottom mirror is not only moving, but it's also changed the direction in which it's emitting light so obviously the path is going to be longer. If the bottom mirror in the second diagram wasn't moving but went all the way from point A to C and emitted the light at that same angle it would result in the same 'time' measurement even though it's not actually moving.

Is the diagram implying that light will be emitted at an angle if the light source starts to travel sideways?

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  • $\begingroup$ Keep in mind that the bottom mirror is moving horizontally along with the photon, and so from the moving frame's point-of-view the photon is not being emitted at an angle. But both agree on the speed of the photon and the separation of the mirrors, so they must disagree on the time interval. Related: What is time dilation really? $\endgroup$ – lemon Mar 6 '16 at 11:42
  • $\begingroup$ Are you saying the mirror moving horizontally will add horizontal momentum to the photon? I didn't think that's how it works. I would have thought that if the bottom mirror continues to emit light vertically, the light when it's in position A will miss mirror B. $\endgroup$ – Kai G Mar 6 '16 at 11:45
  • $\begingroup$ Think of this in a different (but equivalent) way: The setup on the left is stationary. Now suppose that you, the observer, start moving horizontally (to the left), then you will see the setup on the right... Does that make more sense? $\endgroup$ – lemon Mar 6 '16 at 11:49
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    $\begingroup$ The link in your first comment makes more sense to me. If I, the observer, move to the left, both mirrors would remain opposite each other so I wouldn't see the setup on the right. $\endgroup$ – Kai G Mar 6 '16 at 11:59
  • $\begingroup$ ...But A and B do indeed remain opposite each other in the diagram on the right (i.e. when the photon reaches B, A has moved to the middle)... $\endgroup$ – lemon Mar 6 '16 at 12:13
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Perhaps the following animation will help:

enter image description here

Image credit

Note that, from both the rest frame of the light clock and from the relatively moving frame, the mirrors are always vertically aligned and the 'photon' is always located along the line through both mirrors.

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  • $\begingroup$ This definitely makes it clearer. Maybe the wikipedia diagram is supposed to show the same thing but, if it does, it does a very poor job IMO. $\endgroup$ – Kai G Mar 7 '16 at 12:28
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Per general intuition, (I do not have a reference).

For the moving frame of reference, space is curved. Therefore, what seems to be vertically up, actually, is at an angle, as observed by a stationary observer, but it appears to be going straight up and straight down for the moving observer.

When we say vertically up, that is with respect to the curved space. So, "Straight up" itself is different for the moving frame Vs for the stationary frame. Therefore, it is the stationary observer that sees the time being slow, not the moving frame.

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