Question about light clock and derivation of time dilation

Time dilation is typically the first SR effect derived in text books,
and it is usually done with the example of a light clock as follows,
where S is the source and M is a mirror. Since it appears to be so
important, I'm trying to understand every aspect of this example.

--- M

^
|
|
|
|
|
|

| | S

The well-known derivation is based on the fact that, to an observer B
moving horizontally w.r.t. the clock, the light is taking a longer path
from S to M as shown below:

--- --- ---
^
|
^
|

^
|
| | | | | |

But the speed of light is constant and dimensions perpendicular to the
direction of motion don't change. Therefore, B concludes that the time
for the light to go from S to M is longer than the time determined by
an observer stationary w.r.t. the clock.

Fine, but I am trying to reconcile B's observation of the light path
with the fact that the light source is pointed in the vertical
direction. Doesn't that tell B that the light is "really" just moving
up and down? Wouldn't B have to see the light source tilted to make
sense of his observation of the light path?

To make this more concrete, let's suppose that the source S and mirror
M are connected with a narrow fiber optic (with some scattering
material included so that B can still observe the light). How can B
reconcile the observation that the light path is tilted with his
knowledge that the light is confined to move in the fiber? Doesn't he
"really" know that the light is just moving straight up and down?

.

Relevant Pages

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