Re: Light clocks question

From: Tom Roberts (tjroberts_at_lucent.com)
Date: 01/13/05 

Date: Thu, 13 Jan 2005 10:15:30 -0600

Stuart Gall wrote:
> Say we have a sort of light clock with a laser at one end and a target
> at the other.
>
> Why does the observer on the embankment expect to see the light hitting
> the target at all? In order for it to hit the target the light must have
> had some perpendicular velocity component added to it (not possible by
> special relativity)

I assume you are considering the light clock to be perpendicular to the
relative velocity of train and embankment:

     -------------------
     | ---target |
     | | |
     | |light |
     | | |
     | | |===========>
     | |o| | motion
     | | | |
     | | |laser |
     | | | |
     | -m- |Train
     -------------------

/////////////////////////////////////////
Embankment (at rest in this drawing)

In the train frame, the light clock is constructed so the mirrors of the
laser are perpendicular to the line from laser to target, and the light
from the laser consequently hits the target. Note the laser has a small
aperture at its top end (the 'o'), and any light emitted by the laser
must exit this aperture; the laser also has a mirror at its bottom end
(the 'm'). This is a simplified description of the laser....

In the embankment frame, consider the last reflection of light inside
the laser from the mirror at the bottom. In order to get through the
aperture, it must have a nonzero component of velocity to the right,
because by the time this light reaches the aperture the latter will have
moved to the right. But that's OK, because the transform from train
frame to embankment frame gives the light PRECISELY the correct
component to the right to get it through the aperture. After all, the
physical situation does not change depending on which frame one uses to
describe it -- physically the light does emerge through that aperture.

Note the laser itself does not appear rotated to the embankment
observer, nor does the clock consisting of laser plus target. But the
path of the upward-moving light DOES.

        Exercise: describe how the downward-moving light inside the
        laser looks to an embankment observer.

Tom Roberts tjroberts@lucent.com

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