Re: Question about light clock and derivation of time dilation
- From: Paul Stowe <ps@xxxxxxxxxxxxxxxxxxxxxxxxxx>
- Date: Sun, 03 Jul 2005 16:26:42 GMT
On 3 Jul 2005 07:32:44 -0700, john_doe_ph_d@xxxxxxxxx wrote:
>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?
The issue is what observer B 'sees', isn't it? To 'see' the light
from observer A's frame rays must reach out TO observer B. Follow
the ray-paths from their origins to both observer A & B's from their
perspective. Given that the light speed c is an invariant, idependent
OF either A or B motion, the result is what Dirk posted. Note that
g is the Lorentz transform, Sqrt(1 - [v/c]^2). In SR it is all about
what you see...
Paul Stowe
.
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