Re: .....Simple Math Derivation Needed.....

From: Androcles (dummy_at_dummy.net)
Date: 12/17/04 

Date: Fri, 17 Dec 2004 15:47:39 GMT

"SRdude" <cadwgan_gedrych@yahoo.com> wrote in message
news:1103228454.460419.295410@z14g2000cwz.googlegroups.com...
> .................Simple Math Derivation Needed..................
>
> Even after deliberately disregarding all preceding and subsequent
> words in the book, the fact remains that Einstein at one point
> definitely derived the very simple equation w = c - v.
>
> Here are his own words:
> "w is the required velocity of light with respect to the carriage,
> and we have w = c - v.
> The velocity of propagation of a ray of light relative to the carriage
> thus comes out smaller than c."
> ---------------http://www.bartleby.com/173/7.html---------------------
> All I am looking for is one brave soul who will show this derivation.

Its pretty easy.
Take two strips of paper and align them one above the other.
Pinprick through both and call that place O (for origin) on one and
O' on the other. like this.
|__._____________|
    O
|__._____________|
    O'

Now slide one strip past the other with a constant velocity v for a
duration t.
|__._____________|
    O
     |__._____________|
         O'
Now prick through again where the light reaches the other end of the
carriage,
and call that x on one and x' on the other.
|__.___________.__|
    O x
     |__._________.____|
         O' x'
Now, in the upper strip the light has moved a distance x' in time t,
and in the lower strip it has moved a distance x in the same time t.
Can you see that the distance x' = x - vt?

Since by definition velocity = distance divided by time,
if we say the velocity of light is c in the upper strip,
then it must be the distance x' in the lower strip divided by time also,
hence c-v = x/t - vt/t.

Androcles.

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