relativistic problem
- From: Eoghan <lucagalbu@xxxxxxxxx>
- Date: Sat, 29 Mar 2008 03:56:51 -0700 (PDT)
Hi!
I have a question about simultaneity. Suppose there is a person S
looking at a person S'. S' is moving with a velocity v=c/2, where c is
the speed of light. In the reference of S' there is a lamp at a
distance l. The lamp is turned on: according to S', how much time does
the light take to hit S'? And according to S?
If I try to solve this I have: according to S' the light travels at a
constant velocity of c, so it takes l/c time to reach S'.
According to S the light still travels at a velocity of c, but S' is
moving towards the light at a velocity v=c/2, so the equations of
motion are:
xS'=(c/2)t
xL=-ct+l
where xS' is the equation for the motion of S' and xL is the equation
of motion for the light.
The light reaches S' when xS'=xL so when t=(2/3)(l/c)
Now I solve the problem by applying the Lorentz equations: t=t'/
sqr(1-1/4), where t is the time according S while t' is the time
according to S'. The term (b/c)x' isn't there because x'=0 (according
to S' the light reaches him at x'=0) 1/4 comes from b^2=v^2/c^2, v=c/
2.
If I solve the equation I get: t=(2/sqr3)t'.
Why have I got the square root? Shouldn't i get t=(2/3)t' = (2/3)(l/
c) ?
.
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