answer to YBM's bell problem
- From: rbwinn <rbwinn3@xxxxxxxx>
- Date: Tue, 9 Sep 2008 07:21:20 -0700 (PDT)
YBM proposed the folowing problem. Taking the Galilean
transformation equations and no length contraction with frame of
reference B moving in the +x direction relative to frame of reference
A, light is emited at a distance of a either side of the origins of A
and B when they coincide. YBM says there is a bell at the origins
that will ring when light from both sources hits it. Since he did not
specify whether the bell was at the origin of A or the origin of B, we
will work the problem with the bell at the origin of A. In A, the
light is emitted at x=a and x=(-a). In B the light is emitted at
x'=a and x'=(-a). Light emitted at -a has a velocity of c relative
to both frames of reference. Light emitted at a has a velocity of -c
relative to both frames of reference. If the bell is at the origin of
A, it will ring when t=a/c.
The mathematics for this is, for the light from -a, x1=-a, x2=0
x2-x1 = 0-(-a) = a
x=wt=ct =a
t=a/c
For the light from a, x1=a, x2=0 w=(-c)
x2-x1= 0 - a
x=wt=(-c)t = -a
t=a/c
Light from both directions reaches the bell at a time of a/c, and the
bell rings.
To determine what time a clock in B reads when the bell rings,
n'= t(1-v/w)
n'=a/c(1-v/c)
Robert B. Winn
.
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