For part a), the Lorentz-contraction approach is OK.
For part b), the first way you had used, is also OK. But the time-dilation approach is not OK, and no surprise, it gave the answer inconsistent with the one you got first. Time dilation refers to a process taking place in ONE LOCATION of the original RF. In your case, the emission (x = 0) and subsequent absorption (x = 150000 units) of light was not (and could not be) in one place (for this to happen, the first RF should be co-moving with the emitted light).
Another way to find the time interval in your second RF is to apply the Lorentz-transformation to the emission and absorption events, and then find the time difference.
Moses Fayngold,
NJIT
-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu
[mailto:phys-l-bounces@carnot.physics.buffalo.edu]On Behalf Of Jeff
Loats
Sent: Tuesday, January 16, 2007 1:02 AM
To: Phys-l@carnot.physics.buffalo.edu
Subject: [Phys-l] Sample relativity problem giving me fits...
Hi all,
I am new to the forum, but hoping someone out there can help. I teach at
a small, relatively isolated, college and haven't had any luck working
this one with my colleagues.
Assume there is a light emitter at x = 0 and a light absorber at x =
150,000,000 m. Observer O' is moving along the x-axis at -0.8c and
watches some light get emitted and then absorbed. Here are the two
questions I had thought to ask...
a) What is the spatial separation between emitter and absorber according
to O'?
b) How long does the emit-absorb process take according to O'?
For part a) I believe we have simple length contraction, so we get 9x10^7 m.
For part b) I believe I can get this two ways. One I can find the travel
time for light towards the absorber which is moving away from the light.
If I do this I get 1.5 seconds. I also think I should be able to
time-dilate the time observed by O. The time O sees is 0.5 seconds,
which time dilates to 0.833 seconds, not 1.5 seconds.
I hope what I have said is clear. If anyone can point out what I am
doing wrong I would be very appreciative.
Jeff
--
Jeff Loats, Ph.D.
Assistant Professor of Physics
Fort Lewis College
650 Berndt Hall
970.247.7553
loats_j@fortlewis.edu http://faculty.fortlewis.edu/loats_j/