Re: [Phys-l] Sample relativity problem giving me fits...

["Jeffrey Schnick" <JSchnick@Anselm.Edu>]

Hi Jeff L.,

Sounds like a nice example problem you have come up with.  The time you
need to "dilate" is the time on one clock.  If an O frame clock at the
emitter reads zero at the emission event, then, as viewed from the O'
frame at that same instant, in accord with clock desynchronization (the
leading clock trails), an O clock at the absorber would be reading
t_1 = - L_o v / c^2 
with L_o = 1.5e8 m and v = .8 c this yields -.4 s.
At the absorption event the O clock at the absorber (as viewed from any
reference frame) reads
t_2 = .5 s .
Hence the change in the reading of the one O clock at the absorber, as
viewed by observers in the O' frame would be
dt = t_2 - t_1 = .9 s .
"Dilate" this to see how much time elapses on the O' clocks as viewed by
O' observers and you get
1.5 s
which is the same result you got the first way you did part b.

Hope this helps.

Jeff Schnick
Saint Anselm College


> -----Original Message-----
> From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
> bounces@carnot.physics.buffalo.edu] On Behalf Of Fayngold, Moses
> Sent: Tuesday, January 16, 2007 6:41 PM
> To: Forum for Physics Educators
> Subject: Re: [Phys-l] Sample relativity problem giving me fits...
>
> 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/
>
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