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Re: [Phys-l] Relativity Question



-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
bounces@carnot.physics.buffalo.edu] On Behalf Of LaMontagne, Bob
Sent: Wednesday, April 29, 2009 7:06 PM
To: Eric-Lane@utc.edu; Forum for Physics Educators
Subject: Re: [Phys-l] Relativity Question

I'm not sure what you are trying to describe here. However, the
equation is not dimensionally correct.

Bob at PC


Translation: T2-T1 has units of time (seconds), Lo is a distance (meters), the stuff in the square root is unitless. So presumably there's a missing factor having the units of velocity (m/s) on the left side of the equation.

But please also clarify a couple other points:

1. You say: "Here, Lo is the separation of the inertial frames." According to _which_ observer is the separation Lo ? Of course, the two observers will disagree on this (if they are in relative motion).

2. You don't say, but we assume the "v" is the relative velocity of one observer relative to the other. Are there other assumptions? Since this is SR, we'll assume the relative velocity is constant (although years ago my thesis was in extending SR), and I think you may be treating a one-dimensional situation, with the relative motion of the observers along the line separating their positions.

3. If T1 is the time the photon leaves the first observer (according to the first observer) and T2 is the time the photon arrives at the position of the second observer (according to the second observer), then it is important to state when (and whether!) the observers synchronized their clocks. Frequently in 1-d relativity thought experiments we assume that x=x'=0 when t=t'=0, so both observers' clocks read 0 at the instant they pass each other. Is that true here?

Note: It's interesting that in your formula one ends up considering the difference in these times that are measured in different reference frames! I'm surprised that such a mixed entity has significance!

Looking forward to hearing more about this, but meanwhile, back to grading tests!

Ken Caviness
Physics
Southern Adventist U


________________________________________
From: phys-l-bounces@carnot.physics.buffalo.edu [phys-l-
bounces@carnot.physics.buffalo.edu] On Behalf Of Eric Lane, Lane [Eric-
Lane@utc.edu]
Sent: Wednesday, April 29, 2009 4:35 PM

Relativity Question

We would welcome comment and further discussion on the following
apparent corollary in special relativity (SR). Through one-time
application of the Lorentz transformation one can derive a general
expression for the transit time of a photon between two inertial
frames, T2-T1 = Lo*sqrt[(1+v/c)/(1-v/c)]. Here, Lo is the separation of
the inertial frames at the time T1 when the photon is sent from one
frame and T2 is the time when it arrives at the other frame. Each time
is directly recorded by the observer on his own clock, situated in the
corresponding frame. This equation is appropriate for calculations in
various kinematic applications of SR. With it, one can determine time
and space event coordinates in any communications with photons between
frames. The equation of motion of light, as it were, permits rendition
of activity, observed in one inertial frame by a physicist there, to
another observers frame, thereby accomplishing the essential purpose of
SR, namely reconciliatio
n of physics everywhere. In application, no transformations as such of
event coordinates are involved and there is no need for use of the
velocity addition theorem. Everything is reduced to the simple question
of correction to light transit time for signal delay, in form, a
classical operation.

Tom Orofino, Tom-Orofino(at)UTC.edu
Eric Lane, Eric-Lane(at)UTC.edu
Prof. Eric T. Lane eric-lane@utc.edu
Physics Dept. 2352 423-265-7804
The University of Tennessee at Chattanooga 37403-2409
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