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Re: [Phys-l] Relativity Question



On 04/29/2009 01:32 PM, Eric Lane, Lane wrote:

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.

As others have pointed out, the question is ill-posed ... several
times over. For starters:
-- There is no such thing as the "separation" of inertial frames.
-- There is no such thing as the "transit time" "between two inertial
frames".

That's because each of the frames fills all of spacetime. Look at
any spacetime diagram e.g.
http://www.av8n.com/physics/twins.htm#fig-twins-joe
to see what this means.

The canonical well-loved introduction to spacetime is Taylor & Wheeler
_Spacetime Physics_. Anybody who doesn't have a copy ought to get one.
See also
http://www.av8n.com/physics/spacetime-trig.pdf
and references therein.

Constructive suggestion: Restate the question in terms of _events_
(P1 and P2) in spacetime. These events exist as physical objects.
Similarly the displacement vector (ΔP = P2-P1) exists as a physical
object. All such objects exist quite independently of which reference
frame (if any!) you are using at the moment. For more on this, see
http://www.av8n.com/physics/intro-vector.htm

If in addition to these two events there are two or more reference frames,
then there are a lot of things to keep track of. If necessary (and often
it is _not_ necessary) you can project ΔP onto the x-axis of Moe's frame
or the t-axis of Moe's frame or the x-axis of Joe's frame or the t-axis
of Joe's frame or whatever. However, this is usually not the best approach
because it focuses too much attention on arbitrary reference frames. In
the real world, in 99% of the cases, it is better to keep attention focused
on non-arbitrary physically-significant things.

I remember Charlie Peck saying "The goal is not to learn how to do Lorentz
transformations. The goal is to learn how to *avoid* doing Lorentz
transformations." That's really valuable advice. My favorite example of
doing real-world relativity calculations without any Lorentz transformations
is:
http://www.av8n.com/physics/bevatron.htm