Re: The velocity of light going pass a moving train.


"Gerald L. O'Barr" <globarr@xxxxxxxxx> wrote in message
news:1181277065.446748.283770@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
The velocity of light going pass a moving train.

Some on this net (everyone on this net?) have been
saying that we cannot measure the relative
velocity of light between moving objects. I am
sorry that I have been so slow. But if I had been
slower, I am sure I would have caught even more!

********************************************************
When Einstein developed his SR theory, he used an
example of a moving train to do this. The speed of
light going past this train had to be exactly known,
in order for him to develop his SR theory. Einstein
said that the velocity of light relative to the train
that was moving at v on the fixed tracks was exactly:
c +/- v.

In any and all SR inertial frames, the measurement
of the velocity of light pass any moving object can
certainly be done. Let us look at one simple example
of how it can be done:

Let us take a train moving at v, and where we want
to measure the speed that exists between this train
and light that is moving in the same direction as the
train. All we have to do is set up an SR measurement
frame, a grid, along the tracks, with clocks and
rulers, and with all the clocks in proper sync.

Have you forgotten that (at least in theory) no truly "proper" sync can be
established?!

This is what must be done. We need only two
pieces of data, the true length of the train, and the
time it takes for light to go from the end to the
front of the train.

???

The relative velocity of light
within this moving train would then be the true
length of this train, divided by the time it took the
light to go from the end to the front. Just two
simple measurements! One distance measurement and a
time measurement. These are the same facts that one
has to have to make any velocity measurement. Even a
measurement of the velocity of light takes a measured
distance, and the time it takes light to go from the
starting point to the ending point.

O'Barr, I'm afraid you lost it!

First, the true length of the train is measured
while it is moving at v by merely recording the end
of the train and the front of the train at some
specified common point of time. The clocks local to
each of these points on the train at the time of the
measurement is used to accomplish this, and the
distance between the clocks is the true length of the
train. This distance is just the difference in the
location coordinates for these two clocks.

WRONG: by saying "true length", you forgot relativity of simultaneity and
the conventionality of synchronization!

[...]


Of course, for those who like to be mathematical,
one could set up the following math relationships.

1) Let L(0) be the length of the train while not
moving.
2) When it is moving at v, it will have a length of:
L(v) = L(0) * (1-(v/c)^2)^.5

Let c' be the relative speed of light relative to
the moving train as measured in the track frame.
And t is the time for light to go from the end to
the front of the moving train, as measured in the
frame of the tracks.

That's the propagation time *according to the sync convention* in that frame
ONLY.

3) Therefore, c' = L(v)/t (a definition)

4) Light will move a total distance of t*c during
this time,

5) And this total distance will consist of
L(v) + v*t.

8) Thus, t*c = L(v) + v*t.

9) Solving for t we get t = L(v)/(c - v)

10) We can now show c' as L(v)/(L(v)/(c-v) = c - v.

Sure. If you only wanted to show what "relative speed" means in normal
English, then I advice you to remove that nonsense about "true" lengths and
times.

Cheers,
Harald


.

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