Dirk Van de moortel wrote:
> "Thomas" <thomas.smid@gmail.com> wrote in message
> news:1124546336.273518.121610@g47g2000cwa.googlegroups.com...
> > Dirk Van de moortel wrote:
> >
> > > The light acts as the first object.
> > > The source acts as the second object.
> > > Both objects have a velocity as measured by the observer.
> > > The observer uses vector addition and subtraction to calculate
> > > the closing speed between the light and the source.
> >
> > This is exactly the mistaken assumption Einstein was making as well
> > (despite the obvious fact that light behaves very differently to
> > ordinary objects in this respect).
>
> Where is the mistake in the following statements about the
> situation where we talk about the light signal sent by the
> source in the direction away from the observer?
>
> The light signal has velocity c w.r.t. the observer.
> The source has velocity v w.r.t. the observer.
>   After 0 seconds,
>      the distance of the light signal to the observer is 0 meters
>      and the distance of the source to the observer is 0 meters,
>      so the distance between signal and source is
>          0 meters - 0 meters = 0 meters.
>   After 1 second,
>      the distance of the light signal to the observer is c meters,
>      and the distance of the source to the observer is v meters,
>      so the distance between signal and source is
>          c meters - v meters = (c-v) meters.
>   After 2 seconds,
>      the distance of the light signal to the observer is 2 c meters,
>      and the distance of the source to the observer is 2 v meters,
>      so the distance between signal and source is
>          2 c meters - 2 v meters = 2 (c-v) meters.
>    ...
>   After t seconds,
>      the distance of the light signal to the observer is t c meters,
>      and the distance of the source to the observer is t v meters,
>      so the distance between signal and source is
>          t c meters - t v meters = t (c-v) meters.
>
> So, after t seconds (on the observer's clock), the distance as
> (measured by the observer) between the signal and source is
> t (c-v) meters.
> So the time rate of change of the distance between them is c-v.
> This rate of change is *defined* as the "closing velocity" between
> the signal and the source.
> It pops up in the expressions x'/(c-v) and x'/(c+v) in the paper.
>
> Where is, according to you, the error?
> Exercise: which physical assumpion have we made that is
> essential for the paper?

The error impecile Dirt is obvious to any sane mind, this of course
excludes you because you are paranoid. I will try to explain in plain
language without using Poincare Group transformations. You wrote:

> After t seconds,
>      the distance of the light signal to the observer is t c meters,
>      and the distance of the source to the observer is t v meters,
>      so the distance between signal and source is
>          t c meters - t v meters = t (c-v) meters.

The distance between the signal and source, as measured by the
observer, is simply undefined. It is only defined for an observer on
the source. Why is it undefined? Because, it is not a well-founded
phenomenon (an ill-defined spatiotemporal quantity). In order to
actually measure it you need another signal from the source to the
first signal. But then you have to synchronize the clocks of the
observer and the observer on the source emitting the second signal. You
cannot do that on the fly, because you need one more signal. If you do
it before motion starts, you still need another signal to commence
measurement. And that is where the dillema enters the picture: is c
invariant or source dependent? If it is, it turns out that it must not
be in order to be able to measure the distance. If it is not, it turns
out that it must be in order to be able to make the measurement.
Einstein should have learned something from Russell. But he was a
paranoid of major proportions. This is also the reason SR is
inconcistent and paradoxes arise, like the twin paradox. In an attempt
to complete the theory, in a math sense, Einstein forced it to
incorporate an antinomy by assumming c invariance in all interial
frames. If you remove the invariance of c, the theory turns consistent,
but incomplete.

I hope you learned something today, Dirt van der Immortel van der
Fablous   

Mike