🚀 go-pugleaf

On Dec 20, 12:07, Pentcho Valev <pva...@yahoo.com> wrote:
> On Dec 20, 11:11, Pentcho Valev <pva...@yahoo.com> wrote:
>
> > In discussing the Sagnac effect, both relativists and anti-relativists
> > make the following mistake:
>
> >http://www.mathpages.com/rr/s2-07/2-07.htm
> > "Quantitatively, if we let w denote the angular speed of the loop,
> > then the circumferential tangent speed of the end point is v = wR, and
> > the sum of the speeds of the wave front and the receiver at the "end"
> > point is c-v in the co-rotating direction and c+v in the counter-
> > rotating direction.....This analysis is perfectly valid in both the
> > classical and the relativistic contexts."
>
> > The values c-v and c+v above are "perfectly valid" only in the
> > relativistic context. If by "classical" the author means "Newtonian",
> > the analysis is by no means "perfectly valid". According to an
> > observer at rest, in the classical context, the speed of light is c+v
> > in the co-rotating direction and c-v in the counter-rotating direction
> > so the correct text would be:
>
> > "Quantitatively, if we let w denote the angular speed of the loop,
> > then the circumferential tangent speed of the end point is v = wR, and
> > the sum of the speeds of the wave front and the receiver at the "end"
> > point is c in the co-rotating direction and c in the counter-rotating
> > direction."
>
> Of course, the implicit assumption above is that photons' subsequent
> bumping into rotating mirrors does not change their speed
> additionnally (e.g. the speed of photons in the counter-rotating
> direction gets even lower than c-v), which is by no means obvious.

If one sticks to the ballistic theory and assumes that, according to
the observer at rest, the speed of the photons is c-v in the counter-
rotating and c+v in the co-rotating direction all along, the following
observation is relevant. The real path of the photons is a polygon
inscribed in the rotating circular loop. It is easy to see that the
sides of the polygon covered by c-v photons are LONGER than the sides
of the photons covered by c+v photons. This seems to be an advantage
allowing c-v photons to arrive at the end point earlier than c+v
photons. The problem is purely mathematical but its rigorous solution
seems difficult for the moment.

Pentcho Valev
pvalev@yahoo.com