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"Pentcho Valev" <pvalev@yahoo.com> wrote in message 
news:157c5383-980a-47cc-9413-b638dded7bb0@t1g2000pra.googlegroups.com...
: 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


Rotation rate w
Tangential speed wR
Speed of light in rotating frame c
Velocity of light in non-rotating frame wR+c, wR-c
Distance travelled by light in rotating frame  wRt, -wRt
Distance travelled by light in non-rotating frame  ct+wRt, ct-wRt

t(c+wR) = t(c-wR)
OR equivalently,
t(c+v) = t(c-v)
The times are the same, the distances are different.


Einstein set up
x' = x-vt, the transformation from the moving frame to the
stationary frame but
Einstein OMITTED
-x' = -x+vt for the return journey.

Sagnac is isomorphic to Einstein's thought experiment, but Einstein
BLUNDERED the simple algebra at schoolboy level, right here:

  http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img22.gif

He claimed the return distance is x-vt with time t = (x-vt)/(c+v)
when it is in fact t = (vt-x)/(c+v).

From this BLUNDER he calculated the cuckoo malformations that
he blamed on Lorentz and called "transformations".

The rigorous solution is NOT difficult.