"The Ghost In The Machine" wrote in message
...

: http://www.mathpages.com/rr/s2-07/2-07.htm
:
: looks reasonably simple.

And ridiculously wrong.
Written:
t1 = 2piR/(c+wR)
t2 = 2piR/(c-wR)


The author has conveniently forgotten the angle alpha.
Where the idiot gets 2piR and t1&t2 from only he knows, it is
t = (2piR+alpha)/(c+wR) = (2piR - alpha)/(c-wR)


In the frame of reference where the observer is rotating
with the apparatus we have t = 2piR/c

In the frame of reference where the observer is outside the apparatus
t = (2piR+alpha)/(c+wR) = (2piR - alpha)/(c-wR)
It's the same t no matter what frame it is seen from.


It's as ridiculous as saying a car travels 60 miles at 59 mph,
another car coming in the opposite direction travel for 60 miles
at 61 mph and then computing when they DON'T meet.
It's just plain ****ing silly.

The linear equivalent of Sagnac is for an observer
to travel 1 mile in 1 hour, and another observer to remain stationary.

-60--------------------0-1-----------------+60

Stationary observer:
The car on the left travels from -60 to +1 in one hour. 61 mph.
The car on the right travels from +60 to +1 in one hour. 59 mph.

Moving observer:
The moving observer travels from 0 to 1 in one hour. 1 mph.
In his frame of reference both cars are travelling at 60 mph.

Stationary observer:
Points his Doppler radar at each car, gets two different
frequencies, the difference between the frequencies is
what Sagnac measures.

Now all you need do is wrap it around a circle.

The author of that page is a ****wit who left out alpha.

Einstein made the same idiotic blunder in
http://www.androcles01.pwp.blueyonde...ket/eq22.A.GIF
where the equation can be corrected by
1/2(tau(0,0,0,t) + tau( vt, 0,0, t +.....))
---------------------------^^^^

[rest snipped]

The Ghost In The Machine wrote:
In sci.physics.relativity, Tom Roberts
wrote
SR accurately predicts the results of Sagnac's experiment (and
numerous repetitions since).

In the non-rotational frame, certainly. Approximation in
the rotational frame might be possible, with a little work.

One simply applies elementary calculus to relate the rotating
coordinates to the inertial coordinates (no approximation is needed).
But this is IRRELEVANT -- what matters is that SR predicts the fringe
shifts observed, and whether one calculates in the inertial frame or the
rotating frame does not matter (done correctly the two calculations
obtain the same result, of course).


(Were I up on my tensors, GR would resolve the matter
trivially, methinks.)

There is no aspect of GR that is "trivial" (:-)).


Tom Roberts