Let us imagine that a radar located at the terrestrial equator near Quito sends a narrow signal directed eastwards.
We shall also imagine, that on all line of equator the set of reflectors is located and that the reflectors thus deflect the radar signal radiated eastwards in Quito, that it, being propagated near the earth's surface, goes around the Earth along the equator and returns to the radar in Quito from the western side.
Knowing the length of the line, along which the signal is propagated, and the time, which is required to the signal to go around the Earth, the operator of the radar can calculate the signal velocity on the way from Quito to Quito in an eastern direction.
Similarly, the signal velocity in the opposite (western) direction can be calculated.
The following reasonings show that these velocitys will be different one from another and not equal to the fundamental constant C.
Let's mentally place an external nonrotating observer remote from the Earth and motionless fixed relative to the center of the Earth into the point of the imaginary axis of rotation of the Earth. Let him observe the Northern hemisphere of the Earth counterclockwise rotating under him and mentally examine the propagation of the signal along the equator.
Let us agree that one way light velocity in inertial frames of reference in all directions is equal to the fundamental constant C.
In the inertial frame of reference of the external observer the velocity of light propagating along the terrestrial equator, is equal to the fundamental constant C. If the Earth would not rotate, then the time required to the signal for the flying round the hypothetically nonrotating Earth would be equal to the length of equator, divided by the constant C.
But the Earth rotates!
When the signal returns to the starting point in the inertial frame of reference of external observer, the radar in Quito will move in this frame of reference approximately to 62 meters to the east and the additional time, equal to two decamillionths of second, will be required to the signal arrived from the West for the return to the locator.
If the operator would turn the reflector to 180 degrees and direct the signal westwards, then the time required to the signal to go around the Earth and to return to the radar from the other side would be two decamillionths seconds less than the time required to the signal to go around the hypothetically unrotative Earth, since in the time of the circling by the signal the Earth the radar would be displaced by 62 m to the East and for the signal arrived from the East would not be necessary to move over these 62 meters.
The delay and advance of the signals are effects of the first order of smallness with respect to value v/C, where v - linear velocity of the surface of the rotating Earth, and are sufficiently great in comparison with the relativistic effects of the second order of smallness.
In the case of the simultaneous emission of the signals in opposite directions - to the East and to the West, the signals gone around the Earth and returned to the radar would spend different time. The difference of the times would be equal approximately to four decamillionth second. This effect is the effect of Sagnac.
If the operator would send a signal to the East ensuring to the signal arrived to the reflector from the West the possibility to be reflected from the auxiliary reflector on the reverse side of the radar and passage the back route to return to the locator from the East, then the time, necessary for the dual world-encircling voyage of the signal - first from the West to the East, then (after reflection from the auxiliary reflector) from the East to the West - would be in practice not differed from the time, which the signal would spend for a similar dual journey around the hypothetically nonrotating Earth. In this case the measurement of the velocity of signal on the way forth and back would give value, at least with an accuracy to the second order of smallness, equal to fundamental constant C (An account of all circumstances shows, that the western and eastern velocitys lightly differ from the values c+v and c-v, where v is the velocity of equatorial points of the rotating Earth, and that the average velocity of a double " round-the-world travel " of a signal is exactly equal to the constant C).
Such global experiment, similar to the experiment of Michelson- Morley, does not make it possible to reveal the rotation of the Earth. At the same time the measurement of one way speed of light by a single clock makes it possible to reveal it.

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Vadim Matveev

Okay, I'm an utter newbie here, but you yourself admit that the distances travelled are different, and the times are different.

I fail to see how this produces a change in the velocity of c. In one case the time is longer and the distance is longer. In the other the time is shorter and the distance is shorter. As measured from a nonrotating frame outside earth. Since velocity is distance over time, c doesn't change from this perspective, does it?

When you're on earth, you're in a rotating reference frame, and rotating reference frames are distinguishable from other rotating reference frames. That's why nonrotating frames are important in SR. It seems to me that the difference in measured arrival time doesn't mean that the speed of light has changed, but that yes, you can detect the planet is rotating. So the c+v and c-v thing is fictitious -- it just shows you that you're rotating. The speed of light is still c.

I could see the Michelson-Morely experiment being too small scale to measure this kind of effect and designed for a different problem. I thought it was meant to measure differences in light travel time as the result of very fast linear motion (on a small time scale) through space to detect an aether.

What has one got to do with the other?

What am I missing here?

(The sagnac effect has messed up my head more than once, but...)

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"Debugging is twice as hard as writing the code in the first place. Therefore, if you write the code as cleverly as possible, you are, by definition, not smart enough to debug it." - Brian W. Kernighan

Yes. In innertial frames of reference!

No. It doesn’t.

In innertial frames of reference. If you do not consider terrestrial distance over time as velocity, then you are right.

It is correct. I do not dispute purposes and results of Michaelson's experiment, but Michaelson measured the speed on the dual way forth and back, while this measurement makes it possible to reveal neither linear motion nor rotation of the earth (speed of light from Quito to Quito and back to Quito would be equal both on the revolving and on the hypotheticaly nonrotating Earth).

Not so much, but the Michelson-Morely experiment has got nothing to do with one and with another. The experiment was carried out on the revolving Earth for the purpose of the detection of its linear motion.

You are missing nothing. I wrote about the measurement of the velocity of light on the Earth, as I understand this velocity, in eastern and western directions with the aid of the single clock. This velocity is not equal to constant c. If you don’t want to call it velocity, then say, that the terrestrial distances over time are different for eastern and western directions.

…but the speed of light along the outline in one direction was never measured.

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Vadim Matveev

You don't measure c because of the Sagnac effect. People that do work on the appropriate scale (most of them, anyway) understand the time discrepancy that is introduced (~207 ns for moving a clock or signal around the equator). The earth isn't an inertial system. You seem to have mentioned all this. So what's the problem?

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"I have a cunning plan that cannot fail."
S. Baldrick

Besides the error flagged by "swansont" are you aware that you don't need to measure one way speed of light on Earth, it is much easier to do it in space. It has been done successfully several times:

http://en.wikipedia.org/wiki/De_Sitt...tar_experiment