One way Speed of Light measured by a Single Clock

[Vadim Matveev]

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.

 

[meddyn]

Would the experiment be altered if, on the rotation trip, the radar beam encountered a typhoon? Could the speed of light in water (140,000 mps) not offset the experiment enough to make the readings unreliable or compensate for the rotation? The experiment, not held in a vacuum, would be subject to normal external influences. While certainly hypothetical, are not all these exercises to some extent hypothetical? Also, the beam would be slightly blue shifted in one direction and red shifted in the other.

 

[Vadim Matveev]

Originally posted by meddyn
Would the experiment be altered if, on the rotation trip, the radar beam encountered a typhoon? Could the speed of light in water (140,000 mps) not offset the experiment enough to make the readings unreliable or compensate for the rotation? The experiment, not held in a vacuum, would be subject to normal external influences. While certainly hypothetical, are not all these exercises to some extent hypothetical?

Yes, certainly! This is a thought experiment only.
The rotating Earth can be mentally replaced with the rotating Moon (bad, that the Moon rotates too slowly) or with a big fast rotating hypothetical body (planet) without atmosphere. In my message a fundamental, rather than a technical question is considered.
On the Earth a statistical processing of many measurements could be achieved.
The experiment can be also really carried out in the satellite system GPS.

Originally posted by meddyn
Also, the beam would be slightly blue shifted in one direction and red shifted in the other.

Yes, but the colour of the beam would be shifted only in the frame of reference of external observer. On the Earth (for the terrestrial observer in Quito) the frequency of the beam remains unaltered.

 

[Creator]

Originally posted by Vadim Matveev

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. [/B]

Ok, very interesting Vadim; but what's the point you are trying to make? [?]

 

[meddyn]

what's the point you are trying to make?

Kinda thought it was to illustrate a C+ and C- measurement by a single observer.

 

[Vadim Matveev]

Originally posted by Creator
Ok, very interesting Vadim; but what's the point you are trying to make? [?]

In my message I want only to show that on the Earth the velocity C(east) is not equal to the velocity C(west). If we synchronized a set of clocks on the terrestrial equator, using the velocity C(east) or using the velocityC (west), then we obtained the same result. In this case we would not have a jump of time, which occurs, if the clocks are synchronized on the condition: C(east)=C(west)=C.
I am now reading the article of mister Paul Marmet (http://www.Newtonphysics.on.ca/Illusion/index.html ) and agree with him. My thought experiment confirms only what Paul Marmet writes about. Probably I repeat his reasonings (I badly know English and have not fully understood this article). I show what writes Paul Marmet, only not on example of different clocks, but on example of a single clock.

 

[Creator]

Originally posted by Vadim Matveev
In my message I want only to show that on the Earth the velocity C(east) is not equal to the velocity C(west)..

But your experiment did NOT show anything about difference in velocity; it only showed that the DISTANCE the light had to travel going East was DIFFERENT than the distance going WEST.

The only reason one direction takes longer than the other is because (as you pointed out) in a rotating Earth the Eastward traveling light has farther distance to go before getting back to the source.

Creator

 

[Vadim Matveev]

Originally posted by meddyn
Kinda thought it was to illustrate a C+ and C- measurement by a single observer.

By a single clock on the rotating Earth! Not in inertial systems of reference.
It is impossible to do it in inertial systems of reference (with two clocks impossible too). Impossible and not necessary. Suffice it to look at an inertial system from another inertial system.

 

[Vadim Matveev]

Originally posted by Creator
But your experiment did NOT show anything about difference in velocity; it only showed that the DISTANCE the light had to travel going East was DIFFERENT than the distance going WEST.

The only reason one direction takes longer than the other is because (as you pointed out) in a rotating Earth the Eastward traveling light has farther distance to go before getting back to the source.

Certainly. This is the only reason, but only in the inertial reference system of external nonrotating observer. But I write about the speed on the Earth, not in the inertial reference system.
Do You assume that on the rotating Earth it cannot be spoken about the speed?
Then, why do we speak about the speed of a car on the Earth? Let's measure the speed of cars “correctly” - in the inertial reference system.
What a value does the operator of radar obtain, if according to the determination of the speed relative to the Earth's surface, he divides the distance, passed by the signal on the Earth and equal to the length of equator, by the time, which he measured with the aid of the single clock of the radar?
Is it no speed? What is it then?
What did measure Michelson? Was by Michelson the time of propagation of the beam in one direction equal to the time of its propagation in other direction?
What speed do experimenters mean, when they say that they succeeded in measuring the speed on the Earth with enormous precision and that the speed (on the Earth!) was equal to the constant C (http://www.exphy.uni-duesseldorf.de/ )?
How can it be? Did not I show, that it is not true?