Light Traveling in Opposite Directions

[ronandkryn]

Light Traveling In Opposite Directions Around Planet Earth

Assume:
Twenty-Four Space Platforms are placed into space at equal distances. One Platform is a Space Station containing equipment necessary to make this experiment happen. The other twenty-three Platforms contain mirrors configured in angles necessary to make this experiment happen. A beam of light is transmitted in opposite directions [East & West] from the Space Station.

The object is to measure the time that it takes for the two beams to return to the Space Station. Assume that they do not bump into each- other. The Question is: Will both beams of light return to the Space Station at precisely the same time?

 

[LURCH]

If the time is measured by someone within the space station, yes.

 

[George Jones]

Do the satellites orbit or hover? Show frame-dragging by the Earth's rotation be ignored or taken into account?

 

[Cleonis]

Light Traveling In Opposite Directions Around Planet Earth
[...]
A beam of light is transmitted in opposite directions [East & West]
[...]
Will both beams of light return to the Space Station at precisely the same time?

No, the two beams will not arrive back at the point of departure at the same time.

I note the following things:
- The transmission is a relay. The signal can be relayed with mirrors, receiving/resending signals instead is the same thing.
- There are two operative factors:
A) The stations in the formation have no velocity relative to each other; the station-to-station intervals remain the same.
B) The formation of relay stations is circumnavigating a central axis.

Note that the formation of relay stations can be either satellites in orbit, or a set of stations on Earth. You can build 24 relay stations on Earth, along the equator, equally spaced. The factor that matters is the act of collectively circumnavigating a central axis.

The physical effect that is at play is called the Sagnac effect.

The Sagnac effect is used to detect rotation.
The signal consists of light, and the conduit of the signal is a fiber optic cable. The fiber optic cable is coiled many times, to increase sensitivity. Light signals travel in opposite directions, and after the light has exited the fibers an interference pattern is obtained. If the device is physically rotating there is a corresponding shift of the interference pattern.

Even more interesting is ring laser interferometry. In ring laser interferometry the light is not introduced into the conduit, instead light is generated inside the conduit. Part of the ring conduit is a laser cavity, and when the ring laser interferometer is in operation laserlight is traveling in opposite directions. A small portion of the light is allowed to escape the conduit, and an interference pattern is obtained. The co-propagating light and the counter-propagating light are shifted in frequency. Because of that shift the resultant wave of the two waves has a http://en.wikipedia.org/wiki/Beat_(acoustics)"

The process of ring laser interferometry is a self-calibrating process. If the ring laser is non-rotating then no beat frequency arises. There is a beat frequency if and only if the ring laser interferometer is rotating. The beat frequency is proportional to the rotation rate.
The university of Canterbury, New zealand has huge ring laser interferometer setups in deep caverns, to monitor the Earth's rotation.

Cleonis

 

[ronandkryn]

Do the satellites orbit or hover? Show frame-dragging by the Earth's rotation be ignored or taken into account?

Thank you.
Can you give me an answer based on both of the scenarios stated in your response?
Thank you

 

[yuiop]

In the case that the satellites are orbiting, the counter-going light signals do not return at the same time. This includes the case of satellites in geosynchronous orbit that stay stationary above given locations on the Earth's surface. This follows from the Sagnac effect.

In the case that satellites are positioned so that they are not moving relative to the "distant stars" or relative to the microwave background radiation then the light signals will return at approximately the same time. Satellites positioned like this will have to be powered by rockets to make them hover as they can not stay in natural orbit. I say approximately, because there will still be slight rotation of the satellites due the motion of the Earth relative to the Sun and due to the rotation of the Solar system around the Galaxy. The only time the light signals will return at exactly the same time is when the satellites have no absolute rotation at all.

Generally, except in one very special and probably unachievable case, the light signals do not return at the same time and so the answer to your poll question "Will both beams of light return to the Space Station at precisely the same time?" is generally "No".

Consider the following situation to visualise the Sagnac effect. The spacestation and the 23 mirror satellites are orbiting anticlockwise from the point of view of an observer far above the North pole. A signal going in the anticlockwise direction has to travel further than one complete orbit because the motion of the spacestation during the light signals travel time is shortening the distance the signal has to treavel. A signal going in the clockwise direction around the chain of satellites travels a distance that is less than one complete orbit because the motion of the spacestation during the signal travel time is increasing the distance the signal has to travel. Since the speed of light is the same in either direction, the signal travel times will be different.

Frame dragging is a very small effect and very difficult to detect in practical experiments while the Sagnac effect is quite a strong effect and very easy to detect in practical experiments, so it is almost certain that any frame dragging (in the case of the Earth) will not exactly cancel out the Sagnac effect.

If the time is measured by someone within the space station, yes.

Sorry, but this is simply wrong and the location of the observer is unimportant. If two signals arrive back at the spacestation at exactly the same time according to an observer onboard the spacestation then the same will be true according to any observer. If the two signals do not arrive at the spacestation at exactly the same time (which is the most likely case) then all observers will agree that is the case, even though they might disagree on the the time interval between the arrival of the two signals, no observer will see the time interval as zero.

 

[heldervelez]

CMB : A preferred reference frame

kev I agree with you, completely.
to demystify the horror to the aether I bold some words

CMB : A preferred reference frame.

...
In the case that satellites are positioned so that they are not moving relative ...to the microwave background radiation then the light signals will return at approximately the same time. ...

An absolute rotation:

...
... due the motion of the Earth relative to the Sun and due to the rotation of the Solar system around the Galaxy. The only time the light signals will return at exactly the same time is when the satellites have no absolute rotation at all.
...

 

[yuiop]

An absolute rotation:

Yep, rotation has an absolute nature that is lacking in inertial motion.

 

[George Jones]

An observer hovers above the Earth with constant $r$, $\theta$, and $\phi$, so that the observer doesn't change position with respect to the fixed stars. Mirrors (many more than twenty-three) are arranged so that the observer can send light into (non-geodesic) circular orbit in either direction at the same constant $r$. The observer simultaneously emits two "photons'' that use the mirrors to orbit in opposite directions. Because the rotating Earth drags spacetime around with it, the photon that orbits in the same sense as the Earth's rotation arrives back at the observer's position before the photon that orbits in the opposite sense.

If the photons orbit at $r=10000\unit{km}$ (about $4000\unit{km}$ above the Earth's surface), then, according to the observer's watch, I calculate the difference in time between arrivals of the photons is $1.5\times 10^{-16}\unit{s}$. In a new thread, I hope to give details on how this is calculated.

 

[GRDixon]

Light Traveling In Opposite Directions Around Planet Earth

Assume:
Twenty-Four Space Platforms are placed into space at equal distances. One Platform is a Space Station containing equipment necessary to make this experiment happen. The other twenty-three Platforms contain mirrors configured in angles necessary to make this experiment happen. A beam of light is transmitted in opposite directions [East & West] from the Space Station.

The object is to measure the time that it takes for the two beams to return to the Space Station. Assume that they do not bump into each- other. The Question is: Will both beams of light return to the Space Station at precisely the same time?

Presumably the space stations are not at rest in any inertial frame of reference, but orbit in circles. In this case the signals will not return to the original station at the same time. Furthermore, the returning beams will be phase shifted and the orbital rotation rate can be deduced by re-combining the signals and counting the beat frequencies. The experiment is essentially a much enlarged version of the laser gyroscope.