2inq, I have no idea what point you're trying to make with your explosions.

Perhaps you meant to ask where the origin is located? (The coordinates are located everywhere, as for all reference frames.)

The motion of the frame rather than its origin is what matters, but if you like we can place (x,y,z,t)=(0,0,0,0) at the Eastern clock at the time that it emits a westbound signal.
At that moment, the Eastern clock is motionless in this inertial reference frame, and both clocks are close enough to motionless in this inertial reference frame for the duration of the experiment.

Unlike the ECEF, however, the clocks do not remain motionless in this frame. In the same frame 12 hours later, they will be 20,000km or so away and moving at 926m/s. 12 hours after that, they will be motionless once again, but another 20,000 km further along.

Wrong, 2inq. The Earth's surface is stationary in the ECEF frame, and moving at 463m/s (at the equator) in the ECI frame. Look it up.

I have no problem with synchronizing the GPS clocks, 2inq. Please don't try to sidetrack. The GPS clocks and the Earth surface clocks are all synchronized in one inertial frame - the ECI - in accord with SR. If you want to discuss GPS, open another thread. I'd like to focus on the NASA clocks experiment. Do you have a reference to it?

Pete,

Sorry, yes that is what I was asking. I asked because I was having difficulty understanding the reference frame you were using. Something that seems clear in one's own mind can be difficult for others to inderstand. I often have a communication problem getting others to understand what I am trying to illuminate.
The following is from your fist link under the underscored Look:
I have read a considerable number of papers explaining GPS dynamics. Many well educated physicists have diffilculty understanding the clock synchronization used because it does not conform to what they are well versed in with Special Theory. I didn't intend for GPS to enter this discussion in a big way, but Pete you kept referring to the 'ECI' and 'ECEF' frames of reference. Not meaning to knock you, but you were confusing the frames and I was having difficulty understanding your posts.

I, too, would prefer to focus on the NASA fiber optic cable transmission. I have seen several 'summaries' of the experiment mentioned by well respected physicists, but I have as yet to find a complete 'paper' that I can study. Many of the best papers concerning telemetry and advanced interferometer/gyroscopes are in publications that require a subscription.

NASA is supposed to have a new matter-wave gyroscope in orbit now that is 10 billion times more sensitive at detecting rotation than optical gyroscopes. The purpose of the space testing is for using the matter-wave gyroscope for guidance systems in space. I have also read of proposals to use such gyroscope/interferometers to detect the minute variations in Earth's rotation rate. I mention this because it is along the same lines as the optical fiber experiment. Here is a link to NASA's page about the experiment:
http://funphysics.jpl.nasa.gov/techn...cap/smw-g.html

I knew you'd grab that one, where Ashby made a mistake, or at least used sloppy wording.
Read a little further!

The ECI and ECEF frames weren't made just for GPS, 2inq. You don't need to talk GPS to talk those frames.
The reason you were having difficulty understanding is because you are confusing those frames.

Thanks for that link, but it doesn't mention the East-West fiber optic experiment.

A link discussing the experiment isn't necessary, a citation should be sufficient. I can access subscriptions to many journals.

Pete,

No, Ashby did not make a mistake. You do need to read further yourself, Pete! The Earth rotates in the ECEF frame. I don't see how you can think otherwise. Perhaps you misunderstood and did what Ashby warned against:
The underlying inertial frame is the ECI frame, but this does not mean the ECEF frame is not rotating.
Ashby goes through the calculations using Einstein synchronization in the above.
Here he is again giving an example of Einstein synchronization as used on the surface of the Earth that would give errors because the Earth is actually rotating.
Ashby is again stating that using Einstein synchronization to synchronize surface clocks as it they were 'at rest' instead of rotating with the Earth leads to significant error.

Yes, the ECEF is rotating, once per sidereal day.
This means that the Earth is fixed in the ECEF.

It might help if you look for the formal definition of the ECEF under the term WGS-84, or if you look for the closely related Interntional terrestrial reference frame (as pointed out by Ashby): Here, here, here, and here.

Correct.
As SRT predicts, Einstein synchronization synchronizes the clocks in their inertial rest frame, not in the ECEF frame (which is not inertial) or ECI frame (in which the clocks are not at rest).

Pete,
Sorry for the delay, I went to eat. Yes, that is correct. The coordinates of the ECEF rotate with the Earth because they are fixed relative to the Earth. Imagine long poles which pass through the center of the Earth and extend outward throughtout the universe. This is the Earth rotating relative to the ICRF. The ICRF is the frame of the universe, the 'fixed' stars. The ECEF rotates within the ICRF, the fixed stars.
I haven't looked at your links yet because I already know what WGS-84 is. It is a mathematical representation of the Earth's surface, including elevation, latitude and longitude. GPS was designed to use this mathematical representation (WGS-84), but others can be used also if the particular GPS receiver is programed with the correct conversion algorithms. Some countries used different representations of Earth's surface, such at their airports, that may differer slightly in altitude estimations, etc. I think most countries have by now converted to WGS-84 as it is the most popular and accurate. As surface mapping techniques become more accurate, WGS-84 is likely to be either modified or replaced in the future.
Correct.
That is the reason why Einstein synchronizatiom is not used in GPS. The clocks in GPS are synchronized in both the ECEF and the ECI frames! As I said before, once the basic clock synchronization is achieved, Sagnac effects and gravitational effects have to be considered and implimented. Enviromental factors that delay light's propagation, such as the ionosphere, have to be accounted for in the most accurate GPS usage.

Now we're getting somewhere!
So, we've established that the clocks are syncrhonized in the ECEF (rotating, not inertial) and ECI (inertial) frames.
We've established that the clocks are not moving in the ECEF frame.

Do you now agree that the clocks are moving at 463m/s in the ECI frame?

What are you talking about? The ECEF frame is the frame in which surface clocks are rotating wrt the universe. The Earth rotates in this frame.
Uhh, no, Pete. The ECI frame models the satellite clocks' rotation around the center of the Earth. The motion of the Earth's surface plays no role in the ECI frame, just the satellites motion and the center of the Earth. The Earth does not need to rotate in this frame, it just models the orbital motion of the satellites about a point located at the center of the Earth.

2inq, the fact that the clocks and the Earth are rotating with respect to the Universe is not frame dependent... it's unambiguously true. The question is whether the clocks rotate and/or move with respect to the ECEF frame, and with respect to the ECI frame.

As you said, the ECEF coordinates are fixed to the Earth's surface. Hence the Earth does not rotate with respect to the ECEF. Likewise, the clocks are fixed with respect to the ECEF, since they are fixed to the Earth's surface.

Think:
Do the spatial ECEF coordinates of either clock change with time?
They do not - therefore the clocks are not moving in the ECEF frame.

WTF do satellites have to do with whether the clocks are moving in the ECI frame?
The Earth's rotation isn't a matter of "whether it needs to"... it does rotate.

The ECI frame (like any frame) is just a coordinate system, right? Anything and Everything that exists, exists at some coordinates in that frame.
The center of the Earth, for example, exists at (0,0,0) in the ECI frame.
The North Pole exists at (0,0,6357km) in the ECI frame.
A point on the Earth's surface directly under the First Point of Aries exists at (6378km,0,0) in the ECI frame.

Pay attention to that last point. Every part of the Earth's Equator will be at that (6378km,0,0) once per day, and only once. The ECI coordinates of a point on the Earth's surface are changing as the Earth rotates - ie the Earth's surface is moving in the ECI frame.

Correct, Pete. There is only one true rest frame, the rest frame of the universe, the ICRF. You are not 'at rest' while sitting at your computer, you are rotating with the Earth's surface and you are revolving around the sun. Rotation is absolute.
Yes, the coordinates are fixed to the Earth's surface. They are rotating coordinates. No, the Earth does not rotate with respect to the ECEF frame, it is a rotating frame. You are trying to use the ECEF as a 'rest' frame with the universe rotating around it. The sun does not revolve around the Earth, the Earth rotates. READ, again and again, and you will see what I am stating is correct. The only 'rest frame' used in GPS is the ICRF. As I said, it seems to be difficult for those entrenched in Special Theory methodology to understand GPS. Imagine looking at the Earth from the sun with a telescope. What would you see? You would see a rotating ball with a constellation of satellites orbiting it. Both the Earth's surface and the satellites are in motion. You are 'at rest' from your viewing location at the sun. That is the way GPS is modelled, from a distant observer's viewpoint, or the ICRF. The GPS receivers have the rotating frames modelled in their software by algorithms. It is the almanac necessary for the receivers to work. The Sagnac effect only appears in rotating frames. GPS would not work correctly if either the surface or the satellites were modelled as static. Both move while the signal is in transit and the recognization of that fact is necessary to determine distances between satellite and receiver, along with synchronized clocks.

I thought of a simple way to explain GPS clock synchronization. I'll drop the subject after this.

The ECI frame. In this frame, the satellite clocks are synchronized to beat at the same rate as a hypothetical clock located at the center of the Earth. The satellites all travel at the same velocity, and keep the same distance from,the unmoving center of the Earth, so they all can be synchronized (adjusted) to beat at the same rate, satellites and center of Earth.

The ECEF frame. In this frame, clocks on the surface of the Earth (the surface mathematically modelled by WGS-84) are synchronized with the hypothetical clock at the center of the Earth. It is important to understand that the hypothetical clock at the center of the Earth must be adjusted to beat at the same rate as a surface clock. The surface clock is in motion (rotating with the Earth) and, not sure, but probably located at sea level.

This gives the basic clock synchronization, all these clocks beat at the same rate. Obviously, clocks in the satellite constellation are moving relative to the clocks located on the surface. They don't change the clock synchronization because of this relative motion. In the GPS system, they consider the Sagnac effect on signal propagation. If one wishes to consider a 'rest frame', it is the frame of the satellite. The satellite (each of them) sees a point on the Earth's surface approach, pass underneath, then recede from its rest frame. The 'point' is a location on the WGS-84 model of the Earth's surface. The distance to this point will change as the surface moves beneath the satellite. The satellite broadcasts its time and location (ephemeris) by a signal to the moving surface, so the distance this signal must travel changes while the signal propagates, is in flight. That is the Sagnac effect, of course. The receiver on the surface is programed with an almanac with all the satellites orbital planes, and distances between each satellite in the plane, its memory. The GPS receiver on the surface is also programed with a model of the Earth's surface, usually WGS-84, in its memory. If the GPS reciever has an atomic clock already synchronized with GPS time, the receiver can use the ephemeris from three satellite to determine its location relative to the satellites by triangulation. All factors that effect the signal's time-of-flight must be considered for an truely accurate reading, such as ionospheric delays, delays due to humidity in the atmosphere, etc. Once the receiver location relative to the satellites is found, the receiver must apply that information to locate a point on the WGS-84 model of the Earth's surface. Here, the Sagnac effect has to be accounted for, as the GPS receiver is moving relative to the satellites while the signal propagates. Don't ask me about the mathematics, though!

Rotation is absolute, but that doesn't make the ICRF absolutely at rest, any more than it makes the ECI absolutely at rest.
But stop sidetracking .

Now you're getting it!

Or perhaps not.
2inq, any frame can be a rest frame. All that "rest frame" means is that a given object has zero velocity in that frame. Features on the surface of the Earth have zero velocity in the ECEF, which means the ECEF is the rest frame of objects on the Earth's surface.

Yes, we know that the Sun doesn't revolve around the Earth. But, in the rotating reference frame of the ECEF, the Sun's coordinates revolve around the Earth's coordinates.

In the ECEF, the Sun revolves around the Earth. This is an artefact of the rotating coordinates, not a physical thing, but it's true nonetheless. Artefacts like this are to be expected in any noninertial reference frame.

Will you leave the GPS alone? It has *nothing* to do with our discussion of the NASA experiment. If you want to discuss it, open another thread.


The point that I'm trying to get across, and that you appear to be trying to ignore, is that in the Earth Centered Inertial reference frame (in which the two clocks are synchronized), the clocks are moving at 463 m/s as the Earth rotates.

Pete,
You are misquoting me again, Pete. I never said the ICRF was 'absolutely at rest'. I said it was the universal rest frame of the 'fixed stars'. That is not a definition made up by me, it is the accepted scientific terminology you seem to be ignorant of. What do you think the universe moves relative to?
Pete, the ECEF is defined as a rotating frame. Your attempts to deny the coordinates of the frame rotate relative to the ICRF is based on your own ignorance of the definition. Want an explanation of a rotating frame? Here is the very first paragraph from wiki:
[PHP]A rotating frame of reference is a special case of a non-inertial reference frame in which the coordinate system is rotating relative to an inertial reference frame. An everyday example of a rotating reference frame is the surface of the Earth.[/PHP]
Here is just one reference to the ECEF frame by Dr. Ashby, there are many more in many different publications by different authors:
Pete,
No, rotation is absolute. Again, the ECEF models the ROTATING surface of the Earth, whose coordinates rotate relative to the 'fixed' sun and stars, the ICRF. You can't just mix frames and come up with a model that makes any sense.
Again, no the sun does not revolve around the Earth in the ECEF. The Earth rotates and the sun is at rest.
But it does have something to do with the NASA experiment. The reason there is a difference in signal propagation times when comparing west-to-east vs. east-to-west is because rotation is absolute. If you assume the Earth is 'at rest' and the sun revolves around the Earth, there can be no reason for the descrepancy.
I will stop posting about GPS as soon as you stop 'correcting' my post with obvious mistakes.

You said it is the "...one true rest frame, the rest frame of the universe". That sounds pretty absolute to me.
You need to look up the ICRF again, to. The ICRF is the rest frame of the Sun. Its orientation is based on the angular position of astronomical objects which are far enough away that their angular position relative to each other is almost constant.

Do you think the Sun is truly at rest in the Universe?

Yes, like I said.
I made no such denial, 2inq.

Yes, that's correct, 2inq. I have no idea what you think I'm saying, but if you think I don't agree with this, you're clearing misunderstanding me.

Do you really not see that this statement is inconsistent with your previous statement?

Saying "In the ECEF, the sun revolves around the Earth" does not mean that the Sun in revolvcing around the Earth in any absolute way. All it means is that the coordinates of the Sun in the chosen frame of reference rotate about the coordinates of the Earth in the chosen frame of reference.

Get the coordinates of the Sun in the ECEF throughout the course of a day. Mark them on a sheet of graph paper. It makes a circle, right?

Once again, yes. Rotation is absolute.
So why are you incapable of discussing rotation without mentioning GPS?

Who's assuming anything?

In all inertial frames of reference, the Sun revolves around the Earth. Hence rotation is absolute.

However, we can choose noninertial frames of reference to make rotation whatever we want. In such frames, the laws of physics will have a different form, with specific anomalies due to the fact that rotation really is absolute.

For example, the ECEF is chosen specifically to eliminate the Earth's rotation from the coordinate system, and give features on the Earth's surface constant coordinates.

In this reference frame, the discrepancy is due the the different form of the laws of physics - specifically, the speed of light from east to west is faster than the speed of light from west to east. This is the Sagnac effect.


Now please, 2inq, will you please stop avoiding this point:
In the Earth Centered Inertial reference frame (in which the two clocks are synchronized), the clocks are moving at 463 m/s as the Earth rotates.

Can you stop raving about GPS for a moment and focus on the movement of the Earth's surface in the ECI?

Pete,
Well, I mean the coordinates of the ICRF are pretty exact. It does not mean bodies have no motion within those coordinates:
Pete,
Pete, the sun is at rest in a heliocentric reference frame, not in the ICRF. You are the one that needs to look up definitions. I have been posting about the ICRF for about two years and you still don't understand it?? Here is a link to the new website, with an increased number of referenced point nowadays:
with VLBI.
http://www.iers.org/MainDisp.csl?pid=40-25728
Pete,
This is were you keep making the same mistake, Pete. I never said the sun revolves around the Earth in the ECEF, you keep saying that. Again, rotation is absolute. Do you know what that means? It means you can't swap viewpoints like you keep trying. The Earth rotates on its axis, the sun does not revolve around the Earth. The 'fixed' points on the Earth's surface are rotating relative to the ICRF in the ECEF. The sun is not revolving around the Earth in the ECEF, it is at rest relative at a certain point in time, the J2000.0 ephemeris of the ICRF. The sun actually plays no part in current GPS reference frames. Early in GPS operation, the vernal equinox was used as the 'rest' point with respect to which the ECEF rotated. The vernal equinox was replaced with the ICRF when it was formally realized and become the superior inertial 'rest' frame.
Pete,
I have not avoided your statement, I have explained the ECI frame several times. Your question is ambigous, and based on a misconception. Which 'two clocks' are you referring to? One on the surface and one at the center of the Earth, or two clocks located on the Earth's surface, such as with the NASA experiment? First, the Earth DOES NOT ROTATE in the ECI frame. Let me cut & paste from Ashby again:
In the above quote, Dr. Ashby is describing the ECI frame of reference, an inertial frame.
This is where Dr. Ashby introduces the ECEF frame to the system. Notice THIS is the frame that rotates, and notice the reference to the 'earth-fixed, rotating system', ECEF frame.

First you say that the Sun is not at rest in the ICRF, then you say that it is.

The definition of the ICRF is in two parts.

1. It's orientation is defined by the angular positions of many astronomical objects. We agree on this part.
2. It's position and velocity is defined by setting its origin to be the barycentre of the solar system. For our purposes, it's sufficient to say that the Sun is the origin of the IRCF. The Sun wobbles a bit around the barycenter, but it's close enough for us. So, the ICRF is essentially heliocentric.

ICRS overview:
The ICRS is a set of specifications defining a high precision coordinate system with its origin at the solar system barycenter and "space fixed" (kinematically non-rotating) axes.



First you say that the Earth rotates in all frames, because rotation is absolute... then you say that the Earth doesn't rotate in the ECI. I think you're confusing yourself.

Look, we've established that we agree that:

• The Earth is fixed to the ECEF (or vice versa).
• The ECEF rotates with the Earth (it's a rotating frame).
• Objects fixed to the surface of the Earth have unchanging ECEF coordinates.
• The center of the Earth is at the spatial origin of the ECI.
• The ECI does not rotate with the Earth (it's an inertial frame).

So how about we stop pissing about with the terminology of whether object X is rotating in frame Y and cut to the chase.
Let me put it this way:
In the ECI, the coordinates of the two NASA clocks are changing at 463m/s.
Do you agree?

Pete,
I just noticed I made a typo when specifying the J2000.0 time epoc in the post, I left out the '2'. That specifies a particular moment in time, so yes, the sun is at rest, and at a specific location, at that moment in time.
No. The coordinates of the surface clocks are not changing in the ECI frame. The Earth does not rotate in the ECI frame. Also, the sun does not revolve around the Earth in the ECI frame. The satellites orbit a 'stationary' Earth in the ECI frame. The ECI frame is an 'underlying' inertial frame that is used for initial clock synchronization. It is a 'bogus' frame used to synchronize all clocks in three different locations. (1) All clocks located on the Earth's surface, (2) one located at the center of the Earth, and (3) all clocks on all the satellites. The NASA surface clocks would be rotating in the ECEF frame, the frame of reference in which the Earth rotates. I told you these frames are not like you are used to using in SRT or Galilean relativity.

2inq, you're talking nonsense. It's clear that you have a very weak grasp of the concept of a reference frame in general, and also the specific frames involved in our discussion.

This is all absolutely correct, Pete. I'll try another method to explain why Ashby does not model the Earth's surface rotating in the ECI frame. Atomic clocks located at sea level on the surface of the Earth all beat at the same rate, regardless if they are on the equator or at the north pole. It is a simple matter to synchronize that paper clock located at the center of the Earth with any clock located on Earth's surface because of this. If you model a sphere rotating about an axis, the surface speed of the sphere (Earth) will be greater at the equator than at the north pole, leading to problems in clock synchronization. All clocks on the Earth's surface would not be beating at the same rate in that model. It is an unnecessary and unwanted step to model the Earth's surface as rotating in the ECI frame, which is used for clock synchronization. Remember, we adjust the center-of-earth clock to beat at the same rate as a normal atomic clock located on the surface keeping UTC time. That clock on the surface has time dilation already built into it, it beats at the specified SI rate of a cesium clock. Next, all satellites orbit a point located at the center of the Earth at the same, identical velocity. Remember, we have that clock at the center of the Earth beating at the same rate as a surface clock, so when we synchronize the satellite clocks to beat at the same rate as the center-of-earth clock, all clocks are synchronized. It is simple and beautiful! It is difficult for physicists to understand, but not too hard for astronomers. Now, does this make sense to you? I understand it, but it is hard to explain to physicists not used to dealing with state vectors and keplerian orbital elements. I don't know the mathematics, but I do have a visual understanding of the motions. I have had a interest in amature astronomy for many years. I still have a couple of telescopes, but seldom use them nowadays.