Sagnac and the earth's orbit.

The Sagnac effect has an important influence on the system. Since most GPS users are at rest or nearly so on earth's surface, it would be highly desirable to synchronize clocks in a rotating frame fixed to the earth (an Earth-Fixed, Earth-Centered Frame or ECEF Frame). However because the earth rotates, this is prevented by the Sagnac effect, which is large enough in the GPS to be significant. Inconsistencies occurring in synchronization processes conducted on the Earth's surface by using light signals, or with slowly moving portable clocks, are path-dependent and can be many dozens of nanoseconds, too large to tolerate in the GPS. Thus the Sagnac effect forces a different choice for synchronization convention. Also, the path of a signal in the ECEF is not "straight." In the GPS, synchronization is performed in the ECI frame; this solves the problem of path-dependent inconsistencies.
http://www.phys.lsu.edu/mog/mog9/node9.html

The reason they synchronize to a rotating frame is to avoid the calcs in the hand held units for Sagnac. That calc would require the unit to know the relative position of the satellite in order to apply the Sagnac effect since north south does not have an effect. That would be a pain.

In the same light, we should have to synchronize to an earth-sun orbital frame to avoid those sagnac calcs also.

 

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Are you going to contribute anything or just continue splashing dots on the screen.

 

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Hmm. I think he's quibbling semantics. Time in the rotating frame is essentially defined to be equivalent to time in the underlying inertial frame (Ashby says as much here). Or, I could just be wrong. But either way, my explanation wasn't quite right.

I don't know.

I think that it does matter is that the WGS-84, our GPS frame of interest, is rotating once per day, and that we're concerned with clocks synchronized around the Earth, not around the Sun.

No, the basic correction is straightforward, and is performed in the receivers. That's what Ashby is talking about in the article I linked in the last post. More complex calculations are required for moving and synchronising high-precision clocks, but that's not relevant to standard GPS receivers.

 

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Yes, but the clock sychronization is the account for the sagnac effect of the light signals.

Let's say it is done in the receivers, then fine, I am OK with that and I read that also.

I have now read it is ignored because it is so small, which is false, that it is calculated in the receivers and that it is eliminated by making the rotating earth frame "stationary".

What has not been resloved is that the earth - sun orbital frame is a sagnac rotating frame.

That implies the Sagnac equations should hold:

t1 = 2πr(1/(c-v))
t2 = 2πr(1/(c+v))

They are not used that I can see in GPS. Yet, they are huge timing differentials.

Sagnac holds that any rotating frame should measure these timing differentials and not just some, all rotating frames.

 

Thinking further, the reason that synchronizing clocks in a rotating frame is problematic is that you run into a discontinuity. A little bit (but not much) like the time discontinuity at the international dateline.

That's why GPS clocks have to be synchronized in the ECEI frame, which is why we get a Sagnac effect in the ECEF frame - clocks on the surface at the equator are moving at 500m/s relative to the reference frame in which the signal time of flight is defined.

But for the orbital rotation, I think that we can synchronize our clocks in the rotating frame because we're not trying to synchronize clocks all the way around the Sun - we don't have the discontinuity problem. This means that we don't have to use the Sun as our base inertial reference frame - we can use the ever-changing instantaneous inertial reference frame of Earth, which means that our clocks are not moving at 30km/s relative to the frame in which the signal time-of-flight is defined.


Consider this:
We could set up a local positioning system, with ground based transmitters, independent of the GPS. After we synchronize our transmitter clocks by bouncing light signals back and forth between them, we'll find that there is no Sagnac effect correction needed in our receivers. However, if we extend our system East-West around the world, carefully synchronizing all the transmitter clocks as we go, we'll find that when we get back to the start there is a 0.13 second discrepancy between the last clock and the first.
To remove that discrepancy (which is itself due to the Sagnac effect), we'll need to use a different synchronization procedure. (Starting from the South pole and synchronizing only on North-South lines would work.) But once we do so, we'll find that our receivers need Sagnac correction.

 

I am OK with this.

But, the sagnac correction is not a clock issue really though it could be called one.

It is that light travels at one speed. A rotating frame increases/cuts the distance light travels and hence alters the light path.

So, you cannot blindly perform ct = d based on a timing in a rotating frame. You must apply sagnac.

In that same light, the motion of the earth's orbit is also a sagnac effect. We should see light path distance differentials caused by the orbit just like we see if for earth's rotation.

The orbital path is simply longer and nothing else.

 

I've already established that you're either unwilling or unable to provide open minded rational informed discussion. If you're unwilling to accept that there are people on this forum who have a better understanding of physics and mathematics then I've offered to help you submit your work to journals, whose knowledge you can't just dismiss out of hand. Your unwillingness demonstrates your intellectual dishonesty.

You can't throw the "Are you going to contribute anything?" attempt at an insult when you ignore anything people do contribute which contradicts what you claim.

If you believe SR is wrong and the GPS setups have a problem with the Sagnac effect why don't you submit your work to journals? Please answer this direct, simple question. If you're so sure you're right and everyone else isn't why can't you put your maths where your mouth is? Why can't you put your money where your mouth is? Why can't you demonstrate any intellectual honesty?

 

You are off task.

Sagnac works in the lab.

Sagnac works for the earth's rotation in GPS and other experiments.

Sagnac does not seem to show up for the earth's orbit which is a Sagnac application.


If you can figure this out fine. It is inconsistent so any position taken is wrong.

I do hope this was not beyond your ability.

Anyway, if you can figure this out, do it, otherwise, admit you cannot and walk away.

 

Calcs

Here are my calcs. You can use angular velocity and it does not matter. I am using linear velocity.

p = pi

Sagnac calc
4pRv/( c² - v² )

Earth's orbit
Radius of earth orbit
150,000,000km
Light 300000km/sec
earth linear velocity of orbit 30km/sec
c² - v²= 89999999100

4pRv/( c² - v² ) = 0.62831852628318526283185262831853 seconds
Total distance of orbit 2pr=942477780km
Error 6.6666667333333340000000066666611e-10 sec/km

Earth's rotation
6357*km radius of earth
v = (1669.8 km/h). = 0.46383333333333333333333333333333 km/ sec
4pRv = 37053.055248180399999999999999973
( c² - v² ) = 89999999999.784858638888888888889
4pRv/( c² - v² ) = 4.1170061386965526478264664025431e-7 seconds
Total distance of orbit 2pr= 39942.2083164 km
Error 1.030740740743204684806475940255e-11 sec/km

I cannot figure out why the earth's orbital sagnac is not showing up in GPS based on the above calcs.

 

Actually, you can, as long as you're limited to a local area.
Our hypothetical local positioning system can give very precise location fixes, and still not be precise enough to detect the Earth's rotation.

This is actually a clock issue, because we're dealing explicitly with time measurement. Changing the way we synchronize our clocks will obviously change our measurements of time.

It is true that using Einstein synchronization in a rotating reference frame is not perfect (and if we complete an east-west loop we will find it is not consistent), but for a small region it is close enough.

 

But, the earth's orbit is a rotating frame also.

That is the problem here. It does not show up.

I really do not know why.

Do you?

 

Because laboratories and the Earth's major landforms are tied to the rotation of the Earth and the sun appears to rise and set. If the gyroscope's laboratory were tied to the Sun-centric frame where the Earth's revolution was imporant it would appear to use land-based experimenters to turn to follow the sun each day.

How dull this topic is, but I appreciate that Jack_ started it in pseudoscience to try and evade moderation.

 

I think I do, but I'd be willing to stand corrected.

Yes, it's a rotating frame. But our small section of interest approximates very closely to an inertial frame: all the GPS satellites have the same speed with respect to Earth.

If we had a ring of satellites spaced around the Earth's orbit and we tried to synchronize them all in Earth's reference frame, we'd run into trouble, because not the satellites would have different speeds with respect to Earth. Then we'd have to synchronize them in the Sun's inertial frame, and we'd get a Sagnac effect.

 

I believe the WGS84 model of the Earth used in the GPS system is a rotating model. IE fixed to the surface of the rotating Earth. As such it can be used along with Lorentz transformations to calculate adjustments to the signal delay time to compensate for the Earth's rotation during the signal transit time from each GPS satellite.

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This does not follow to refute Sagnac for the earth's orbit.

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

It is a loop and the earth is moving along the loop in its orbit around the sun.

The point I was making is all I listed are loops, but the earth's orbit is the only one not to follow the rules of Sagnac.

And, spend some time thinking about it.

The earth's orbit would not affect a gyroscope in any measureable way. Only rotations close to the gyroscope's would affect its results.


So, you did nothing with this.

 

The issue is not synchronization.

When a hand-held unit receives a signal, that signal contains the satellite's position and the time the signal was sent.

Then, after the Sagnac correction, d=ct for the time differential between the hand-held unit and the time the message was sent. Then, we have the distance to the satellite.

That is the part I am talking about.

The Sagnac correction for the earth's rotation is applied because as the light moves toward the receiver, the receiver rotates with the earth changing the distance the signal travels.

In the same light, if the unit had been at the equator at noon, then it should see the full effect of the Sagnac effect of the earth's revolution around the sun.

This does not appear to occur unless it is simply not published.

In other words, assume a satellite is low on the horizon in the east at the equator.

We should measure a sagnac correction for the earth's rotation on its axis and a sagnac correction of the earth's rotation/revolution around the sun.

Here is what I have.

If sagnac is true for the earth's rotation, then light travels at one speed c. the speed of light cannot be increased by circular motion and presumably not by linear motion either.

If light travels at one speed c, then as the earth moves in it's revolution loop at 30k/s, while light moves c through space, the unit at the equator at noon would move with the earth' rotation and the earth's revolution cutting the distance the signal must travel to meet the unit.

There is definitely something wrong.

Maybe they do not publish the revolution correction. But, that seems highly unlikely.

 

Yes, it is.

Consider our local positioning system with fixed land-based transmitters.
We have a choice for how we synchronize the transmitter clocks:

1) Synchronize them all with GPS satellites - Sagnac correction required at the receivers
2) Synchronize them locally using Einstein synchronization - no Sagnac correction required.

There's nothing wrong. It's special relativity in action.
We don't see a Sagnac effect for locally synchronized clocks for exactly the same reason that the Michelson-Morley experiment produced a null result - the locally measured speed of light is not affected by our motion through space.

 

Quite.

I have repeatedly offered to help Jack submit his 'results' to journals in a manner which means that he'll be evaluated on what he says, not the layout of his work. Journals are picky like that. He's never taken me up on the offer, as its equivalent to having his work heavily moderated for justified results and he knows he'll fail such review.

As it happens I have a free month on my hands. I've done the corrections to my thesis, required after my viva. I've got myself a job but it doesn't start till mid May. In that time I have various things to do (holiday, family wedding, moving across the country) but I've plenty of time to format his work if he provides me with his work typed up. To account for equations he can PM me a lengthy message with the tex tags and all and I'll convert that into a pdf for him, including providing him with the master .tex file. He'll then have his work correctly formatted for a pre-agreed upon reputable journal and can get his Nobel Prize for killing relativity. What's stopping him? He's got the time to make the posts here. Why doesn't he cut to the ending and just submit his work? Journals mean you don't have to write out your work 10 times to 10 different groups of people. If he's confident he's go zero excuse.

Thus one concludes he doesn't actually believe his claims are deeply as he professes to.

 

Nope, the correction is not used for synchronization.

It is about the change in the distance light travels because of motion in the loop.

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


But, I will think on this more from different angles.

 

Wrong.

I know for a fact my twins contradiction refutes SR.