Relativity and Cosmology Blog

# Relativity and Cosmology

This is a Blog on relativity and cosmology for engineers and the like. My website "Relativity-4-Engineers" has more in-depth stuff.

Comments/questions of a general nature should preferably be posted to the FAQ section of this Blog (http://cr4.globalspec.com/blogentry/316/Relativity-Cosmology-FAQ).

A complete index to the Relativity and Cosmology Blog can be viewed here: http://cr4.globalspec.com/blog/browse/22/Relativity-and-Cosmology"

Regards, Jorrie

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# GPS and Relativity Misconceptions 3

Posted November 03, 2011 12:00 AM by Jorrie
Pathfinder Tags: GPS relativity Sagnac effect

The Sagnac effect is important in the GPS system, but not in the way many people imagine it is. Ron Hatch missed the boat completely in his discussion of the Sagnac effect. One must keep in mind that in his RELATIVITY AND GPS, he attempted to refute Einstein by using the GPS.

Hatch: "The most commonly held erroneous belief is that the [Sagnac] effect is caused by rotation. Ashby states:

(Quoting Ashby): "In the rotating frame of reference, light will not appear to go in all directions in straight lines with speed c. The frame is not an inertial frame, so the principle of the constancy of the speed of light does not strictly apply. Instead, electromagnetic signals traversing a closed path will take a different amount of time to complete the circuit." "

Hatch continues: "In point of fact, rotation is only incidentally involved with the Sagnac effect. The Sagnac effect is the result of a non-isotropic speed of light and arises any time an observer or measuring instrument moves with respect to the frame chosen as the isotropic light-speed frame." (My emphasis).

The truth is that the Sagnac effect is only present in rotating reference frames. Linear, non-accelerated movement does not cause any Sagnac effect. Hatch seems to confuse the Sagnac effect with straightforward relativistic desynchronization of clocks in inertial frames that are moving relative to each other.

In fact, in an inertial reference frame like the ECI frame used in the GPS,(a) no Sagnac effect is present and none is being corrected for. In a satellite's rotating frame, the Sagnac effect is present, but AFAIK, that frame is not used in any of the calculations, so it's irrelevant. (b) The Sagnac effect is obviously also present in the rotating ECEF frame of the ground receivers. That correction is done by the receivers because it depends on the direction from a receiver to each satellite it detects.

One is tempted to conclude that from a relativistic POV, Hatch understands neither linear nor rotating frames correctly. This is reinforced by his insistence that the Sagnac effect is compatible with Lorentz ether theory (LET), but not with special relativity (SR). The truth is that there are no predictions that differ between LET and SR, if both are correctly applied to the low-speed, weak gravity case.(c)

There are numerous other relativistic blunders in Hatch's subsection on the Sagnac effect, but IMO, this one takes the cake and eats it: "If the receiver is moving in the chosen absolute frame, the speed of light is not isotropic; and the Sagnac effect is simply the adjustment for the non-isotropic light speed. The Sagnac effect on GPS signals in transit proves that the special theory magic does not keep the light speed isotropic relative to the moving receiver."

It is easy to spot his "absolute-frame-mindedness". Plus a total misapplication of the special theory, as shown above. Hatch fails to recognize that SR's synchronization of clocks and LET's non-isotropic light speed boils down to the same thing - same math, just different philosophy.

"... for the path of the radiation from the GPS satellite, to the receiver clearly follows a straight line and the instantaneous velocity of the receiver, while due to the earth's spin, is not affected significantly by the radial acceleration during the instant of reception."

Yes, a straight line in the ECI frame, not in the ECEF frame, where the Sagnac effect is applicable. And there are more, but I won't bore the reader with all of them.

-J

(a) The ECI frame is in inertial movement around the sun, centered on earth, but not rotating relative to the fixed stars. The ECEF frame is also centered on earth, but is rotating with earth and hence is not a strict inertial frame of reference. The operative letters to remember when reading is I (inertial) and EF (earth fixed).

(b) A satellite's altitude and speed in the ECI frame are obviously used to calculate the clock rate offset and the synchronization offset relative to the GPS 'paper clock'. But, the rotating frame of the satellites are not used, AFAIK.

(c) In highly relativistic cases, the full relativistic version of Sagnac is important, but it is negligible in the GPS (low speed, weak field case). Actually, the low speed Sagnac effect is just a manifestation of Einstein's clock synchronization in SR. The Sagnac time difference Δt in the theory section of the referenced Wiki article can very simply be rewritten as twice the Einstein clock synchronization offset - twice because light goes in both directions around the frame. In order to keep this Blog entry to reasonable length, I will write a new Blog article on the Sagnac effect as a test of the validity of Einstein's clock synchronization procedure - that is if anyone is interested in more detail...

This discussion was "closed" on 11/22/2011 12:05 AM. No new comments are allowed.
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#1

### Re: GPS and Relativity Misconceptions 3

11/03/2011 7:07 AM

Hatch wrote, "... for the path of the radiation from the GPS satellite, to the receiver clearly follows a straight line and the instantaneous velocity of the receiver,..."

And it isn't really a straight line because the signal is significantly refracted by the ionosphere. He is over simplifying the problem, but it may be immaterial to the point in this case.

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#4

### Re: GPS and Relativity Misconceptions 3

11/03/2011 10:57 AM

The oversimplification for ionosphere effect one can perhaps overlook more readily than his failure to consider the curved path that the signals follows from satellite to the ground relative to the receiver frame, or relative to the satellite frame, for that matter.

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#2

### Re: GPS and Relativity Misconceptions 3

11/03/2011 8:29 AM

I have a question which I give below, but first just some notes on a dead link and a few typos which I've noted by bold and underline:

The Sagnac effect is important in the GPS system, but not in the way many people imagine it is. Ron Hatch missed the boat completely in his discussion of the Sagnac effect. One must keep in mind that in his RELATIVITY AND GPS [busted link], he attempted to refute Einstein by using the GPS.

Hatch: "The most commonly held erroneous belief is that the [Sagnac] effect is caused by rotation. Ashby states:

(Quoting Ashby): "In the rotating frame of reference, light will not appear to go in all directions in straight lines with speed c. The frame is not an inertial frame, so the principle of the constancy of the speed of light does not strictly apply. Instead, electromagnetic signals traversing a closed path will take a different amount of time to complete the circuit." "

Hash [Hatch?] continues: "In point of fact, rotation is only incidentally involved with the Sagnac effect. The Sagnac effect is the result of a non-isotropic speed of light and arises any time an observer or measuring instrument moves with respect to the frame chosen as the isotropic light-speed frame." (My emphasis).

The truth is that the Sagnac effect is only present in rotating reference frames. Linear, non-accelerated movement does not cause any Sagnac effect. Hatch seems to confuse the Sagnac effect with straightforward relativistic desynchronization of clocks in inertial frames that are moving relative to each other.

In fact, in an inertial reference frame like the ECI frame used in the GPS,(a) no Sagnac effect is present and none is being corrected for. In a satellite's rotating frame, the Sagnac effect is present, but AFAIK, that frame is not used in any of the calculations, so it's irrelevant.(b) The Sagnac effect is obviously also present in the rotating ECEF frame of the ground receivers. That correction is done by the receivers, because it depends on the direction from a receiver to each satellite it detects.

Now my question:

I don't understand why the Sagnac Effect is relevant to ground receivers as you mention in (b) directly above. I thought that the Sagnac effect describes the change in frequency and differential arrival time for light signals taking reverse paths in a closed loop system that is rotating -- like a ring laser gyro. I could see a ground based receiver detecting the doppler shift in frequencies between an approaching and receding GPS satellite, but that's not really the Sagnac effect, is it? What did I miss?

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#5

### Re: GPS and Relativity Misconceptions 3

11/03/2011 11:54 AM

Hi Usb, that link is the only one I could get to work for my system/country. If you have trouble, drop me a CR4 mail, give me an email address and I'll send you the pdf. The document is not available at the usual places...

"I thought that the Sagnac effect describes the change in frequency and differential arrival time for light signals taking reverse paths in a closed loop system that is rotating -- like a ring laser gyro."

You are right, that's the proper Sagnac effect, but part of the effect is present in a one-way signal that reaches the receiver from anywhere else but precisely vertical (in receiver frame). Despite the fact that the GPS clocks are all synchronized in the non-rotating ECI frame, they are not synchronized in the rotating earth (ECEF) frame.

Clocks cannot be synchronized by sending light signals (a-la Einstein's method) in a rotating frame. You have to correct for the Sagnac effect. Hatch and LET view this as the result of non-isotropic propagation of light in the 'moving' frame and SR views it as simple clock synchronization (1st order in ω and hence appreciable) plus velocity time dilation (2nd order in ω and hence negligible in the GPS).

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#6

### Re: GPS and Relativity Misconceptions 3

11/03/2011 1:00 PM

Me: "... (1st order in ω and hence appreciable) plus velocity time dilation (2nd order in ω and hence negligible in the GPS)"

Should rather read "(1st order in v/c and hence appreciable) plus velocity time dilation (2nd order in v/c and hence negligible in the GPS)", where v = rω.

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#8

### Re: GPS and Relativity Misconceptions 3

11/03/2011 4:28 PM

Thanks Usb, I corrected the typos.

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#3

### Re: GPS and Relativity Misconceptions 3

11/03/2011 10:50 AM

I'm not bright enough to answer this. Could the Sagnac effect apply to the "neutrinos too fast" measurement under the alps?

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#7

### Re: GPS and Relativity Misconceptions 3

11/03/2011 1:18 PM

"Could the Sagnac effect apply to the "neutrinos too fast" measurement under the alps?"

IMO, there is a very small chance that some error in the clock synchronization (Sagnac) between the two sites can be the source of the anomaly. I think it's more probable that it lurks in the very complex statistical extraction of the travel-time from the data.

I believe the 'retest' will be with shorter pulse lengths, in order to eliminate some of the uncertainty. I'm pretty sure that this time they also went through the clock synchronization procedure with a magnifying glass.

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#9

### Re: GPS and Relativity Misconceptions 3

11/04/2011 2:13 PM

I'm convinced. I take it that you think Ashby is legit. What do you know about either one's credentials? Tom Van Flantern has his own pet theory. I think he is on your list of cranks.

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#10

### Re: GPS and Relativity Misconceptions 3

11/04/2011 3:39 PM

AFAIK, Prof. Ashby is still working in the physics dept of Colorado State Univ. He is definitely a 'protector of the canon' and as such legit. His publications support that.

I do not take credentials like this as the clincher, but one just have to look what and where a person has published and read a few late editions to find out if he/she has gone off the rails, so to speak. The late Dr. Tom van Flandern was an example of a relativistic heretic in his later career.

-J

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