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.

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.

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?

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).

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.

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

"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.

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.

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