Re: The Speed of Gravity – What the Experiments Say
- From: Sam Wormley <swormley1@xxxxxxxxx>
- Date: Mon, 04 May 2009 02:34:14 GMT
Surfer wrote:
http://ldolphin.org/vanFlandern/gravityspeed.html
Tom Van Flandern
[as published in Physics Letters A 250:1-11 (1998)]
From http://math.ucr.edu/home/baez/RelWWW/HTML/wrong.html (google archive)
In a paper remarkable chiefly for the extraordinary number of obvious errors it contained (see above), Tom Van Flandern, ("The speed of gravity-- what the experiments say" Phys.Lett.A 250 (1998) 1-11, also available here), stated:
the Global Positioning System (GPS) showed the remarkable fact that all atomic clocks on board orbiting satellites moving at high speeds in different directions could be simultaneously and continuously synchronized with each other and with all ground clocks. No "relativity of simultaneity" corrections, as required by SR, were needed. This too seemed initially to falsify SR. But on further inspection, continually changing synchronization corrections for each clock exist such that the predictions of SR are fulfilled for any local co-moving frame. To avoid the embarrassment of that complexity, GPS analysis is now done exclusively in the Earth-centered inertial frame (the local gravity field). And the pre-launch adjustment of clock rates to compensate for relativistic effects then hides the fact that all orbiting satellite clocks would be seen to tick slower than ground clocks if not rate-compensated for their orbital motion, and that no reciprocity would exist when satellites view ground clocks.
At first glance, Van Flandern here appears to be claiming that the fact that the GPS continues to operate with great accuracy has in fact disproven the predictions of str concerning moving clocks (Van Flandern doesn't mention the gtr effects, but they are also significant). On careful reading, in this paper he actually appears to be saying in effect that anything that can be explained using str can be explained just as well using the Lorentz ether theory (let), a theory which he has never specified but which is usually taken to be mathematically equivalent to str, but with a different interpretation of Lorentz transformations, one which most physicists since Lorentz's day have found implausible.
....
Before we can understand why, contrary to Van Flandern's assertions, relativity theory is actually working just fine in the GPS, we need to understand the basic principles behind its design and daily operation, so I'll begin by explaining (in an oversimplified way) how the GPS works, what the most important non-relativistic sources errors are, and how they are overcome. Once this is out of the way, I'll discuss the relativistic sources of error, and how they are overcome.
....
A good way to start thinking about the general principle behind GPS is as follows. Suppose you know your precise range r1 to an object S1 with precisely known position x1 (a point in E^3, ordinary Euclidean space). Then you know you are located somewhere on a sphere of radius r1 and center x1. Next, suppose you also know your precise range r2 to a second object S2, with precisely known position x2. Then you know you are located somewhere on the circle which is the intersection of the first sphere with the sphere of radius r2 and center x2. Now suppose you also know your precise range r3 to a third object S3, with precisely known position x3. If you know all three things at the same time, then you know you are located on one of the two points in which three circles intersect! This process is called trilateration by geographers.
The basic idea behind GPS is to adapt this idea by providing users with a "constellation" of satellites as "orbiting landmarks", which always know their precise position with respect to the Earth's surface, as well as the precise UTC at their location, and which continually transmit this dual information at regular intervals. The current (Block 2) GPS constellation consists of (at least) 24 Earth orbiting satellites, called SV's, in circular orbits about 11,000 nm (20,200 km) above the Earth's surface (that is, 26,750 km above the center of the Earth), traveling at 4 km/sec, giving an orbital period of precisely twelve sidereal hours; that is, the satellites rotate once every twelve hours with respect to the fixed stars, not with respect to the Earth, which is of course itself rotating underneath the satellites. (The actual number of satellites in orbit varies from time to time because new ones are launched, with a Delta 2 rocket, as old ones begin to wear out. The design life of each satellite is 7.5 years.)
This means that each satellite comes over the same location along the same track over a fixed location on the surface of the Earth every 24 hours, or rather, four minutes earlier each day; the four minute discrepancy is due to the Earth's advance in its own orbit around the Sun. Incidentally, a common question is: why are the satellites not in geostationary orbits, like many communication satellites? The answer is that geostationary orbits are only possible over the equator, and as we've seen, trilateration won't work unless you can measure your distance to satellites in more than one plane. Since the designers of GPS were also looking ahead to future space-based applications, e.g. actively steering spacecraft in perfect formation (despite buffeting from the solar wind) by keeping their position using GPS, arranging the satellites so that their orbital period is precisely 12 sidereal hours turns out to be the simplest choice.
Each satellite is visible above the horizon of a stationary user for about five hours. The satellites each orbit in one of six equally spaced planes (sixty degrees apart), each inclined at about 55 degrees to the equatorial plane of the Earth, and with (at least) four SV's in each plane. This configuration ensures that at any given at time and any given place on the Earth, five to eight satellites are in a direct line-of-sight from the user.
Now, if one can provide a way for a ground receiver to synchronize its clock with the satellite clock, a simple measurement of the time delay in the signal received from a satellite in view of the Earthbound user, should result in a precise range to that satellite. Imagine for example a ground receiver which finds and locks onto one visible satellite, synchronizes its clock with the satellite clock, measures the time delay, computes the range, stores this number along with the reported position of the satellite, then locks onto a second visible satellite, and repeats this process until ranges and positions from three satellites have been obtained. This isn't how GPS works, but it's getting close!
Before delving into a more accurate explanation of how GPS works, let's examine some nonrelativistic sources of error in the simple procedure I have just outlined. As I said, in principle, determining the range to each satellite is a matter of a simple computation: the time delay of each signal from the satellite, multiplied by the speed of light, gives the range! However, the signals are not in fact transmitted in along the geometric line of sight, because they are diffracted at the upper boundary of the ionosphere (at about 1000 km above the Earth's surface) and then again at the boundary between the ionosphere and the troposphere (at about 70 km above the Earth's surface). These boundary layers are move up and down, depending upon the time of day, the latitude, and other factors. Moreover, the lower 8-13 kilometers to the atomosphere are active participants in local weather conditions, and the speed of light in air is different from the speed of light in vacuo (and the temperature of the air matters!). In addition, satellites which are closer to the horizon will transmit signals which are subject to more atmospheric disturbance than those near the zenith. In sum, ionospheric, tropospheric, and local weather conditions can result in errors of ten meters or more. Furthemore, it is possible for the same signal to arrive at the receiver at different times, having taken multiple paths to get there; this can account for another half meter or so of inaccuracy. All these sources of error must be taken account of and corrected by the GPS system.
Further "Newtonian" sources of error arise in determining the precise position of each satellite. In principle, a Keplerian orbit about the Earth is determined by six orbital parameters, usually taken to be the following:
the eccentricity of the elliptical orbit,
semi-major axis of the orbit,
the inclination of the orbital plane to the equatorial plane of the Earth,
the right ascension of the ascending node
the angular location of the perigee (point of closest approach),
the time at which the satellite passes the perigee
ow, as I said, I have not yet described how GPS really works. There are two fundamental issues I have not addressed:
* How does the ground receiver synchronize its (cheap, inaccurate) clock with the (highly accurate and expensive) atomic clocks carried aboard a given SV?
* How do the SV's synchronize their atomic clocks with each other, and how is this collaborative timekeeping (called GPS time) converted by the receiver to the correct UTC for a given location on the ground?
There is also a further component to the GPS system which I have not yet discussed. In addition to the satellites themselves, the space segment of the system, and the millions of hand held GPS receivers operated by people around the world, the user segment, there are also four unmanned ground stations (one located in Hawaii, a second on Kwajalein, an atoll in the Pacific Ocean; a third on Diego Garcia, an island in the Indian Ocean, and a fourth on Ascension Island in the Atlantic Ocean), which are devoted to carefully tracking the position of each GPS satellite, taking readings twice every three seconds. Each station automatically uses local weather and ionospheric conditions to average the tracking data, and every quarter hour, reports its best estimate of the position of each visible satellite to the master ground control station, which is located at Schriever AFB, Colorado Springs, CO. Here, the orbits and on-board clocks of each satellite can be adjusted if neccessary, using more sophisticated computer models (and bigger computers!) than can be carried on the SV's. This is the third component of GPS, the control segment.
....
[At this point, Baez mentions a number of technical issues relating to signal frequencies of the satellites etc.]
....
So, how can the ground receiver synchronize its clock with the satellite clock, in order to carry out the basic time delay computation outlined above? The answer is that it doesn't--- instead of sequentially locking onto and synchronizing clocks with four different satellites, as suggested above, the simplest (and cheapest) GPS receivers first lock onto the signal of one satellite, i.e. compare their internally generated C/A signal with the satellite signal until they get their own (cheap, inaccurate) clock in "roughly in synch" (modulo a still undetermined offset) with GPS time, and then records a reception time (by its own clock). It then locks onto the next signal, and repeats this process until four reception times (modulo undetermined offsets) have been recorded. Only then does it combine this data to determine the common offset of its clock from the satellite clocks, in effect resynchronizing its clock with three on-board atomic clocks. It then uses trilateralization and the declared position of each satellite as described above to determine the its own position. One way to think about this is that by locking onto four satellite signals, the receiver can determine its position and one more number, the offset of its clock from the highly stable, accurate, and mutually synchronized clocks carried by the satellites.
The grand result is that SPS users can obtain their position accurate to within 100 meters (latitude and longitude), their altitude to within 150 meters, and the universal time to within 350 nanoseconds. PPS users can obtain their position accurate to within 20 meters, their altitude to within 30 meters, and the universal time to within 200 nanoseconds. Actually, even this is merely the tip of the iceberg--- more sophisticated users can use two or more sequential ground receivers, or a parallel receiver capable of locking onto several satellite signals at once, and can use various least squares estimations to collate the data collected in order to considerably improve on the stated accuracies, typically to a few meters in the position accuracy. Furthermore, stationary receivers (e.g. used by geologists to study the motion of tectonic plates, or volcanic terrain) currently achieve position accurracy on the order of one mm!
....
[And now that you have a sense of how complicated the system is, we get to the relativity part]
....
The first 10 GPS satellites, comprising Block I, were used for testing and for military geolocation, and were launched beginning in 1978. The next 24 satellites, comprising Block II, were launched between 1989 and 1994; these are the SV's used in the operational GPS system. The way in which Van Flandern's claims quoted above are misleading is now easily summarized:
It is true that the current (Block II) satellites carry clocks which are occasionally adjusted from the master ground control station.
It is completely false that the GPS somehow defies the predictions of relativity theory. Indeed, when the first atomic clock was sent into orbit in June 1977 (aboard a satellite which was a testbed for the Block I GPS), and I quote from Ashby's paper:
there were some who doubted that relativistic effects were real. A frequency synthesizer was built into the satellite clock system so that after launch, if in fact the rate of the clock in its final orbit was that predicted by GR, then the synthesizer could be turned on bringing the clock to the coordinate rate necessary for operation. The atomic clock was first operated for about 20 days to measure its clock rate before turning on the synthesizer. The frequency measured during that interval was +442.5 parts in 10^12 faster than clocks on the ground; if left uncorrected this would have resulted in timing errors of about 38,000 nanoseconds per day. The difference between predicted and measured values of the frequency shift was only 3.97 parts in 10^12, well within the accuracy capabilities of the orbiting clock. This then gave about a 1% validation of the combined motional and gravitational shifts for a clock at 4.2 earth radii [the radius of the satellite's orbit].
It is true that GPS is not used as a test of gtr, because it is simply not designed for that purpose. In particular, the orbiting clocks are occasionally reset from the ground to maintain the best possible synchrony of the orbiting clocks with one another and with UTC time.
It is completely false that the design of the GPS system ignores relativity theory. Relativistic effects in the GPS system are vitally important. The total difference in the rate of atomic clocks on board a GPS satellite and the reference clock at the USNO amounts to some 38,600 nanoseconds per day. (This is mostly due to a combination of the Sagnac effect for a clock which is moving wrt the GPS receiver, and the relative gravitational time dilation between a stationary clock on the Earth's surface and a stationary clock 20,200 km above the surface, as mentioned in the above quoted paragraph from Ashby's paper; frequency shifts in clocks on the ground wrt UTC due to inhomogeneties in the shape of the Earth also play a role.) In contrast, in order to maintain the accuracies listed above, the GPS system must maintain a timekeeping synchrony within 10 nanoseconds variation per day, indefinitely! The major way in which the 38,600 nanosecond per day discrepancy due to relativistic effects is accounted for is by building into the GPS software used to keep the satellite clocks in synch with each other and to synchronize GPS time with UTC an effective downward frequency shift of 446.47 parts per trillion in the orbiting atomic clocks. In addition to this basic conversion factor, GPS receivers are programmed to take account for the fact that slight eccentricities in the satellite orbits result in tiny periodic changes in the frequency of the orbiting clocks.
At this point, I can do no better than send readers who have not already been there to Neil Ashby's paper for a detailed accounting of str and gtr effects which are significant in the GPS system. ... You can also try this paper by Charles W. Misner (Physics, University of Maryland), and this one by Clifford Will (Physics, Washington University). You can find additional references in the posts by Tom Roberts included in this collection.
.
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- The Speed of Gravity – What the Experiments Say
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