From: jthorn@galileo.thp.univie.ac.at (Jonathan Thornburg)
Subject: Re: A quality index for physical theory
Date: 9 May 2000 13:17:16 GMT
Newsgroups: sci.physics.research
Summary: history of misunderstandings of general relativity effects in GPS

In article <CkUQ4.10672$sB3.7084@news.indigo.ie>,
Gerry Quinn <gerryq@indigo.ie> wrote:
> If engineers had launched the GPS satellites unaware of GR, they would 
> soon have found that radio waves and the electronics dependent on them 
> went faster further from the Earth.
  ==================================

That's not what general relativity says.


>  Software corrections for this would 
> have been easy to implement.

Ironically, the US Air Force and contractor personnel involved in the
early GPS design *were* insufficiently knowedgable about GR, and both
software and hardware corrections were (are) needed.  Quoting from
reference [1] cited below,

   [[due to general relativity effects]]  Each [GPS] satellite clock
   must be adjusted so that when it is next to the GPS master clock
   (located at the earth's surface), it will run slow by 44,000 ns/day.
   Then, when it is place in orbit, it will run in synchronization
   with the GPS master clock.

   There was considerable uncertainty among the Air Force and contractor
   personnel designing and building the system whether these effects
   were being correctly handled, and even, on the part of some, whether
   the effects were real.  This last group was not satisfied until a
   gravitational frequency shift was measured with a GPS test satellite
   [[...]]

   [[...]]

   A common mistake in dealing with relativistic time was also made
   by one of the Air Force contractors in relation to the GPS.  This
   is the notion that electromagnetic radiation changes frequency (or
   a photon changes energy) as it propagates through a gravitational
   potential difference.  If the physical clock adjustments have been
   made as described above so that all clocks are keeping a common
   coordinate time, then there is no effect on the frequency of
   radiation as meausred in that coordinate time.  However, the
   contractor had included in the computer programs to operate the
   system just such a correction, effectively correcting twice for
   the relativistic effects.  Actual experience with test GPS equipment
   in orbit was required to persuade some engineers and physicists
   of their error.

Quoting from reference [2] cited below,

   There is an amusing anecdote about this frequency offset.  At the
   time of launch of the NTS-2 satellite (23 June 1977), which contained
   the first cesium atomic clock to be placed in orbit, there were some
   who doubted that relativistic effects were truths that would need
   to be incorporated.  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 general
   relativity, then the synthesizer could be turned on bringing the
   clock to the coordinate rate necessary for operation.


>  I doubt (correct me if I'm wrong) 
> whether the full tensor formulation of GR would have been needed.

I'm not sure.  I strongly suspect a quasi-Newtonian theory would not
be adequate -- one must consider time-time as well as space-space terms
in the metric.


References:

[1]
@inbook
        {
        Alley-1982-GR-rods-and-clocks,
        author = "Carroll O. Alley",
        title = "Proper Time Experiments in Gravitational Fields
                 With Atomic Clocks, Aircraft, and Laser Light Pulses",
        X-pages = "FIXME",
        editor = "P. Meystre and M. O. Scully",
        booktitle = "Quantum Optics, Experimental Gravitation,
                     and Measurement Theory",
        publisher = "Plenum",
        address = "New York",
        year = 1982,
        snote = "++good discussion on `rods and clocks' experiments
                 testing special/general relativity",
        }

[2]
@incollection
        {
        Ashby-in-GR15,
        author = "Neil Ashby",
        title = "Relativistic Effects in the Global Positioning System",
        pages = "231--258",
        editor = "Naresh Dadhich and Jayant Narlikar",
        booktitle = "Gravitation and Relativity:
                     At the Turn of the Millennium",
        booksubtitle = "Proceedings of the GR-15 Conference
                        held at IUCAA, Pune, India,
                        during December 16--21, 1997",
        publisher = "Inter-University Center for Astronomy and Astrophysics",
        address = "Post Bag 4, Ganeshkhind, Pune 411 007, India",
        year = 1998,
        isbn = "81-900378-3-8",
        note = "Also available at
           http://www.colorado.edu/engineering/GPS/Papers/RelativityinGPS.ps",
        }

-- 
-- Jonathan Thornburg <jthorn@galileo.thp.univie.ac.at>
   http://www.thp.univie.ac.at/~jthorn/home.html
   Universitaet Wien (Vienna, Austria) / Institut fuer Theoretische Physik
   "He who joyfully marches to music in rank and file has already earned
    my contempt.  He has been given a large brain by mistake, since for
    him the spinal cord would fully suffice."       -- Albert Einstein