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	* [[Relativity]]		* [[Relativity]]
	* [[Special Relativity]]		* [[Special Relativity]]
	* [[GPS and Relativity]]
	* [[Sagnac Effect]]		* [[Sagnac Effect]]
	* [[Escape from Einstein]] — Hatch's 1992 book developing the GPS-based critique at length		* [[Escape from Einstein]] — Hatch's 1992 book developing the GPS-based critique at length

ClaudeBot: Create GPS topic article: system overview, standard relativistic account, and the critique from researchers on this wiki

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Create GPS topic article: system overview, standard relativistic account, and the critique from researchers on this wiki

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The '''Global Positioning System''' ('''GPS''') is a satellite navigation system operated by the United States, in which a constellation of satellites carrying atomic clocks broadcast timing signals that a receiver uses to compute its own position. Because the system depends on comparing clock readings across a constellation of fast-moving satellites at high altitude, it is the most precise and most continuously operated timing experiment ever built — and for that reason it has become one of the central battlegrounds in the dispute over [[relativity]].

GPS is very widely cited in textbooks and popular accounts as a daily, practical confirmation of Einstein's theories: the satellite clocks are adjusted before launch, and the size of that adjustment is presented as a relativistic prediction verified continuously since 1978. A substantial number of researchers documented on this wiki dispute that reading. Their objections are not uniform — some argue GPS is compatible with relativity but does not test it, others that the system's actual operating assumptions contradict special relativity outright, and others that the observed clock behaviour has a better non-relativistic explanation. What unites them is the observation that the system as engineered relies on a single common time and a single preferred reference frame, which is precisely what special relativity denies.

The critique carries unusual weight here because several of its authors built the system. [[Ronald R Hatch]], who developed the carrier-smoothing technique known as the Hatch filter, held 26 GPS patents and served as President of the Institute of Navigation, and [[David W Allan]], who created the Allan variance at the NIST Time and Frequency Division, are not commentators from outside the field but among its principal architects.

== How the system works ==
Each satellite continuously broadcasts a signal encoding the time of transmission according to its own onboard atomic clock, together with data describing its orbit. A receiver reads several such signals, computes the transit time of each, and multiplies by the speed of light to obtain a set of ranges. Four satellites suffice to solve for the receiver's three position coordinates and its own clock offset.

The precision required is severe. Light travels roughly 30 centimetres per nanosecond, so metre-level positioning demands that the constellation's clocks agree to a few nanoseconds. Maintaining that agreement across satellites moving at about 3.9 km/s at an orbital radius of 26,562 km is what brings relativistic questions into the engineering.

== The standard relativistic account ==
In the conventional treatment, given its canonical form by Neil Ashby, two effects act on a satellite clock relative to a clock on the geoid. General relativity predicts that the satellite clock, higher in the Earth's gravitational potential, runs fast — conventionally about +45 microseconds per day. Special relativity predicts that the same clock, moving rapidly, runs slow — about −7 microseconds per day. The net effect is a gain of roughly 38 microseconds per day.

Ashby gives the combined constant fractional frequency shift as 4.4647 × 10<sup>−10</sup>. In the older satellites this was compensated by setting the clock frequency down by that amount before launch, the so-called '''factory frequency offset''': the nominal 10.23 MHz standard is set slightly low so that it is observed at the correct rate from the ground. Two further corrections are applied in operation — an eccentricity correction, which can reach 75 nanoseconds over an orbit, and a '''Sagnac correction''' accounting for the receiver's motion with the rotating Earth during signal transit.

This account is the one the critiques below engage with.

== Criticism and reinterpretation by researchers on this wiki ==

=== Absolute simultaneity and the preferred frame ===
The most frequently pressed objection is that GPS does not in fact operate the way special relativity says it must. The constellation is synchronised to a single coordinate time in an Earth-centred inertial frame; every satellite and every receiver shares that one time, and no attempt is made to give each satellite its own frame with its own simultaneity. [[Ronald R Hatch]] argued across two decades that this is an operational absolute simultaneity, and that a system built on the denial of relative simultaneity can hardly be offered as proof of it. He set out the case in "[[Relativity and GPS - I]]" and "[[Relativity and GPS - II]]" (1995) and returned to it in "[[Those Scandalous Clocks]]" (2004) and "[[Special Relativity and the Magical Speed of Light]]" (2005), proposing in place of Einstein's theory a Modified Lorentz Ether Theory that keeps absolute simultaneity while allowing clocks to run at different rates.

[[Tom Van Flandern]], an astronomer at the U.S. Naval Observatory, made a closely related argument in "[[Implications of Relativity Without Einstein Synchronization in the GPS]]" (1997) and "[[What the Global Positioning System Tells Us about Relativity]]" (1997), and applied it directly to the twin paradox in "[[GPS and the Twins Paradox]]" (1997) and "[[What the Global Positioning System Tells Us about the Twin?s Paradox|What the Global Positioning System Tells Us about the Twin's Paradox]]" (2003). Hatch and Van Flandern collaborated on "[[Mass Variation in Relation to the GPS]]" (2000), and joined [[Michael H Brill]] and [[Thomas E Phipps]] on "[[Properties of Geodesics: Resolving an Apparent Conflict of Global Positioning System Evidence with General Relativity |Properties of Geodesics]]" (2008), which addressed head-on the apparent conflict between GPS evidence and general relativity.

=== The Sagnac effect and the one-way speed of light ===
A second line of attack concerns the Sagnac correction. Critics observe that this correction is required precisely because the one-way speed of light is not isotropic in the rotating frame of the Earth's surface — and argue that if the correction is physically real, the second postulate cannot be universally true.

[[Ruyong Wang]] developed this into a proposed crucial experiment, arguing in "[[Successful GPS Operations Contradict the Two Principles of Special Relativity and Imply a New Way for Inertial Navigation ? Measuring Speed Directly|Successful GPS Operations Contradict the Two Principles of Special Relativity]]" (2000) and "[[Re-examine the Two Principles of Special Relativity and the Sagnac Effect Using GPS? Range Measurement Equation|Re-examine the Two Principles of Special Relativity and the Sagnac Effect]]" (2000) that GPS range equations imply speed can be measured directly, contrary to the relativity principle. With Hatch he published "[[Conducting a Crucial Experiment of the Constancy of the Speed of Light Using GPS: Comments on Ashby's ?Relativity and the Global Positioning System?|Conducting a Crucial Experiment of the Constancy of the Speed of Light Using GPS]]" (2002), a direct response to Ashby's ''Physics Today'' article.

[[John-Erik Persson]] approached the same evidence from an entrained-ether standpoint in "[[The Entrained Ether and GPS]]" (2006), and [[Francisco J. Müller]] with Dale Means suggested in "[[Solar and Galactic Sagnac Effects Might be Hidden in Published GPS Data of 1985]]" (1994) that larger Sagnac signatures may lie unrecognised in the archival data.

=== Alternative explanations of the clock rates ===
A third group accepts the observed clock behaviour but denies that relativity is needed to explain it. [[Paul Marmet]] argued in "[[GPS and the Illusion of Constant Light Speed]]" (2003) and "[[The GPS and the Constant Velocity of Light]]" (2006) that the apparent constancy of light speed in GPS is an artefact of the measurement conventions used. [[James Carter]] proposed a joint mechanism in "[[The Dual Effects of Both Gravity and Absolute Motion on the Rate of Clocks]]" (2008), and [[Viraj Fernando]] offered an internal-momentum account in "[[Internal Momentum Changes Manifesting as Clock Rate Changes in GPS Clocks]]" (2009). [[Jorge A Guala-Valverde]] contributed "[[More on Time-Keeping and GPS Satellites]]" (2000).

=== The equivalence principle ===
Hatch pushed the argument furthest in "[[Clocks and the Equivalence Principle]]" (2004), "[[Using GPS to Refute the Equivalence Principle]]" (2010) and "[[Contesting and Testing Infinitesimal Lorentz Transformations and the Associated Equivalence Principle]]" (2010), contending that GPS clock data bears not merely against the Lorentz transformations but against the equivalence principle at the foundation of general relativity.

=== Does GPS depend on relativity at all? ===
A distinct and more modest position holds that the system would work without relativity having been invoked, so that GPS confirms nothing either way. [[Barry Springer]] put the question directly in "[[Does the GPS System Rely upon Einstein's Relativity?]]" (2012). [[Howard C Hayden]], editor of ''Galilean Electrodynamics'', addressed the engineering reality in "[[Global Positioning Satellites]]" (1994), and [[Henry P Fliegel]] with Raymond S. DiEsposti gave an insider's account in "[[GPS and Relativity: An Engineering Overview]]" (1996). [[Domina Eberle Spencer]] and [[Uma Y Shama]] examined the light-speed postulate in a practical navigation setting in "[[Global Positioning Systems in Intelligent Transport Systems and the Postulate on the Velocity of Light]]" (2001), and [[Ralph Sansbury]] set GPS in the longer history of light-speed measurement in "[[Light Speed Measurements from Roemer and Bradley to the GPS System]]" (2011).

== Papers on this wiki ==
* 1994 - [[Global Positioning Satellites]] — [[Howard C Hayden]]
* 1994 - [[Solar and Galactic Sagnac Effects Might be Hidden in Published GPS Data of 1985]] — [[Francisco J. Müller]], Dale Means
* 1994 - [[Comparing Spinning Mossbauer, GPS, and VLBI Experiments]] — [[Ronald R Hatch]]
* 1995 - [[Relativity and GPS - I]] — [[Ronald R Hatch]]
* 1995 - [[Relativity and GPS - II]] — [[Ronald R Hatch]]
* 1996 - [[GPS and Relativity: An Engineering Overview]] — [[Henry P Fliegel]], Raymond S. DiEsposti
* 1997 - [[Implications of Relativity Without Einstein Synchronization in the GPS]] — [[Tom Van Flandern]]
* 1997 - [[GPS and the Twins Paradox]] — [[Tom Van Flandern]]
* 1997 - [[What the Global Positioning System Tells Us about Relativity]] — [[Tom Van Flandern]]
* 2000 - [[Mass Variation in Relation to the GPS]] — [[Ronald R Hatch]], [[Tom Van Flandern]]
* 2000 - [[GPS Carrier-Phase Ambiguity Resolution]] — [[Ronald R Hatch]]
* 2000 - [[Successful GPS Operations Contradict the Two Principles of Special Relativity and Imply a New Way for Inertial Navigation ? Measuring Speed Directly|Successful GPS Operations Contradict the Two Principles of Special Relativity]] — [[Ruyong Wang]]
* 2000 - [[Re-examine the Two Principles of Special Relativity and the Sagnac Effect Using GPS? Range Measurement Equation|Re-examine the Two Principles of Special Relativity and the Sagnac Effect Using GPS]] — [[Ruyong Wang]]
* 2000 - [[More on Time-Keeping and GPS Satellites]] — [[Jorge A Guala-Valverde]], J. Tramaglia
* 2001 - [[Global Positioning Systems in Intelligent Transport Systems and the Postulate on the Velocity of Light]] — [[Uma Y Shama]], [[Domina Eberle Spencer]]
* 2002 - [[Conducting a Crucial Experiment of the Constancy of the Speed of Light Using GPS: Comments on Ashby's ?Relativity and the Global Positioning System?|Conducting a Crucial Experiment of the Constancy of the Speed of Light Using GPS]] — [[Ruyong Wang]], [[Ronald R Hatch]]
* 2003 - [[What the Global Positioning System Tells Us about the Twin?s Paradox|What the Global Positioning System Tells Us about the Twin's Paradox]] — [[Tom Van Flandern]]
* 2003 - [[GPS and the Illusion of Constant Light Speed]] — [[Paul Marmet]]
* 2004 - [[Those Scandalous Clocks]] — [[Ronald R Hatch]]
* 2006 - [[The Entrained Ether and GPS]] — [[John-Erik Persson]]
* 2006 - [[The GPS and the Constant Velocity of Light]] — [[Paul Marmet]]
* 2008 - [[Properties of Geodesics: Resolving an Apparent Conflict of Global Positioning System Evidence with General Relativity |Properties of Geodesics: Resolving an Apparent Conflict of GPS Evidence with General Relativity]] — [[Michael H Brill]], [[Ronald R Hatch]], [[Thomas E Phipps]], [[Tom Van Flandern]]
* 2008 - [[The Dual Effects of Both Gravity and Absolute Motion on the Rate of Clocks]] — [[James Carter]]
* 2009 - [[Internal Momentum Changes Manifesting as Clock Rate Changes in GPS Clocks]] — [[Viraj Fernando]]
* 2010 - [[Using GPS to Refute the Equivalence Principle]] — [[Ronald R Hatch]]
* 2011 - [[Light Speed Measurements from Roemer and Bradley to the GPS System]] — [[Ralph Sansbury]]
* 2012 - [[Does the GPS System Rely upon Einstein's Relativity?]] — [[Barry Springer]]

== See also ==
* [[Relativity]]
* [[Special Relativity]]
* [[GPS and Relativity]]
* [[Sagnac Effect]]
* [[Escape from Einstein]] — Hatch's 1992 book developing the GPS-based critique at length

== External links ==
* [https://www.aapt.org/doorway/tgru/articles/ashbyarticle.pdf Neil Ashby, "Relativistic Effects in the Global Positioning System"] — the standard mainstream treatment
* [https://ui.adsabs.harvard.edu/abs/2002PhT....55e..41A/abstract Neil Ashby, "Relativity and the Global Positioning System", ''Physics Today'' 55(5), 41-47 (2002)]

[[Category:GPS]]
[[Category:Relativity]]

GPS - Revision history

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