Relativity and GPS - I: Difference between revisions

Scientific Paper
Title	Relativity and GPS - I
Read in full	Link to paper
Author(s)	Ronald R Hatch
Keywords	GPS, relativity, satellites
Published	1995
Journal	Galilean Electrodynamics
Volume	6
Number	3
No. of pages	17
Pages	51-62

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Latest revision as of 09:54, 21 July 2026

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Abstract

The satellites of the global positioning system (GPS) travel around the earth in 12-hour periods in near-circular orbits. All of the satellites contain extremely precise atomic clocks whose rates depend both upon satellite velocity and altitude. An observer bound to the earth, in an airplane or in a satellite may determine his precise location by obtaining signals from several satellites simultaneously. This paper discusses the implications of GPS on Einstein's special theory of relativity. A subsequent paper will discuss the general theory.

Overview

This is the first of two papers in which Ronald R. Hatch — a navigation engineer who spent his career on GPS carrier-phase processing — argues that the working practice of the global positioning system supports Lorentz ether theory rather than Einstein's Special Relativity. The target is a specific mainstream account: Neil Ashby's 1993 GPS World article "Relativity and GPS". Hatch takes the three effects Ashby treats — velocity effects on clock rate, gravitational-potential effects on clock rate, and the Sagnac Effect — and argues that Ashby's explanation of each is "patently incorrect", even where the numerical result is right.

His central claim is one of frame dependence. GPS does not adjust satellite and receiver clocks according to their relative velocity, as the special theory would require; it adjusts them according to their velocity with respect to a chosen frame, the earth-centred non-rotating frame. That is exactly what an ether theory prescribes and what special relativity forbids as a matter of principle, because the special theory insists the speed of light is isotropic relative to any observer. Hatch's conclusion for Part I is that the two theories are not merely metaphysically distinguishable: the Sagnac effect is a direct experimental discriminator, and it favours the ether.

The argument

Velocity effects and the "Star Wars" thought experiment

Ashby writes that "important relativistic effects arise from relative motions of GPS satellites and users" and that "clocks in relative motion suffer time dilation". Hatch's reply is a thought experiment. Take two spacecraft carrying GPS receivers in the same orbit as a GPS satellite, one trailing it at constant separation and one travelling the opposite way. Using f = f₀(1 − (v/c)²)^1/2 and the nominal GPS orbital speed of 3.87 km/s, the satellite clock is slowed by 8.32 parts in 10¹¹. The trailing spacecraft has the same speed in the earth-centred frame, so sees no relative shift — which special relativity also predicts, since their relative velocity is zero. But the counter-orbiting spacecraft also has the same speed in that frame and so also sees no relativistic offset, even though its closing speed on the satellite is 7.74 km/s. On Ashby's stated rule the offset would instead be 33.28 parts in 10¹¹.

Hatch concedes the discrepancy is not directly detectable, and explains why: Jorgensen, working from Ashby's own results, showed that if one instead adopts the instantaneous frame of the second receiver, the special-relativistic clock shift, the Doppler shift and aberration recombine to give the same received frequency. Hatch's point is that this equivalence is a Lorentz-ether result, not a special-relativistic vindication: "whenever a frame is chosen which does not coincide with the receiver or observer, experiment demands that the speed of light be treated as non-isotropic as far as the receiver is concerned."

Gravitational effects and the conservation of cycles

Hatch introduces a scale factor s = 1 − GM/rc² and writes the clock rate as f = sf_e. He lists three demonstrations internal to GPS: the mile-high Colorado Springs monitor station clock running fast; the exact cancellation of the earth's spin effect against the oblateness-induced potential difference, so that equatorial and polar sea-level clocks run at the same rate; and the orbital eccentricity correction Δt = −4.42807633 × 10⁻¹⁰ e A^1/2 cos E, in which the velocity and potential contributions are exactly equal and add.

The interesting part is his objection to the usual account of gravitational blueshift. Ashby, following the Equivalence Principle and the accelerating-elevator argument, describes photons as gaining energy as they fall. Hatch argues this violates conservation of cycles: "the number received plus the number in transit must equal the number transmitted". If the emitted gamma rays in the Pound–Rebka experiment already have a higher frequency because the source clock runs faster, then adding a further gravitational gain would double the observed effect. He then invokes Shapiro's radar delay to Venus and Mercury, which shows light slowed by two units of the scale factor, c = s²c_e. Since a local clock only accounts for one factor, lengths must contract by the same factor: l = sl_e. The bending of light near the sun, twice the naive Newtonian value, follows entirely from this light-speed gradient. He notes the pre-launch GPS frequency offset: +5.311 parts in 10¹⁰ from potential, −8.32 parts in 10¹¹ from speed, net +4.479 parts in 10¹⁰, compensated by setting the clock low by 4.45 parts in 10¹⁰.

The Sagnac effect as the discriminator

This is the heart of the paper. Hatch rejects every account that makes the effect a product of rotation or acceleration. Ashby attributes it to the rotating frame being non-inertial; Post attributes it to modified constitutive relations of the medium; Ashtekar and Magnon derive it within general relativity; Deines claims it arises from "missing relativity terms". Hatch answers each: the GPS signal path from satellite to receiver is a straight line and the receiver's radial acceleration during reception is negligible, so rotation cannot be the cause; Deines recovers the effect only by choosing integration limits that would require collocating receiver and satellite at launch, which Hatch calls "magic — choose whatever limits are needed"; and the general-relativistic derivations, to the extent they work, work precisely because they do not give isotropic light speed relative to the moving receiver, which puts them in conflict with the special theory rather than in support of it. He cites Ives (1938), who showed the Sagnac result is unchanged if the phase detector moves along the chord of a hexagonal light path instead of rotating — the effect without rotation or acceleration.

Hatch's own statement is simple: "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." A GPS receiver flown on a curved path such that its track is a straight line at constant velocity in the earth-centred frame still requires the Sagnac correction.

Lorentz ether theory versus the special theory

Figure 1 of the paper sets out the relationship. The cosmic background radiation frame is taken as the absolute ether frame. The Mansouri–Sexl transformation (earlier Tangherlini's) maps it to an earth-centred frame with non-isotropic light speed; it is reciprocal rather than symmetrical, preserves absolute Simultaneity, and is "nothing more than a Galilean transformation adjusted for clock slowing and length contraction". Poincaré's principle — that clock-synchronisation biases hide the anisotropy — then converts that frame into the isotropic earth-centred frame. So the Lorentz transformation is reached by two routes, but the interpretation differs: in the ether theory one may pick any frame as the isotropic frame, but one may not change frames mid-experiment, so Lorentz boosts are invalid.

Hatch illustrates with the Twin Paradox at β = 0.6. Stella's clock reads 4 years, Terrance's 5. Videoing Terrance's clock on Stella's monitor gives a record that is consistent with any chosen absolute frame. But the special theory, at turn-around, must rewrite the history of the signal already in transit — 1.5 light-years of it — converting a Doppler that doubled the wavelength into one that halves it. Hatch calls this "magic so that the speed of light can always be isotropic", and notes that abandoning Lorentz boosts costs him the standard derivation of Thomas precession, for which he supplies a replacement based on the unbalanced Length Contraction and mass increase of a spinning body.

Assessment

The paper's strength is that it is written by someone who actually processes GPS data, and it is at its most convincing where it stays close to that practice. The observation that GPS clock rates are referenced to a chosen frame and not to relative velocity is simply correct as a description of the system, and it is a genuinely useful corrective to popularisations that describe GPS corrections as pairwise time dilation between satellite and user. The demolition of Deines' integration limits is fair and specific. The conservation-of-cycles objection to the falling-photon picture is a real point about bookkeeping, and Hatch is right that the shift cannot be counted twice. His use of Shapiro delay to argue for a light-speed gradient, and thence for a length scale factor, is an internally coherent construction that reproduces the observed light bending.

The weaknesses are conceptual rather than numerical, and they cluster around what the argument actually establishes. Standard relativity does not claim that the earth-centred frame is dispensable; it claims any frame will do provided the transformations are applied consistently — which is exactly what Jorgensen showed and what Hatch himself reproduces. That the earth-centred frame is convenient does not show it is preferred. Similarly, the Sagnac effect is not in dispute as a phenomenon: it is a standard consequence of using a rotating, non-inertial coordinate system, in which the coordinate speed of light is not c. Hatch's claim that this contradicts the special theory rests on reading "the speed of light is isotropic relative to the observer" as a claim about arbitrary frames rather than about local inertial frames, which is not what the postulate asserts. His Ives citation shows the effect can be produced without rotation, but a detector moving along a chord is still not at rest in an inertial frame for the whole circuit.

Two further difficulties are worth naming. First, Hatch's identification of the CBR frame as the ether frame is a choice, not a result — he offers no experiment in this paper that isolates it, and concedes we "cannot tell which frame is the true frame". Second, the Thomas-precession replacement is asserted, not derived here; the reader is referred to a conference paper. Against this, the empirical record is not on the side of a detectable preferred frame: modern Michelson–Morley-type experiments with cryogenic optical resonators constrain anisotropy in the one-way speed of light to parts in 10¹⁷, and Ives–Stilwell measurements confirm the transverse Doppler factor to comparable precision. Hatch's theory is constructed to be observationally indistinguishable from special relativity in exactly these cases, which is its safety and also its limitation: on his own account, the two theories differ in interpretation everywhere and in prediction almost nowhere. The place where he claims a genuine difference — the Sagnac effect — is the place where his reading of the special theory is most contestable.

@@ Line 17: / Line 17: @@
 The satellites of the global positioning system (GPS) travel around the earth in 12-hour periods in near-circular orbits. All of the satellites contain extremely precise atomic clocks whose rates depend both upon satellite velocity and altitude. An observer bound to the earth, in an airplane or in a satellite may determine his precise location by obtaining signals from several satellites simultaneously. This paper discusses the implications of GPS on Einstein's special theory of relativity. A subsequent paper will discuss the general theory.
+==Overview==
+This is the first of two papers in which Ronald R. Hatch — a navigation engineer who spent his career on GPS carrier-phase processing — argues that the working practice of the global positioning system supports [[Lorentz ether theory]] rather than Einstein's [[Special Relativity]]. The target is a specific mainstream account: Neil Ashby's 1993 ''GPS World'' article "Relativity and GPS". Hatch takes the three effects Ashby treats — velocity effects on clock rate, gravitational-potential effects on clock rate, and the [[Sagnac Effect]] — and argues that Ashby's explanation of each is "patently incorrect", even where the numerical result is right.
+His central claim is one of frame dependence. GPS does not adjust satellite and receiver clocks according to their ''relative'' velocity, as the special theory would require; it adjusts them according to their velocity with respect to a chosen frame, the earth-centred non-rotating frame. That is exactly what an ether theory prescribes and what special relativity forbids as a matter of principle, because the special theory insists the speed of light is isotropic relative to any observer. Hatch's conclusion for Part I is that the two theories are not merely metaphysically distinguishable: the Sagnac effect is a direct experimental discriminator, and it favours the ether.
+==The argument==
+===Velocity effects and the "Star Wars" thought experiment===
+Ashby writes that "important relativistic effects arise from relative motions of GPS satellites and users" and that "clocks in relative motion suffer time dilation". Hatch's reply is a thought experiment. Take two spacecraft carrying GPS receivers in the same orbit as a GPS satellite, one trailing it at constant separation and one travelling the opposite way. Using ''f'' = ''f''<sub>0</sub>(1 − (''v''/''c'')<sup>2</sup>)<sup>1/2</sup> and the nominal GPS orbital speed of 3.87 km/s, the satellite clock is slowed by 8.32 parts in 10<sup>11</sup>. The trailing spacecraft has the same speed in the earth-centred frame, so sees no relative shift — which special relativity also predicts, since their relative velocity is zero. But the ''counter-orbiting'' spacecraft also has the same speed in that frame and so also sees no relativistic offset, even though its closing speed on the satellite is 7.74 km/s. On Ashby's stated rule the offset would instead be 33.28 parts in 10<sup>11</sup>.
+Hatch concedes the discrepancy is not directly detectable, and explains why: Jorgensen, working from Ashby's own results, showed that if one instead adopts the instantaneous frame of the second receiver, the special-relativistic clock shift, the Doppler shift and aberration recombine to give the same received frequency. Hatch's point is that this equivalence is a Lorentz-ether result, not a special-relativistic vindication: "whenever a frame is chosen which does not coincide with the receiver or observer, experiment demands that the speed of light be treated as non-isotropic as far as the receiver is concerned."
+===Gravitational effects and the conservation of cycles===
+Hatch introduces a scale factor ''s'' = 1 − ''GM''/''rc''<sup>2</sup> and writes the clock rate as ''f'' = ''sf''<sub>e</sub>. He lists three demonstrations internal to GPS: the mile-high Colorado Springs monitor station clock running fast; the exact cancellation of the earth's spin effect against the oblateness-induced potential difference, so that equatorial and polar sea-level clocks run at the same rate; and the orbital eccentricity correction Δ''t'' = −4.42807633 × 10<sup>−10</sup> ''e''&nbsp;''A''<sup>1/2</sup> cos ''E'', in which the velocity and potential contributions are exactly equal and add.
+The interesting part is his objection to the usual account of gravitational blueshift. Ashby, following the [[Equivalence Principle]] and the accelerating-elevator argument, describes photons as gaining energy as they fall. Hatch argues this violates ''conservation of cycles'': "the number received plus the number in transit must equal the number transmitted". If the emitted gamma rays in the Pound–Rebka experiment already have a higher frequency because the source clock runs faster, then adding a further gravitational gain would double the observed effect. He then invokes Shapiro's radar delay to Venus and Mercury, which shows light slowed by ''two'' units of the scale factor, ''c'' = ''s''<sup>2</sup>''c''<sub>e</sub>. Since a local clock only accounts for one factor, lengths must contract by the same factor: ''l'' = ''sl''<sub>e</sub>. The bending of light near the sun, twice the naive Newtonian value, follows entirely from this light-speed gradient. He notes the pre-launch GPS frequency offset: +5.311 parts in 10<sup>10</sup> from potential, −8.32 parts in 10<sup>11</sup> from speed, net +4.479 parts in 10<sup>10</sup>, compensated by setting the clock low by 4.45 parts in 10<sup>10</sup>.
+===The Sagnac effect as the discriminator===
+This is the heart of the paper. Hatch rejects every account that makes the effect a product of rotation or acceleration. Ashby attributes it to the rotating frame being non-inertial; Post attributes it to modified constitutive relations of the medium; Ashtekar and Magnon derive it within general relativity; Deines claims it arises from "missing relativity terms". Hatch answers each: the GPS signal path from satellite to receiver is a straight line and the receiver's radial acceleration during reception is negligible, so rotation cannot be the cause; Deines recovers the effect only by choosing integration limits that would require collocating receiver and satellite at launch, which Hatch calls "magic — choose whatever limits are needed"; and the general-relativistic derivations, to the extent they work, work precisely because they do ''not'' give isotropic light speed relative to the moving receiver, which puts them in conflict with the special theory rather than in support of it. He cites Ives (1938), who showed the Sagnac result is unchanged if the phase detector moves along the chord of a hexagonal light path instead of rotating — the effect without rotation or acceleration.
+Hatch's own statement is simple: "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." A GPS receiver flown on a curved path such that its track is a straight line at constant velocity in the earth-centred frame still requires the Sagnac correction.
+===Lorentz ether theory versus the special theory===
+Figure 1 of the paper sets out the relationship. The cosmic background radiation frame is taken as the absolute ether frame. The Mansouri–Sexl transformation (earlier Tangherlini's) maps it to an earth-centred frame with non-isotropic light speed; it is reciprocal rather than symmetrical, preserves absolute [[Simultaneity]], and is "nothing more than a Galilean transformation adjusted for clock slowing and length contraction". Poincaré's principle — that clock-synchronisation biases hide the anisotropy — then converts that frame into the isotropic earth-centred frame. So the Lorentz transformation is reached by two routes, but the interpretation differs: in the ether theory one may pick any frame as the isotropic frame, but one may not ''change'' frames mid-experiment, so Lorentz boosts are invalid.
+Hatch illustrates with the [[Twin Paradox]] at β = 0.6. Stella's clock reads 4 years, Terrance's 5. Videoing Terrance's clock on Stella's monitor gives a record that is consistent with any chosen absolute frame. But the special theory, at turn-around, must rewrite the history of the signal already in transit — 1.5 light-years of it — converting a Doppler that doubled the wavelength into one that halves it. Hatch calls this "magic so that the speed of light can always be isotropic", and notes that abandoning Lorentz boosts costs him the standard derivation of Thomas precession, for which he supplies a replacement based on the unbalanced [[Length Contraction]] and mass increase of a spinning body.
+==Assessment==
+The paper's strength is that it is written by someone who actually processes GPS data, and it is at its most convincing where it stays close to that practice. The observation that GPS clock rates are referenced to a chosen frame and not to relative velocity is simply correct as a description of the system, and it is a genuinely useful corrective to popularisations that describe GPS corrections as pairwise time dilation between satellite and user. The demolition of Deines' integration limits is fair and specific. The conservation-of-cycles objection to the falling-photon picture is a real point about bookkeeping, and Hatch is right that the shift cannot be counted twice. His use of Shapiro delay to argue for a light-speed gradient, and thence for a length scale factor, is an internally coherent construction that reproduces the observed light bending.
+The weaknesses are conceptual rather than numerical, and they cluster around what the argument actually establishes. Standard relativity does not claim that the earth-centred frame is dispensable; it claims any frame will do provided the transformations are applied consistently — which is exactly what Jorgensen showed and what Hatch himself reproduces. That the earth-centred frame is ''convenient'' does not show it is ''preferred''. Similarly, the Sagnac effect is not in dispute as a phenomenon: it is a standard consequence of using a rotating, non-inertial coordinate system, in which the coordinate speed of light is not ''c''. Hatch's claim that this contradicts the special theory rests on reading "the speed of light is isotropic relative to the observer" as a claim about arbitrary frames rather than about local inertial frames, which is not what the postulate asserts. His Ives citation shows the effect can be produced without rotation, but a detector moving along a chord is still not at rest in an inertial frame for the whole circuit.
+Two further difficulties are worth naming. First, Hatch's identification of the CBR frame as the ether frame is a choice, not a result — he offers no experiment in this paper that isolates it, and concedes we "cannot tell which frame is the true frame". Second, the Thomas-precession replacement is asserted, not derived here; the reader is referred to a conference paper. Against this, the empirical record is not on the side of a detectable preferred frame: modern Michelson–Morley-type experiments with cryogenic optical resonators constrain anisotropy in the one-way speed of light to parts in 10<sup>17</sup>, and Ives–Stilwell measurements confirm the transverse Doppler factor to comparable precision. Hatch's theory is constructed to be observationally indistinguishable from special relativity in exactly these cases, which is its safety and also its limitation: on his own account, the two theories differ in interpretation everywhere and in prediction almost nowhere. The place where he claims a genuine difference — the Sagnac effect — is the place where his reading of the special theory is most contestable.
+==See also==
+* [[Ronald R Hatch]] — the author
+* [[Relativity and GPS - II]] — the companion paper on the general theory
+* [[Escape from Einstein]] — Hatch's book
+* [[GPS]]
+* [[Sagnac Effect]]
+* [[Lorentz ether theory]]
+* [[Special Relativity]]
+* [[Twin Paradox]]
+* [[Simultaneity]]
+* [[Galilean Electrodynamics]]
+* [[Howard C Hayden]]
+* [[Cynthia Kolb Whitney]]
+* [[Herbert E Ives]]
 [[Category:Scientific Paper|relativity gps -]]
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 [[Category:GPS]]
+[[Category:Aether|relativity gps -]]
+[[Category:Time|relativity gps -]]