Relativity and GPS - II

Scientific Paper
Title	Relativity and GPS - II
Read in full	Link to paper
Author(s)	Ronald R Hatch
Keywords	GPS, satellites, Lorentz ether theory
Published	1995
Journal	Galilean Electrodynamics
Volume	6
Number	4
No. of pages	17
Pages	73-82

Read the full paper here

Abstract

In the first paper we showed that the global positioning system (GPS) strongly supports the Lorentz ether theory over that of Einstein's special theory. In this second paper, we take a close look at several problems with the general theory. In the second paper, we take a close look at several problems with the special theory. Particular attention is focused on the claim of the general theory that an object in free-fall is not acted upon by any forces and, hence, defines its own Lorentz frame. One aspect of this claim can be refuted by the new GPS satellites which are capable of inter-satellite tracking. A modification of the Lorentz ether theory is proposed which resolves the general theory problems. In addition, the new theory predicts experimental results at variance with the general theory for several experiments to be performed in the near future.

Overview

Part II turns from the special to the general theory. Where Part I argued that GPS practice implies a preferred frame, Part II argues that the general theory has four concrete defects, proposes a solid elastic ether as a replacement, and closes with three falsifiable predictions. The proposed medium is an extension of the Lorentz ether theory of Part I into gravitation: matter consists of spinning standing-wave structures in an elastic ether, mass corresponds to a local decrease of ether density inside the structure, and gravitational potential corresponds to the compensating increase outside it. Gravity is then a density gradient, and what the general theory calls curvature of space is the gradient of ether density.

The departure from the mainstream account is sharper here than in Part I, because Hatch is not merely reinterpreting agreed results. He denies that black holes can form, denies that gravitational radiation exists as anything other than electromagnetic radiation, and predicts a geodetic precession one-third larger than the general theory's. He notes that "the equations for an elastic solid ether are virtually identical with the general theory equations" — the difference is that the general theory ascribes clock-rate changes to a change in the flow of time, whereas the ether theory ascribes them to an environmental effect on the clock, with a universal flow of time left untouched.

The argument

Four problems with the general theory

Hatch lists them briefly. First, Yilmaz's claim that the general-theory equations predict no attraction between two parallel plates of infinite extent. Second, the vacuum-energy problem as stated by Schwarzschild: the zero-point energy of vacuum fluctuations is so large that the equations imply a curvature "at least 120 powers of 10 greater than that actually observed". Third, Shapiro and Teukolsky's demonstration that a football-shaped mass distribution can collapse to a singularity not enclosed by a horizon, violating cosmic censorship. Fourth, the claim that a freely falling object is acted on by no force and defines its own Lorentz frame.

The elastic solid ether

Matter is assumed to be ether standing-wave structures. Spin and the nonlinearity of the ether's elasticity produce a net density decrease inside the structure (mass) and an increase outside (gravitational potential). Taking the speed of light inversely proportional to the square root of density gives

ρ = ρ_e/s⁴ ≈ ρ_e(1 + 4GM/rc²)

with s the scale factor of Part I. Mass in a potential is taken as m = m_e/s³. Together with the clock rate and length relations of Part I this fixes a local gauge for all three fundamental units, and Hatch notes the immediate consequence that "the source of gravitational potential energy is the decrease in rest-mass energy with decreased gravitational potential."

The velocity effects are recovered in two steps. First, an energy-free step: since a standing-wave structure's integrity is maintained by disturbances crossing it at c, motion requires the transverse dimensions to shrink by 1/γ and the longitudinal by 1/γ², with energy and mass unchanged. Second, an energy-dependent step: the gravitational effect of a mass is equated to a "vacuum ball" of radius GM/c² from which ether is wholly excluded (0.45 cm for the earth), and since the ether can only react at c, moving the ball enlarges it by γ. Combining the two steps yields longitudinal contraction by 1/γ, unchanged transverse dimensions, time dilated by γ and mass increased by γ — the Lorentz ether results.

Addressing the four problems

Yilmaz's parallel plates: the elastic ether also predicts no attraction, because all shells surrounding the two plates are compressed equally, so there is no gradient and hence no force; Hatch adds that finite plates should show reduced attraction, which he suggests is experimentally checkable. The vacuum-energy problem: a uniform energy density produces no density gradient and hence no curvature, so the 10¹²⁰ discrepancy evaporates. The naked-singularity problem: if a body approached its gravitational radius the ether would be entirely excluded, and since particles are standing waves in the ether they could not exist there — so black holes cannot form, and the gravitational force is in any case self-limiting. Colliding neutron stars would therefore "largely disintegrate into electromagnetic radiation" rather than collapse. Hatch suggests this disintegration radiation may be the source of gamma-ray bursts, and argues against Piran's colliding-binary model that Piran's own mechanism is directional, whereas the Compton Observatory appears to see every collision in its field of view — implying a near-isotropic mechanism.

Free fall, gravity-gradient frames, and a proposed Sagnac test

The fourth problem gets the most space. Anderson, Bilger and Stedman had written that Michelson's suggestion of detecting the earth's orbital rotation with a large enough ring interferometer "is not consistent with general relativity: a freely falling point object (the whole earth in this context) defines a local Lorentz frame." Hatch takes this at face value and, following a remark by Hayden, notes that it implies a Sagnac experiment using the inter-satellite links of the newer GPS satellites should give a null result relative to a frame rotating once per year.

He first shows that four freely falling objects near each other cannot in general be mapped by any single transformation — objects above, below, ahead of and behind a circular orbiter change their relative arrangement over an orbit, and if all four are put in exact circular orbits they diverge. If the four are joined and gravity-gradient stabilised, like the moon, they keep a fixed orientation; and then the potential gradient and the velocity gradient exactly cancel, since df/dr ≈ GM/r²c² from the clock equation and df/dr ≈ −rθ̇²/c² from the velocity equation, with θ̇² = GM/r³ for a circular orbit. So as far as clocks are concerned the free-fall Lorentz frame claim survives — for circular orbits. But, Hatch argues, it is the clock behaviour that changes, not time; a universal time still flows; and therefore the Sagnac Effect due to orbital rotation remains detectable. Analysing a wedge-shaped light path with outer and inner legs r_oθ and r_iθ, and dividing by the respective light speeds from c = s²c_e, he finds the outer transit time longer even after the potential correction — so a cross-linked GPS Sagnac experiment should not null out at one revolution per year. He adds that Stedman's own ring laser, twelve orders of magnitude more precise than Michelson–Gale, must already contain the orbital rate, and asks pointedly why the measured rotation rate was not reported.

Three predictions

The paper closes with them explicitly: (1) gravitational radiation will never be detected; (2) unambiguous evidence for a black hole will never be found; (3) Gravity Probe B will measure a geodetic precession of 9.2 arcsec/year rather than the general theory's 6.9, because when time is measured by a clock external to the field the "space curvature" — the ether density gradient — is twice what the general theory predicts. Frame dragging is put at about 0.05 arcsec/year. Thomas precession is retained but reattributed: gravity acts on the centre of mass, not the centre of spin, so it induces no precession.

Assessment

The paper is more ambitious than Part I and more honest in its exposure. Hatch does not hide behind interpretive equivalence; he states three predictions that would decide the matter, and he identifies a specific instrument for each. That is exactly how a rival theory ought to behave. Several of his internal moves are also genuinely elegant. The resolution of the vacuum-energy problem by noting that a uniform density has no gradient is a clean argument within his own framework and does more work than the corresponding move in most ether papers. The demonstration that the potential gradient and velocity gradient cancel exactly on a gravity-gradient-stabilised body is a real calculation with a real result. And the four-freely-falling-objects argument is a fair way of pressing on what "local" means in "local Lorentz frame".

The difficulties begin with what is asserted. The relations ρ = ρ_e/s⁴ and m = m_e/s³ are introduced with the admission that "there are heuristic arguments which can be made; but, again, for brevity, let us simply assume" — yet the factor of three in the mass gauge is what drives prediction (3). The claim that matter consists of ether standing waves is called "simply a presupposition". The two-step derivation of the velocity effects produces a transverse contraction by 1/γ in the first step which is then cancelled in the second; the cancellation is arranged to land on the Lorentz results rather than derived independently.

Against measurement the record is now decisive, and it went against all three predictions. Gravitational radiation was detected: the LIGO observation of GW150914 in September 2015 recorded a binary black-hole inspiral waveform, and the 2017 event GW170817 was a binary neutron-star merger observed jointly with the gamma-ray burst GRB 170817A — precisely the coincidence test Hatch said "will never be executed". Gravity Probe B, launched in 2004 and reporting in 2011, measured a geodetic precession of 6.60 ± 0.02 arcsec/year and a frame-dragging drift of 0.037 ± 0.007 arcsec/year, in agreement with the general theory's 6.606 and 0.039 and excluding Hatch's 9.2 by a very wide margin. Evidence for black holes has likewise accumulated rather than evaporated: the resolved orbit of the star S2 about the compact object at the Galactic Centre, and the Event Horizon Telescope images of M87\* and Sgr A\*, are not readily reinterpreted as ether standing-wave configurations. Hatch's model also predicts that gamma-ray bursts come from a near-isotropic disintegration mechanism, but observed bursts are strongly beamed, with achromatic jet breaks in their afterglow light curves. Finally, the objection that the Anderson–Bilger–Stedman remark implies a null orbital Sagnac result reads a passing sentence about a point object as a claim about an extended interferometer; modern large ring lasers do resolve the earth's sidereal rotation and its small variations, without any of the anomalies the paper anticipates. What remains valuable in the paper is its diagnostic half — the genuine puzzles it names in the general theory and the clarity with which it separates "clocks slow" from "time slows".

See also

• Ronald R Hatch — the author
• Relativity and GPS - I — the companion paper on the special theory
• Escape from Einstein — Hatch's book
• General Relativity
• Lorentz ether theory
• Aether
• Sagnac Effect
• GPS
• Gravitational Waves
• Gravity
• Galilean Electrodynamics
• Howard C Hayden