Clock Behavior and the Search for an Underlying Mechanism for Relativistic Phenomena
| Scientific Paper | |
|---|---|
| Title | Clock Behavior and the Search for an Underlying Mechanism for Relativistic Phenomena |
| Read in full | Link to paper |
| Author(s) | Ronald R Hatch |
| Keywords | Special Relativity |
| Published | 2002 |
| No. of pages | 10 |
Read the full paper here
Abstract
Proceedings of the ION 58th Annual Meeting & CIGTF Guidance Test Symposium, Albuquerque, NM, June 24-26, 2002, pp 70-81. The Special Relativity Theory (SRT) and the General Relativity Theory (GRT) sometimes exhibit clock effects of equal magnitude which cancel and sometimes exhibit clock effects of equal magnitude which are additive. This cannot be coincidence, yet there is nothing within the two disjoint relativity theories to suggest an underlying mechanism. The effects appear to be related to energy, but the SRT treats energy as relative and the GRT treats an orbiting body as following a force-free trajectory. Thus an alternative to the Einstein theories seems to be required. I have proposed what I call a Modified Lorentz Ether Theory (MLET) which extends the Lorentz ether concepts to cover gravitational phenomena. Following a brief review of MLET concepts, it is contrasted with SRT concepts. Current data available from a number of modern experiments are evaluated with regard to both MLET and SRT. In general, MLET provides a more coherent and consistent explanation of the data. In the principal section of the paper it is shown that in the earth-centered inertial (ECI) frame Global Positioning System (GPS) clocks must not be adjusted for the gradient of the sun's gravitational potential. MLET shows that the differential effect of the sun's gravitational potential is absorbed into the clock bias which converts the Selleri transformation into an apparent Lorentz transformation. By contrast, there is no valid explanation for this phenomenon which is consistent with SRT/GRT and they are thereby refuted. This is very strong evidence that some form of Lorentz ether theory is valid and that Einstein's relativity theories are invalid.
Overview
Ronald R. Hatch was a working GPS engineer — twelve patents, President of the Institute of Navigation at the time this was presented to that body's 2002 annual meeting — and the paper argues from the operating practice of satellite navigation rather than from thought experiments. Its opening observation is that two well-known clock effects of exactly equal size arise from what are supposedly two separate theories. At sea level on the equator, the slowing due to the Earth's spin velocity (special relativity) is exactly cancelled by the speeding due to the equatorial bulge lifting the clock in the Earth's potential (general relativity). In a GPS satellite near perigee, the slowing due to increased speed and the slowing due to deeper potential are again exactly equal — but this time they add. "Why should the magnitude of the clock effects be exactly equal in the two examples above? It is a highly unlikely coincidence."
Hatch's answer is that both are manifestations of a single quantity, the energy of the clock, and that a theory which makes kinetic energy frame-relative and gravitation pure geometry cannot supply the connection. His alternative is a Modified Lorentz Ether Theory (MLET), also called an Ether Gauge Theory, which extends Lorentz's absolute-ether treatment to gravity. The paper's centrepiece — headed "THE COUP de GRÂCE" — is the claim that GPS clocks are correctly modelled by ignoring the Sun's gravitational potential gradient across the Earth's neighbourhood, that MLET explains why, and that relativity cannot, and is thereby "refuted".
The argument
What MLET says
Material particles are modelled as standing waves in an absolute ether. Because the two-way speed of light relative to a moving particle is lower, length contraction and clock slowing follow automatically rather than being derived from a postulate. The scale factor is the familiar γ = 1/√(1 − v2/c2), but with v the absolute velocity. Clock rates and lengths are divided by γ, inertial mass is multiplied by it, and "structural" or gravitational rest mass is divided by it. Hatch is blunt about his motive: "the major reason for choosing an ether theory over SRT is the choice of science over magic. Fundamentally, SRT is a magic theory. The speed of light is magically constant in all inertial frames — no mechanism is given."
Gravity enters through ether density: standing waves lower the internal ether density, raising it externally, and the excess decays with distance. This yields a gravitational scale factor differing from the relativistic one at second order:
GRT: s = (1 − 2GM/rc2)1/2 ≈ 1 − GM/rc2 − G2M2/2r2c4
MLET: s = e−GM/rc2 ≈ 1 − GM/rc2 + G2M2/2r2c4
The transformation used is Selleri's (equivalently Tangherlini's), which is reciprocal rather than symmetrical: an observer in the moving frame sees absolute-frame clocks running faster and lengths expanded. Adding an appropriate position-dependent clock bias converts it into an "apparent Lorentz transformation", and Hatch's recurring point is that ordinary synchronisation procedures supply exactly that bias automatically. He notes a consequence usually passed over: "The Lorentz transformation achieves a slower running clock by actually increasing the clock rate but then more than counteracting that effect with a clock bias that is a function of position."
Four test cases
Thomas precession. Special relativity obtains it from non-collinear Lorentz boosts, which Hatch calls magic — a torque-free precession produced by a change of bookkeeping. MLET instead gives a real torque: a spinning object constrained by a non-gravitational force has spin and orbital velocities adding on one side and subtracting on the other, so that side contracts and gains inertial mass, displacing the centre of mass from the geometric centre, and the applied force then exerts a torque. He adds a consistency complaint: if orbiting bodies follow geodesics and no Lorentz boosts apply, why is the Lorentz transformation invoked to explain stellar aberration on the Earth?
Twin paradox. In MLET "the soul of simplicity": pick any inertial frame, call it absolute, never change frames, let each clock run at the rate its velocity in that frame dictates. The differential ageing comes out the same whichever frame is chosen.
Sagnac effect. Hatch argues that large-scale systems in fact use the "MLET template" — moving sensors do not see isotropic light speed — while invoking relativity for the explanation. The 1971 JPL document specifying deep-space tracking uses a Sun-centred isotropic-light-speed frame and accounts for the Earth-observer's spin, orbital and Earth–Moon barycentric motion during signal transit. GPS does the same in an Earth-centred non-rotating frame. His key claim is that this cannot be about rotation: "The path the receiver followed during the time of flight of the signal is completely irrelevant" — only the emission and reception positions matter. He cites Ives (1938) to the same effect and Wang's Fiber Optic Conveyer as a direct demonstration that linear motion produces the same effect as circular.
Rotating Mössbauer experiments. Textbooks treat these null results as excluding ether drift. Hatch, following Ruderfer's own 1961 erratum, argues that any ether theory predicts a clock-rate effect that cancels the transit-time effect, so a null result is exactly what an ether predicts. Since the GPS system independently establishes that spin velocity affects clock rate, the null results "actually imply that an ether drift must exist". He judges the textbook treatment "poor science, if not deliberate fraud".
The coup de grâce
The core calculation concerns a clock moving on the Earth in the direction of the Earth's orbital velocity. Combining spin and orbital velocity, the frequency shift is
Δf/f ≈ −vo2/2c2 − vo·vs/c2 − vs2/2c2.
The first term is common to all clocks near the Earth. The third is cancelled by the equatorial-bulge potential. The middle cross-term, integrated along the clock's displacement, gives Δt = −vox/c2 — precisely the clock bias needed to turn the Selleri transformation into the apparent Lorentz transformation. The same result follows for slow clock transport.
Hatch then asks what happens when the orbital velocity vector changes direction. For the bias to stay correct the frame would have to rotate once per year, which would make clocks farther from the Sun move faster and run slower: taking the radial gradient of Δf = −f r2θ̇2/2c2 and using θ̇2 = GM/r3 gives df/dr = −fGM/r2c2. But the Sun's potential gives Δf = −fGM/rc2, whose gradient is df/dr = +fGM/r2c2. "Indeed, because equation (20) is identical except for sign with equation (18)", the two cancel exactly, and the required bias is maintained without any rotation of the frame. For an eccentric orbit the same result holds with the force resolved along and normal to the path, each equation acquiring a factor cos γ.
Hatch rejects Neil Ashby's appeal to the equivalence principle, citing Friedman that a local Lorentz frame is of only infinitesimal extent, and argues that the GPS orbital planes demonstrably do not rotate to keep a fixed angle to the Sun. His conclusion is that since GPS works while ignoring the solar potential gradient, "we must conclude that SRT/GRT is wrong." He notes the same argument also excludes any ether-drag theory.
The closing pages list further MLET consequences: because the exponential scale factor makes gravity self-limiting, "'Black Holes' are ruled out"; large stellar masses are underestimated by an inverse-square analysis, which he offers as a gravitational explanation for the anomalous redshift of OB stars and for excess galactic rotation "without WIMPS, MACHOS or any other form of strange mass". He proposes a decisive test: a drag-free spacecraft measuring the solar gravitational force against distance. A final section collects quotations from Gleick, Lanczos, Davies and Gribbin, Asimov and Clifford Will to argue that Einstein has been accorded "the status of a 'God of Science'", closing with Einstein's own 1949 letter: "There is not a single concept of which I am convinced it will stand firm."
Assessment
Hatch writes from inside the discipline he is describing, and the descriptive parts of the paper are accurate and valuable. He is right that operational systems — JPL deep-space tracking, GPS, pulsar timing — are built in a single privileged frame with a single common time, and that receivers must account for their own motion during signal transit regardless of whether that motion is rotational. His observation that this is "the MLET template", widely used though rarely acknowledged as such, is a fair description of engineering practice. The reading of the rotating Mössbauer experiments is likewise a genuine and underappreciated point: Ruderfer's own erratum does show that the transit-time and clock-rate effects cancel, so those experiments were never the clean ether tests the textbooks claim. And the remark that the Lorentz transformation reaches a slow clock by raising the rate and over-compensating with a position-dependent bias is a real feature of the algebra that is seldom stated.
The two "coincidences" that motivate the whole paper, however, are theorems rather than coincidences, and the derivation is short. In relativity a clock's fractional rate offset is Φ/c2 − v2/2c2, gravitational and kinematic terms in one expression. The geoid is defined as a surface of constant effective potential Φ + Φcentrifugal = Φ − v2/2, which is exactly that combination — so all sea-level clocks running at the same rate is not a cancellation of two effects but a restatement of what "sea level" means. For the satellite, the vis-viva relation v2 = GM(2/r − 1/a) gives −v2/2c2 = −GM/rc2 + GM/2ac2, whose r-dependent part is identical to the potential term Φ/c2 = −GM/rc2. Equal magnitudes, same sign, hence the familiar factor-of-two eccentricity correction. The "underlying mechanism" Hatch says relativity lacks is the conserved orbital energy, and it is already in the standard formula. His two examples are consequences of one equation, not of two disjoint theories.
The central argument has the same character. Hatch's equations (18) and (20) — df/dr = −fGM/r2c2 from the velocity term and +fGM/r2c2 from the potential — are correct, and their exact cancellation is a real and slightly surprising result worth deriving. But that cancellation is precisely what the equivalence principle asserts: in the freely falling, non-rotating frame of the Earth's centre, the Sun's field appears only through its second derivative, the tidal term, because the leading gradient is absorbed by the frame's own acceleration. Hatch has rederived the equivalence principle in coordinates and then declared that the equivalence principle cannot explain it. His objection that GPS orbit planes do not rotate once per year misses the point, since the standard account requires no rotation either; the free fall of the frame origin does the work, and Ashby's argument is the one Hatch's own algebra confirms.
Friedman's caution that a local Lorentz frame has only infinitesimal extent is well taken, and it has a quantitative answer rather than a rhetorical one. The residual solar effect on an Earth-surface clock is the tidal term, of order GM☉R⊕2/r3c2 ≈ 2×10−17. That is far below GPS clock stability, which is why GPS legitimately ignores it — a null result at the 10−14 level does not distinguish two theories that differ at 10−17. Modern optical lattice clocks do reach the 10−18 level, so this is now a live measurement rather than a matter of principle, but as of 2002 the "coup de grâce" rested on a cancellation both theories predict and a residual neither could then measure.
Elsewhere the paper's confidence outruns its evidence. The MLET exponential scale factor is offered as "substantially" supported, but the second-order coefficient in which it differs from Schwarzschild is exactly what solar-system tests constrain; the post-Newtonian parameter β is measured to better than one part in 104 from Mercury's perihelion precession and lunar laser ranging, and any second-order modification has to survive that. The consequence Hatch draws most confidently — that black holes are ruled out because gravity becomes self-limiting — has since been tested directly: the orbit of the star S2 around Sgr A* confines 4.3 million solar masses within a few tens of astronomical units and shows the relativistic pericentre advance, and the Event Horizon Telescope images of M87* and Sgr A* show shadows of the predicted angular size. The suggestion that underestimated stellar masses explain the anomalous redshift of OB stars and flat galactic rotation curves is asserted rather than computed, and no numbers are given for either. The final section's collection of triumphalist quotations is fair comment on a real cultural problem, but it is rhetoric rather than argument, and the accusation of "deliberate fraud" against the Mössbauer experimenters is not supported by anything in the paper beyond their having reached a conclusion Hatch rejects.
Read narrowly, this is a well-informed account of how precision timing systems actually work, from someone who built them, together with a serious and largely correct calculation. Read as its abstract intends — as a refutation of relativity — it does not succeed, because the phenomenon it identifies is one both frameworks predict and the difference between them lies two or three orders of magnitude below the data adduced.