Light and Clock Behavior in the Space Generation Model of Gravitation
| Scientific Paper | |
|---|---|
| Title | Light and Clock Behavior in the Space Generation Model of Gravitation |
| Read in full | Link to paper |
| Author(s) | Richard Benish |
| Keywords | gravitation, Vessot-Levine, Shapiro-Reasenberg, clock rate, light speed anisotropy, matter expansion |
| Published | 2008 |
| Journal | Apeiron |
| Volume | 15 |
| Number | 3 |
| No. of pages | 13 |
| Pages | 222-234 |
Read the full paper here
Abstract
General Relativity's Schwarzschild solution describes a spherically symmetric gravitational field as an utterly static thing. The Space Generation Model describes it as an absolutely moving thing. The light propagation time-delay experiment of Shapiro-Reasenberg [i] and the falling atomic clock experiment of Vessot-Levine [ii] provide the ideal context for illustrating how, though the respective world views implied by these models are radically different, they make nearly the same predictions for the results of these experiments.
Overview
Benish's Space Generation Model (SGM) takes a deliberately literal reading of what accelerometers and clocks report. In general relativity an accelerometer resting on the ground reads g because it is being held out of free fall in a static curved spacetime; the reading indicates a potential to cause motion. Benish instead insists that a motion-sensing device indicates the existence of motion: "we adopt the simple and consistent approach of regarding these instruments as indicating not the potential to cause motion, but the existence of motion." A gravitating body is therefore treated as strictly analogous to a uniformly rotating body — an object in perpetual, unchanging, absolute motion, whose surface is moving outward even though the body never gets any bigger. Matter continually generates space; the field is not static but stationary.
The purpose of this particular paper is narrower than the model as a whole. It asks what the SGM predicts for the two experiments usually taken as the cleanest confirmations of the Schwarzschild solution's treatment of light and clocks: the Shapiro–Reasenberg radar time-delay measurements using the Viking lander on Mars, and the 1976 Vessot–Levine hydrogen-maser rocket flight. Benish's finding is that despite describing the world in radically different terms — a static refracting medium versus an outwardly streaming one, isotropic light speed versus gross anisotropy — the two models make numerically almost identical predictions for both experiments. His conclusion is not that the SGM is thereby confirmed, but that these celebrated tests are far less discriminating than they are advertised to be, and that a decisive experiment must be sought elsewhere.
The argument
Stationary versus static
Benish opens with the distinction between "static" and "stationary". He notes that de Sitter's cosmological solution has been called by Robertson and Noonan "the only non-static stationary model," and that the models of C. J. Masreliez and his own share this non-static stationary character. Uniform rotation is the everyday example: a wheel-shaped space station carries a range of accelerations and velocities across its rigid parts while looking the same forever.
The distinction matters for light. The Schwarzschild field, he notes following Møller, is "a near perfect analogy to a static medium with varying refractive index," so the light speed varies only with position. In a rotating system light speed depends also on direction — slower with the rotation, faster against it, the Sagnac Effect. If gravitation is genuinely a stationary motion rather than a static curvature, radial light speed must likewise be direction-dependent.
Clock rate reinterpreted
Both models accept the standard external clock rate
- f(r) = f0 (1 − 2GM/rc2)1/2
where f0 is the rate at infinity. General relativity reads the coefficient as the analogue of the static Newtonian potential GM/r. The SGM reads the speed inside it, √(2GM/r), as the analogue of the tangential speed of a rotating body — the actual, absolute outward velocity of the ground at radius r. On this reading the clock is slow because it is moving, not because it sits in a potential well.
The reasoning is developed with a thought experiment. Drop a clock from the top of a pole reaching almost to infinity. A co-moving accelerometer reads zero the whole way down, so on the literal interpretation "nothing has ever caused it to accelerate"; its speed does not increase and its rate does not fall. The relative velocity that develops is attributed absolutely to the pole, where the accelerometers do read non-zero. It follows that light speed is isotropically c only with respect to a clock falling radially from infinity. Benish calls these trajectories maximal geodesics. Crucially, "in the SGM there is no single global preferred ether frame. The preferred frames are the maximal geodesics determined by locally dominant gravitating bodies."
Shapiro–Reasenberg
The radial speed of light measured from the pole is then c↑↓ = c −/+ √(2GM/r), upper sign upward, generalised in a plane through the centre to a direction-dependent expression combining sin2θ and cos2θ terms. Numerically integrating that anisotropic light-speed law along the Earth–Mars signal path through superior conjunction gives a maximum delay of 227.4589 μs, against the Schwarzschild prediction of 227.4584 μs. The quoted observational error is 0.2 μs, so the 0.0005 μs difference is roughly three orders of magnitude below detectability. A gross first-order anisotropy in light speed and a static isotropic metric agree, in this test, to well within the noise.
Vessot–Levine
The 1976 flight carried a hydrogen maser to about 1.6 Earth radii (~10,000 km) on a near-vertical trajectory, its rate monitored by a three-link system designed to cancel first-order Doppler shifts; agreement with general relativity was at the level Δf/f ~ 10−4.
Here the two models superficially diverge sharply. The SGM's prediction for the actual probe-clock rate replaces the potential difference with two velocities — the stationary outward velocity of the ground √(2GM/rG) and that at the probe's momentary height √(2GM/rP) — and adds the probe's velocity v relative to the ground to the latter before squaring. Because that sum depends on whether the probe is rising or falling, the predicted curve is strongly asymmetric between ascent and descent, quite unlike the symmetric general-relativistic curve.
The paper's central result is that this asymmetry very nearly cancels once the three-link Doppler-cancellation system is folded in. Writing W = √(2GM/rG) and V = √(2GM/rP), Benish assembles the three links into a single expression whose difference from the general-relativistic prediction is
- ΔF/fG ≈ [(±v − V + W)/c] (v/c)2
— that is, the models part company only at order (v/c)3. The residuals lie within the experiment's envelope, though "near launch and impact the residuals go slightly beyond the 10−4 margin."
He draws a pointed methodological moral. Vessot and Levine claimed their flight was "the first direct, high-accuracy test of the symmetry of the propagation of light," concluding Δc/c < 6×10−8. Benish argues the word "direct" was "obviously misguided," because the analysis tacitly excluded models that reproduce the data through a gross light-speed anisotropy tightly correlated with an equally gross direction-dependence of clock rate. The clock-rate claim may hold at apogee; the light-speed claim, he says, may not hold at all.
Proposed discriminating tests
Three are offered. First, repeating the Vessot–Levine flight with one more order of magnitude of sensitivity would separate the predictions. Second, comparing elapsed time on the ascent leg against the descent leg: general relativity makes them equal, the SGM makes the descent longer by about 10−6 s. Third, and most drastic, the interior prediction. General relativity puts the slowest clock at the centre of a body, at the bottom of the potential well, and predicts that an object dropped down a hole through the centre oscillates from end to end. The SGM predicts clock rates increase toward the centre, reaching the infinity rate there — so a dropped object "would not pass the center." Benish notes this needs only "a modest laboratory."
Acknowledged incompleteness
The conclusion is unusually frank about the model's state. The "stationary outward motion" central to the scheme "cannot be consistently modeled or visualized in three-dimensional space," and Benish concedes that "the lack of a mathematical model corresponding to the conceptual one is, of course, a valid objection." His proposed remedy is a four-space-dimensional continuum of matter and space perpetually regenerating itself, in which the local inhomogeneous expansion goes as 1/r2 while the cumulative cosmic effect is an exponential expansion.
Assessment
The paper's real contribution is its negative result, and it is a genuinely interesting one. Benish has taken a model that denies the isotropy of light speed at first order in √(2GM/r)/c — an enormous violation by the standards of modern tests — and shown that both the Shapiro delay and the Vessot–Levine maser flight are, to their achieved precision, blind to it. The mechanism of the blindness is instructive: the anisotropy in light propagation and the direction-dependence of clock rate are correlated in just such a way that the round-trip and Doppler-cancelled observables come out the same. This is a legitimate point about what those experiments actually constrain, and it is made honestly, with the residuals plotted and the near-launch excursions beyond 10−4 reported rather than hidden. The interior-clock prediction is also a real virtue: it is unambiguous, cheap to test, and diametrically opposed to the standard prediction. A model that volunteers a falsifiable tabletop discriminator is doing something many alternatives never do.
The difficulties are correspondingly serious. The most important is the one the author himself names: there is no mathematics. The SGM is a set of substitution rules — read √(2GM/r) as a real velocity, add velocities before squaring — applied by hand to the two experiments in question. Equations (2), (3), (8) and (9) are assembled by analogy with rotation rather than derived from a field equation or an action, and there is no demonstration that the recipe is consistent, covariant, or even single-valued when more than one gravitating body is present. The "maximal geodesic" preferred frames are asserted to be set by "locally dominant" bodies, but no criterion of dominance is given and no account is offered of what happens in the transition region between, say, Earth and Sun — which is precisely the regime of the Shapiro test the paper computes. Equally, the claim that a co-moving accelerometer reading zero means "in a strict sense, its speed therefore does not increase" is an assertion about what velocity means, not a result; it is the whole model compressed into one sentence, and everything downstream depends on it.
The empirical exposure is also narrower than the paper's framing suggests. Two experiments are examined, and both are radial or near-radial. The SGM's first-order radial light-speed anisotropy would show up directly in one-way and closed-path optical experiments of much higher precision than 1976 maser telemetry — modern optical clock comparisons over height differences of a metre, Michelson–Morley-type resonator experiments constraining light-speed anisotropy at the 10−17 level, and lunar laser ranging — and none of these is addressed. The Sagnac Effect analogy is invoked to motivate the anisotropy, but the Sagnac shift is a genuinely observed rotational effect, and its magnitude is fixed by the rotation rate; nothing is done to show that the gravitational analogue reproduces the observed absence of a corresponding terrestrial signal. Nor is the interior prediction reconciled with the fact that clock rates below the surface, and the corresponding potential, are already constrained by the ordinary Newtonian dynamics of bodies moving inside mass distributions.
The cosmological coda is the weakest part. The claim that the local 1/r2 expansive process cumulates into an exponential cosmic expansion is stated in a sentence, without derivation and without any confrontation with the quantities such a model must reproduce — the (1+z) time dilation of Type Ia supernova light curves, the acoustic peak structure of the Cosmic Microwave Background, or primordial nucleosynthesis abundances. Benish's philosophical argument that "regarding motion as the cause of curvature makes more sense than regarding static curvature as the cause of motion," and that it is unnatural for first-order effects to be caused by second-order ones, is a statement of taste rather than of physics; general relativity's curvature terms are second order in GM/rc2 by construction, and their producing first-order coordinate accelerations is a feature of the geodesic equation, not an anomaly needing repair.
Judged on its own stated terms, though, the paper does what it sets out to do. It does not claim to have established the SGM; it claims that two experiments routinely cited as decisive do not decide, and it backs that with explicit numbers — 227.4584 against 227.4589 μs, and a residual entering only at (v/c)3. That much is a fair and checkable result.