Space Generation Model of Gravity, Cosmic Numbers & Dark Energy
| Scientific Paper | |
|---|---|
| Title | Space Generation Model of Gravity, Cosmic Numbers & Dark Energy |
| Read in full | Link to paper |
| Author(s) | Richard Benish |
| Keywords | Gravity, Cosmology, Relativity, Einstein, Large Numbers, Dark Energy |
| Published | 2009 |
| No. of pages | 29 |
Read the full paper here
Abstract
This is an updated and augmented version of the previously published paper, Space Generation Model of Gravitation and the Large Numbers Coincidences. The basis of the gravity model is that motion sensing devices---most notably accelerometers and clocks---consistently tell the truth about their state of motion. When the devices are attached to a uniformly rotating body this is undoubtedly true. Uniform rotation is sometimes referred to as an example of stationary motion. It is proposed here, by analogy, that gravitation is also an example of stationary motion. Einstein used the rotation analogy to deduce spacetime curvature. Similar logic suggests that in both cases the effects of curvature are caused by motion. A key distinction is that, unlike rotation, gravitational motion is not motion through space, but rather motion of space. Extending the analogy further, gravitation is conceived as a process involving movement into a fourth space dimension. Space and matter are dynamic, continuous extensions of each other, which implies that the average cosmic density is a universal constant. Assuming this to be the case leads to a cosmological model according to which ratios such as the gravitational to electrostatic force, electron mass to proton mass, Bohr radius to cosmic radius, and constants such as the fine structure constant, Hubble constant, the saturation density of nuclear matter and the energy density of the cosmic background radiation are all very simply related to one another. Measured values of these numbers are discussed in sufficient detail to facilitate judging whether or not the found and predicted relationships are due to chance. The notorious "cosmological constant" (dark energy) problem is also addressed in light of the new gravity model. Finally, it is emphasized that the model lends itself to a relatively easy laboratory test.
Overview
This 2009 paper by Richard Benish is an expanded version of his 2008 Apeiron article Space Generation Model and the Large Numbers Coincidences. It develops the Space Generation Model (SGM), in which gravity is not an attraction at all but a perpetual outward motion — specifically, the generation of space itself, directed into a fourth spatial dimension. The argument begins not from a field equation but from an epistemological demand: that accelerometers and clocks be taken at their word. An accelerometer resting on the Earth's surface reads positive; Benish insists this means the device is genuinely accelerating outward, and that the whole apparatus of Newtonian "trying but failing to accelerate downward" and of GR's "acceleration of a particle at rest" is an elaborate way of disbelieving one's own instruments.
From that premise the paper moves outward in scale. Because matter and space are treated as continuous extensions of one another, the average cosmic density must be a genuine constant rather than a time-varying parameter; and once that is granted, a chain of relations connects the CMB temperature, the Hubble constant, the matter density, the nuclear saturation density, the fine structure constant, the electron-to-proton mass ratio and Newton's G into a single closed scheme. This puts the paper in the Large Numbers tradition of Dirac, Eddington and Sciama, but with a different aim: Benish is not claiming the constants vary, he is claiming they are all facets of one fixed structure. The paper closes with the "cosmological constant" problem and, crucially, with a benchtop experiment that Benish says would settle the whole question in an afternoon.
The argument
Stationary motion and the rotation analogy
Benish distinguishes static (no motion) from stationary (motion that persists unchanged). On a uniformly rotating body, accelerometers read negative accelerations varying as r and clocks run at f(r) = f0√(1 − r2ω2/c2); on a gravitating body, accelerometers read positive accelerations varying as 1/r2 and clocks run at f(r) = f0√(1 − 2GM/rc2). Einstein used the rotating disc to argue that a rotating observer may regard himself as at rest and that the geometry is non-Euclidean. Benish reverses the inference: on the rotating body the non-Euclidean effects are caused by the motion, so by the principle of attributing the same cause to the same effect, the gravitational case should also be caused by motion. Einstein's move, he argues, amounted to "a denial that accelerometer readings and clock rates are reliable indicators of motion," and preserved "the ancient notion of self-rest."
Why a fourth dimension of space
Gravitational motion cannot be motion through space, since bodies do not visibly fly apart. Benish therefore takes it to be motion of newly generated space, and argues that a coherent inverse-square outward expansion of a spherically symmetric body cannot be modelled in three dimensions. The dimensional hierarchy is his analogy: a line sweeps a plane, a plane sweeps a volume, and gravitation is the way a volume sweeps a hypervolume. He extracts two by-products. Inertial mass becomes the resistance to being accelerated in one direction, proportional to the space a body generates in every direction; and the arrow of time follows because "space and matter also only increase."
The interior-field test
The SGM's sharpest divergence from both Newton and Einstein is inside matter. In the SGM, clock rates indicate existing motion rather than the potential for motion, so a clock at the centre of a massive body ticks at the same maximum rate as a clock at infinity, and a body dropped down a tunnel through the sphere does not oscillate through the centre — it approaches the centre asymptotically after reaching a maximum apparent speed. Benish proposes a modified Cavendish balance in which the balance arm can move into a hole in the large masses: "to oscillate or not to oscillate?" If it oscillates, Newton and Einstein are right and the SGM is wrong. He stresses that this interior region has never actually been tested, and argues that the experiment should precede any attempt to build the model into rigorous hyperdimensional mathematics.
Cosmic redshift and the density parameter
Constant cosmic density plus smoothed-out inhomogeneity gives an exponential expansion r = r0exp(βΔt). Matter is "clock-like" and gains energy with cosmic time; light is not a clock and retains only the energy it had at emission. Since lengths go as exp(βΔt) and density is fixed, masses go as exp(3βΔt), and the de Broglie relation f = mc2/h makes observed frequency proportional to mass. With β = c/RC this yields
z = exp(3r0/RC) − 1,
so for small z, z ≈ 3r0/RC and the cosmic length is three times the Hubble radius, RC = 3RH. Taking the scale relation RC = GMC/c2 — a relation Benish notes has appeared repeatedly in Machian cosmologies (Dicke, Sciama, Bondi) and which he retains purely for scale-setting — gives ρC = 3c2/4πGRC2 and hence a density parameter ΩM = 2/9 = 0.2222. Because the redshift arises from matter gaining energy rather than from recession, this is a variant of the intrinsic-redshift family of proposals, and Benish explicitly compares it to the Steady State models of Hoyle, Bondi and Gold — with the difference that in the SGM density stays exactly constant because existing particles grow rather than new ones appearing.
The cosmic numbers chain
Section 5 is an extended review of the COBE temperature determinations, tracking them from 2.735 ± 0.060 K (1990) to 2.725 ± 0.001 K (2002) and noting that the dipole-derived values ran persistently low (2.714 ± 0.022 K in 1994; 2.717 ± 0.007 K in 1996) and were only brought into line by later reanalysis — a point on which Benish quotes P. M. Robitaille's objection that it is "inappropriate to make so many adjustments for 'systematic errors'... long after completion of an experiment."
The chain then runs: convert TCOBE to an energy density μ = aT4; assume the radiation-to-matter density ratio is ρμ/ρC = ½(me/mp); solve for RC; and read off H0 = 3c/RC = 63.9 km s−1 Mpc−1. Benish notes that Sandage and Tammann's team persistently favour a low value (h = 0.623 ± 0.013) against the h ≈ 0.72 consensus. He then compares the gravitational-to-electrostatic force ratio in hydrogen, FG/FE = 4.4068 × 10−40, with the Bohr-radius-to-cosmic-radius ratio a0/RC = 1.2185 × 10−37; their quotient is 276.4451, which is 2/α to within a factor 0.9914. Imposing exact equality fixes ρC = 1.6754 × 10−27 kg m−3 and back-predicts TSGM = 2.7133 K — within 0.03% of the 1994 dipole value and 0.14% of the 1996 dipole value, though 0.43% from the final combined COBE figure.
Section 8 does the same auditing exercise for the nuclear saturation density ρN, showing that thirty years of literature has not improved on two significant figures (0.17 mp fm−3, with Santra and Lombardo giving an explicit ±0.02). Requiring (FE/FG)/(ρN/ρC) = α2/4 exactly gives ρN = 0.1707 mp fm−3 = 2.8552 × 1017 kg m−3, within 1% of the value implied by Fermi and Segrè's equilibrium volume built on the charged pion Compton wavelength — a length that happens to be close to half the classical electron radius, α2a0/2. The scheme's centrepiece is then an expression for Newton's constant:
G = 8[(ρμ/ρN) · (c2a0/me)],
which Benish reads as "acceleration of volume per mass" (c2a0/me, of order 1036) times a dimensionless strength (8ρμ/ρN, of order 10−48). A further relation, 2EGH/VH = μα6, connects the gravitational energy of the hydrogen ground state to the CMB energy density; Benish reports it as exact in the SGM and correct to 0.11% with the 1994 dipole value.
Maximum force and the vacuum
Replacing (at) by √(2GM/r) in the relativistic velocity relation gives a stationary velocity VS = √[2GM/(r + 2GM/c2)] that never reaches c, from which the SGM curvature coefficient [1 + 2GM/rc2]−1 follows. Because this cannot vanish, the model has no horizons and no singularities: the Schwarzschild radius survives only as a length rγ = r + 2GM/c2. The limiting acceleration gS = ¼c4/GM gives a mass-independent maximum force FMAX = c4/4G = 3.03 × 1043 N. Dividing by LP2 and by the SGM matter density reproduces the notorious 10122, but Benish dismisses its significance on two grounds: the Planck mass is roughly a grain of sand, whose Compton wavelength means nothing; and in the SGM the Schwarzschild radius has no deep meaning. His positive suggestion is to recast the Λ-term of Gμν = 8πGTμν/c4 − Λgμν as a non-uniform space-creating term sourced by matter according to an inverse-square law, which would dispense with gravitational attraction altogether. "Perhaps thinking of gravity as an attraction and insisting on the validity of the energy conservation law were Einstein's biggest blunders."
Assessment
What makes this paper worth reading, whatever one concludes, is that it stakes everything on a specific unperformed measurement. Benish is unusually clear that the numerological half of the paper is worthless if the interior-field prediction fails: "If a test object oscillates through a hole spanning opposite sides of a massive sphere in accord with Newton, one could hardly escape the conclusion that the near exactitude of these numerical connections is an unfortunate accident." That is exactly the right instinct, and the modified Cavendish geometry is a cheap, decisive test of a region of the gravitational field that has indeed never been directly probed. The metrological sections are also genuinely valuable independent of the model: the audit of how the COBE dipole and monopole temperatures were reconciled, and the demonstration that ρN's stated uncertainty has grown rather than shrunk over three decades while its provenance is rarely cited, are careful pieces of work. And the complaint that G "stands isolated from the rest of physics" is a real one, not a crank's grievance.
The central difficulty is that the numerical agreements are not predictions. In each case Benish computes a ratio, observes that it is close to a simple expression in α, and then imposes exact equality and propagates the adjusted value forward. Equation (29) is off by 0.86%, equation (39) by 0.41%, and equation (41) by 1.04%; the scheme absorbs each discrepancy by redefining RC and ρC, which are precisely the quantities not independently measured. The chain therefore has enough freedom that its self-consistency is close to guaranteed. The one place it makes contact with a well-measured number is the CMB temperature, and there the model's 2.7133 K disagrees with the final COBE/FIRAS value of 2.72548 ± 0.00057 K by roughly twenty standard deviations. Benish's response — that the dipole determinations were "nudged" and may be nearer the truth — is a serious enough observation to raise, but it requires the reader to prefer a superseded, wider-error-bar analysis precisely because it fits, which is the same move he criticises the COBE team for.
The cosmological predictions face harder tests than the paper acknowledges. H0 = 63.9 was defensible in 2009 amid the long-value dispute, but Cepheid-calibrated Type Ia distance-ladder determinations now sit near 73 km s−1 Mpc−1 and CMB-inferred values near 67, both far from 63.9 relative to their quoted errors. More seriously, the redshift law z = exp(3r/RC) − 1 arises from clock rates rather than recession, and any such mechanism must reproduce the (1 + z) stretching of Type Ia supernova light curves measured by Goldhaber et al. — an effect that scales with the observed redshift and which distinguishes genuine expansion from static alternatives. The paper does not address it. Nor does it engage the acoustic peak structure of the CMB anisotropies, which the standard model fits with a handful of parameters and which any constant-density cosmology must also explain.
Finally, the interpretive core — that an accelerometer reading positive at rest on the Earth must mean real outward motion — is asserted more than argued. The standard reading is that a stationary accelerometer registers the non-gravitational contact force holding it off a geodesic, which is neither a denial of the instrument nor a claim of "self-rest"; and the outward-motion picture has to explain, as Benish concedes it cannot yet do rigorously, why the Earth's surface does not visibly recede from anything. The extra dimension is invoked to absorb exactly that problem, and until it is developed mathematically the model cannot be checked against the tests GR passes — perihelion precession, frame dragging, binary pulsar orbital decay. Benish's answer is that the experiment should come first, and on his own terms that is a coherent position; but it means the paper is best read as a well-posed challenge and a proposed test rather than as a completed theory.