On Gravitation

Scientific Paper
Title	On Gravitation
Read in full	Link to paper
Author(s)	Ove Tedenstig
Keywords	Gravity, Experiment, Hubble constant, background radiation, push gravity, proton radius
Published	1989
Journal	The Toth-Maatian Review
Volume	7
Number	4
Pages	3895-3900

Read the full paper here

Abstract

This paper describes the process of gravitation in terms of an inflow process of matter into material bodies, with a rate over time corresponding to Hubble's cosmical constant, H. The source of this flux is the thermal radiation in space of 2.7 K, known as the background radiation of space.

Overview

Tedenstig proposes that gravitation is not an attraction at all but a shadowing effect produced by matter absorbing a cosmic flux. The flux is identified with the 2.7 K background radiation, treated as a stream of material particles with mass rather than as a wave in an aether; each impact retards a proton's spin and, as a secondary effect, causes matter to be absorbed into the particle. A body therefore steadily gains mass, at a fractional rate set equal to the Hubble constant H — the body doubles its mass in a Hubble time. Because a body consumes the flux, it creates a deficit around itself, and a second body at distance D is pushed toward the first by the imbalance. Newton's inverse square follows from the 1/4πD² dilution of the flux.

The paper's claim to strength is that it does not merely reproduce the form of Newton's law but computes the value of G from the temperature of the background, the Hubble constant and the size of the proton — and, further, that the same mass-inflow idea disposes of three other problems in one move: the cosmological redshift (a slowing of light rather than recession), Olbers' paradox, and the continuous creation of matter required by a steady-state universe. The background radiation itself is then re-explained as the degraded remnant of ancient starlight that has lost its energy in transit.

The argument

Setting the scene

An opening section reviews what is known about gravity and stresses its weakness: for two electrons, Coulomb's law gives F_e = 2.3 × 10⁻²⁸/D² and Newton's law F_g = 5.53 × 10⁻⁷¹/D², a ratio of about 4 × 10⁴². Tedenstig notes that gravity appears indifferent to every property of matter except quantity — chemistry, temperature, density, charge, phase, energy content, state of motion — and reviews the Eötvös repetitions, Dirac's 1938 varying-G proposal, graviton exchange and general relativity, dismissing the last as describing gravitation "in a more proper and exact mathematical way" without explaining it physically.

Deriving G

The derivation proceeds by matching two independent expressions for the mass density q_f of the cosmic flux.

The first comes from thermodynamics. The Stefan-Boltzmann law gives the power per unit area as dP/dA = ST⁴; treating the same flux mechanically, dP = ½(dm/dt)v² with dm = vq_fdA dt, so dP/dA = ½q_fv³. Equating them,

q_f = 2ST⁴/v³

The second comes from the absorption hypothesis. If a body doubles its mass in time T, and R = 1/T is identified with H, then dm_t/m_p = H dt, while the hydromechanical inflow onto a proton of interaction area A_p is dm_t = q_fA_pv dt. Hence

q_f = Hm_p/(A_pv)

Eliminating q_f gives the interaction velocity v = T²√(2SA_p/Hm_p), which Tedenstig identifies with "the spinning velocity of a proton".

For the force, the inflow density near a body M₁ of total interacting area A₁ is q_x = M₁H/(A₁v); diluted over 4πD² it becomes q_D = M₁H/(vA_d). A second body presents area A₂ = (M₂/m_p)A_p, and the negative inflow gives a force F = q_DA₂v², which rearranges to

F = (M₁M₂/D²)·(HA_pv/4πm_p)

so that G = HA_pv/(4πm_p).

Two further assumptions close the calculation. The proton is taken to be a torus, so its interaction area is A_p = 4π²R_p²; and protons and electrons are assumed to have "the SAME INHERENT MASS DENSITY", so that R_p = r_e(m_p/m_e)^1/3 with r_e the classical electron radius. Tedenstig then tabulates: at T = 2.7 K and H = 3 × 10⁻¹⁸ s⁻¹, G = 5.0 × 10⁻¹¹; at H = 5.26 × 10⁻¹⁸ s⁻¹, G = 6.67 × 10⁻¹¹, the measured value. He footnotes that "the exact value of the Hubble constant is not known" and cites two 1992 New Scientist reports as pointing to a larger H.

Redshift, Olbers and continuous creation

If light too is matter subject to the same inflow, a travelling photon gains mass and slows: constant mass impulse mc = (m + dm)c′ gives c′/c in terms of dm/m = Ht, from which the frequency shift is df = f₀Ht. Tedenstig is explicit that "the wave-length of the travelling wave is constant but the frequency varies", and adds that substituting an equivalent wavelength shift "makes no difference in measurements made by spectrometers". Converting time to distance by d = ct reproduces Hubble's law without recession.

The same idea supplies continuous creation — "during each period of about 10-15 billions of years, the mass in a body (the earth for example) has doubled its content" — and disposes of Olbers' paradox, since starlight decays in transit. What is left of that starlight is "only a common electromagnetic noise which we now observe as the common background thermal radiation of 2.7 °K".

Assessment

Tedenstig's numerical work is correct. Recomputing from his stated inputs, R_p = 2.8179 × 10⁻¹⁵ × 1836.15^1/3 = 3.451 × 10⁻¹⁴ m, A_p = 4π²R_p² = 4.70 × 10⁻²⁶ m²; at H = 3 × 10⁻¹⁸ s⁻¹ the interaction velocity is 7.51 × 10⁶ m/s and G = 5.04 × 10⁻¹¹, matching his 5.0 × 10⁻¹¹; at H = 5.26 × 10⁻¹⁸ the same formulae give 6.675 × 10⁻¹¹, matching his 6.67 × 10⁻¹¹. The electron force ratio is right too (2.308 × 10⁻²⁸, 5.531 × 10⁻⁷¹, ratio 4.17 × 10⁴²). The expression G = HA_pv/4πm_p is dimensionally sound, and the shadowing construction is a legitimate member of the Le Sage family (see Category:Push Gravity) — it is a real derivation of an inverse square, not an assertion of one.

But the agreement with G is manufactured by two adjustable inputs, and the paper is candid enough that this can be seen directly.

G scales as √H, and the fit demands a Hubble constant of 162 km/s/Mpc. Because v ∝ H^−1/2 and G ∝ Hv, the prediction is G ∝ √H. The value that produces the measured G, H = 5.26 × 10⁻¹⁸ s⁻¹, is 162 km/s/Mpc — more than twice any modern determination, and outside even the wide 1992 range the footnote appeals to. Inserting the current value instead, H₀ = 67.5 km/s/Mpc = 2.19 × 10⁻¹⁸ s⁻¹, the formula returns G = 4.31 × 10⁻¹¹, thirty-five per cent below the measured 6.674 × 10⁻¹¹. The Planck and SH0ES determinations bracket H₀ between about 67 and 73; nothing near 162 survives.

G scales as the cube of an invented proton radius. Since A_p ∝ R_p² and v ∝ A_p^1/2, G ∝ A_p^3/2 ∝ R_p³. Tedenstig's R_p = 34.5 fm comes from equating proton and electron "inherent mass density" using the classical electron radius. The classical electron radius is not a size — it is the length e²/4πε₀m_ec², and electron scattering at LEP bounds any electron structure below 10⁻¹⁸ m. The proton's charge radius, by contrast, is measured: 0.84 fm from muonic hydrogen Lamb shift spectroscopy, 0.877 fm in the CODATA average from elastic electron scattering and ordinary hydrogen spectroscopy. Tedenstig's radius is forty-one times too large, and because G goes as R_p³, substituting the measured radius collapses the predicted G by a factor of 7 × 10⁴, to about 10⁻¹⁵. The number doing the work in this derivation is a geometric guess about the proton, not the temperature of the background.

The flux density is thirty thousand times the background it is identified with. This is the sharpest internal check. Tedenstig's own relations give q_f = 2ST⁴/v³ = 1.42 × 10⁻²⁶ kg/m³ at v = 7.51 × 10⁶ m/s. The actual mass-equivalent density of a 2.7 K blackbody field is aT⁴/c² = 4.47 × 10⁻³¹ kg/m³. The two differ by a factor of 3.2 × 10⁴, and the reason is visible in the algebra: the density inferred from a fixed energy flux goes as v⁻³, so letting the field particles travel at 0.025c instead of c inflates the required density by (c/v)³. Setting v = c recovers 2.24 × 10⁻³¹ kg/m³, within a factor of two of the correct value — but it also destroys the derivation, because v is the quantity the two expressions for q_f were solved for. The field cannot both be the 2.7 K background and be dense enough to make gravity.

An SI artefact is treated as a physical density. The paper states that the base potential behind gravity "is actuated by the vacuum itself with a pseudo material mass density of 1/E_o", quoted as 1 × 10¹¹ kg/m³. The number is right — 1/ε₀ = 1.129 × 10¹¹ — but its dimensions are m³·kg·s⁻²·C⁻², not kg/m³. It is 1.13 × 10¹¹ only because the coulomb, the metre and the kilogram happen to be sized as they are; in Gaussian units ε₀ = 1 and the "density" would be unity. Nothing that depends on the accident of a unit system can be a property of the vacuum. This claim is imported from a companion paper rather than used in the derivation above, but it is the same habit of reading a unit-dependent number as a physical quantity.

Continuous mass gain is excluded by three orders of magnitude. A doubling per Hubble time is a fractional rate of 9.5 × 10⁻¹¹ per year. Lunar laser ranging measures the Earth-Moon system's GM over five decades and limits any secular change, including Ġ/G, to below about 7 × 10⁻¹⁴ per year; planetary ephemerides give comparable bounds on the Sun. Tedenstig's rate is roughly a thousand times larger than what the ranging data allow. It also implies the Earth was some 35 per cent lighter when the oldest rocks formed, which is not compatible with the stability of the lunar orbit over that interval.

The redshift mechanism is testable and fails. Tedenstig states plainly that the wavelength is unchanged and only the frequency shifts, and asserts this makes no difference to a spectrometer. It makes every difference: a grating or prism spectrograph disperses by wavelength, so an optical spectrum of a distant galaxy would show no shift at all under this mechanism. More decisively, both quantities are measured independently on the same objects. Radio observations of the neutral hydrogen 21 cm line determine redshift directly as a frequency shift; optical spectroscopy of the same galaxies determines it as a wavelength shift; the two agree. A model in which λ is fixed and f varies predicts that they should disagree by exactly the redshift.

The equations 23-27 do not say what the text says. As printed, f = w/c inverts the relation between frequency and wavelength, and c′/c = m/(m + dm) is then written as "1 + dm/m" when the expansion is 1 − dm/m. Equation 26 chains three mutually inconsistent equalities. The magnitude that emerges, |Δf|/f = Ht = Hd/c, is the right Hubble relation, but it survives the derivation rather than following from it.

Finally, the account is circular at its centre. The 2.7 K background is the energy source that drives the mass inflow; the mass inflow is then invoked to explain the 2.7 K background as degraded starlight. Beyond the circularity, degraded starlight cannot be what is observed: COBE's FIRAS instrument found the background to be a blackbody at 2.725 K to within about 50 parts per million, the closest approach to a Planck spectrum ever measured, and a superposition of redshifted stellar spectra has no mechanism for thermalising to that precision. What remains genuinely attractive is the ambition: unlike most shadowing schemes, this one attempts a number for G from independently measured quantities and prints its inputs so that the attempt can be audited. The audit is what shows that the two inputs it needs are not the measured ones.

See also

• Ove Tedenstig
• Gravity
• Category:Push Gravity
• Hubble Constant
• Cosmic Microwave Background
• Tired Light
• Redshift
• Olbers' Paradox
• Steady State Theory
• Blackbody Radiation
• Proton