Scale Expanding Cosmos Theory II – Cosmic Drag

Scientific Paper
Title	Scale Expanding Cosmos Theory II – Cosmic Drag
Read in full	Link to paper
Author(s)	C Johan Masreliez
Keywords	Cosmic drag, galaxy formation, angular momentum problem, planetary ephemerides, planetary acceleration
Published	2004
Journal	Apeiron
Volume	11
Number	4
No. of pages	29
Pages	1-29

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Abstract

In a previous article the author introduced the Scale Expanding Cosmos (SEC) theory and showed that this new theory could resolve several problems with the Standard Cosmological Model. This new theory better agrees with observational data, for example the number count test, the angular size test, the surface brightness test and the supernovae Ia observations. In addition it provides a simple explanation to the Pioneer anomaly. The SEC theory predicts new and testable cosmological features among them cosmic (velocity) drag, which is the subject of this paper. I will show that currently there is substantial evidence for cosmic drag and suggest how this new and unexpected aspect of the universe may be confirmed by observations in the solar system.

Overview

This is the second paper in C Johan Masreliez's Scale Expanding Cosmos (SEC) series, published in Apeiron in October 2004 following the introductory paper in the July 2004 issue. Where the first paper set out the SEC line element and tested it against the classical cosmological observations, this one isolates a single consequence — cosmic drag — and argues both that it explains features of galaxies and the solar system that the standard model handles awkwardly, and that it makes the SEC theory falsifiable by measurements available now.

Cosmic drag is the claim that in an SEC universe the relative velocity of any freely moving body decays exponentially with the Hubble time T, and the angular momentum of any rotating system decays with time constant T/2. Light is exempt: the speed of light is not affected by drag, though light is redshifted. This asymmetry is the engine of the whole paper. It means that the SEC universe generates its own preferred rest frame — not postulated as Newton's absolute space, nor tied to distant matter as in Mach's formulation, but "self-induced" by the mutual decay of relative motion. It also means that matter is perpetually settling inward: stars spiral toward galactic cores and planets spiral toward the Sun. Masreliez turns each of these into an observational claim, respectively about flat rotation curves without a dark matter halo and about a secular angular acceleration of the inner planets that he says has already been detected.

The argument

The two drag relations

Masreliez begins from the SEC geodesic equations derived in Masreliez (1999) and Masreliez (2004). For normalized velocity β = v/c,

β = β₀e^−t/T / √[1 − β₀² + β₀²e^−2t/T].

If β₀ = 1 then β = 1 for all times — a photon always moves at c — while for β₀ ≪ 1 the relation reduces to β = β₀e^−t/T, i.e. β̇ = −β/T. Because c is untouched, the Lorentz transformation still holds locally; what fails is the equivalence of inertial frames. The angular analogue, obtained by setting φ = 0 in the SEC geodesic, gives r²θ̇ = r₀²θ̇₀e^−2t/T at low velocity: angular momentum decays exponentially.

A self-induced cosmological reference frame

Special Relativity recognizes no preferred frame and General Relativity extends that indifference to all smooth coordinate changes, yet, Masreliez notes, galaxies have peculiar velocities well under one percent of c and the CMB dipole shows the Local Group moving relative to the radiation. He argues that drag supplies the missing frame by "bootstrapping": every observer sees every other galaxy's relative velocity decay with time constant T, so absent other forces all galaxies converge on a common state of relative rest, and that state is the cosmological frame. He adds that a unique rest frame makes gravitational field energy definable — impossible in the standard model, where the Schwarzschild exterior solution satisfies the field equations with a vanishing energy–momentum tensor even though the gravitational field energy ought to be negative. In the SEC, he asserts, no counterpart of the exterior Schwarzschild solution exists, so matter necessarily modifies the vacuum energy–momentum tensor.

Spiral galaxies and flat rotation curves

If drag operates, matter falls continuously toward galactic cores, so galaxies must be dynamic steady-state objects — possibly "tenths or even hundreds of billion years old" — with some process ejecting matter back out, a role Masreliez assigns to active galactic nuclei. He adopts one postulate: the matter flow toward a galaxy's core is constant and is the same at all radii. From mass conservation through a surface at radius r, ρ(r,t)·A(r)·v(r,t) = constant, he derives M(r(t)) · t = constant and hence a linear mass distribution outside a central bulge M_b. Inserting the decaying angular momentum J = J₀e^−t/T into the radial equation of motion and neglecting the small ṙ/T term yields r(t) = r₀e^−2t/T/M_f(t) and a tangential velocity v_t(t) = v_t(0)·e^t/T·√M_f. Together these define both the spiral trajectory and the rotation curve. Masreliez reports that the curves are generically flat provided less than about one third of the mass sits in the bulge, and that partitioning the galaxy into bulge, a matter-poor transition region and an outer region reproduces the dip-then-rise structure and the low-luminosity annulus seen around many bulges. Four observed rotation curves from Sofue and Rubin (2001) were tested; three were closely matched by adjusting three parameters — core mass fraction, core radius and the time constant T_c — and the fourth, with an unusually sharp inner peak, reasonably well. On this account the "hidden" mass is cool gas in the arms rather than a spherical halo.

Planetary accelerations

Decaying angular momentum plus Kepler's third law (which survives because the SEC gravitational potential P = (GM/r)[1 + O((r/T)²)] departs from the post-Newtonian potential by only ~10⁻²⁸ in the solar system) gives ω̇ = 3ω/T, ṙ = −2r/T and v̇ = v/T. Planets therefore spiral inward while their angular and tangential velocities increase. With T = 14 billion years the Earth's secular angular acceleration is about 2.8 arcsec/century² and its orbital radius shrinks by roughly 20 metres a year. Masreliez sets his predicted semi-accelerations against Kolesnik's values from thirty years of optical observations timed by atomic clocks:

Planet	Predicted by SEC (arcsec/cy2)	Observed (arcsec/cy2)
Mercury	5.77	8.6 ± 3.0
Venus	2.26	1.9 ± 0.5
Earth	1.39	1.4 ± 0.2

Why it was not seen before

Much of section 6 is devoted to explaining the absence of the effect from modern ephemerides. Before atomic time, astronomical timekeeping used Universal Time (Earth's rotation) and Ephemeris Time (Earth's orbit), so any uniform planetary acceleration vanished by definition — Spencer Jones's 1939 solar semi-acceleration of 1.23 arcsec/cy², conventionally attributed to tidal slowing of the Earth, is close to the SEC value for the Earth. Modern JPL ephemerides are fitted chiefly to radar ranging with the time argument derived inside the fitting process; Masreliez argues (with a supporting transformation in Appendix 1) that because a locally Minkowskian coordinate system always exists in a curved SEC spacetime and differs from it only at order (r/T)², the fit will succeed perfectly while its coordinate time accelerates relative to atomic time — about 2–3 seconds of quadratic drift in fifty years, reduced by a factor of at least eight by JPL's fitting procedure and so barely detectable. Optical observations timed by atomic clocks escape this and show the drift. He cites Oesterwinter and Cohen (1972), who found old ET drifting ~7 seconds in 50 years against atomic time against his predicted 7.5 s, and positive tangential accelerations of Mercury and Venus from Reasenberg & Shapiro (1978) and Krasinsky et al. (1986). Pulsar spin-down rates are also said to fall close to the SEC prediction without requiring a dissipation mechanism that would radiate solar-scale heat.

Appendix 2: the CMB from AGN

In an SEC universe the Planck spectrum is preserved under expansion, so a blackbody background can arise by thermalization of ordinary radiation rather than as a relic. Setting (CMB energy density)/T equal to the radiated power density and assuming each galaxy ejects a fraction a ≈ 0.10–0.15 of its mass per Hubble time through AGN activity, Masreliez obtains a radiated power of p(2.2–3.3)×10³⁹ W per galaxy — consistent with observed AGN luminosities of 10³⁸–10⁴² W — and a power density of 1.3–2.0p×10⁻³⁰ W/m³ against a CMB loss rate of 10⁻³¹ W/m³, giving a required conversion efficiency p = 0.05–0.08.

Assessment

The paper's real strength is that it commits. Many alternative cosmologies are constructed to reproduce what is already known; cosmic drag is a genuinely risky prediction, quantitative, tied to a single parameter T, and testable within the solar system rather than at cosmological distance. The predicted ratios are fixed by theory and not adjustable: ω̇/ω : v̇/v : −ṙ/r = 3 : 1 : 2, so the pattern across planets is a signature, not a fit. Masreliez is also unusually clear-eyed about the methodological trap he is claiming to have found — that an ephemeris whose time argument is determined inside the fitting process cannot by construction reveal an acceleration common to all planets. That is a legitimate point about circularity in ephemeris construction, independent of whether the SEC is right. Similarly, the galaxy section is honest that its results follow from one postulate (constant mass flow at all radii) and shows the resulting curves against real data rather than in the abstract.

The difficulties are correspondingly concrete. The rotation-curve fits use three free parameters per galaxy and succeed on three of four selected curves; that is a fit, not a prediction, and the standard dark-matter halo does the same job with comparable freedom, so nothing is decided between them here. The dark-matter alternative offered — cool gas confined to the arms — is asserted rather than estimated, and it must contend with the fact that the halo evidence now rests on weak gravitational lensing and on the offset between lensing mass and X-ray gas in colliding clusters, neither of which is addressed. The planetary comparison in Table I is thinner than it appears: Venus and Earth agree well, but Mercury's predicted 5.77 falls outside the quoted 8.6 ± 3.0 only marginally while being 33% low, and three data points from a single analyst's residuals cannot carry the weight put on them, particularly since Masreliez himself notes that Kolesnik's characterisation of the residuals as quadratic came from personal communication rather than from Kolesnik's own published fit. An inward drift of 20 m/yr in the Earth's orbit is a strong claim to make while conceding that the corresponding ranging signature is "of the same size as the ranging uncertainties"; lunar laser ranging now measures the Earth–Moon distance to millimetre precision and planetary ranging to metres, and modern radio-science solutions bound anomalous secular changes in the astronomical unit far below what is required here.

There is also a tension internal to the paper's own logic. Drag is asserted to act on all relative motion but not on light; no mechanism is offered for the exemption beyond its being a property of the SEC metric, and it is precisely the exemption that generates the preferred frame. The pulsar argument is presented in a single paragraph with no numbers, though pulsar spin-down is conventionally accounted for by magnetic dipole braking with measured braking indices — a comparison the paper does not attempt. And the AGN thermalization of the CMB in Appendix 2 matches only a power budget; it says nothing about the observed blackbody fit to better than 10⁻⁴, about the isotropy, or about the acoustic structure of the anisotropies, all of which any thermalization scenario must reproduce.

Taken on its own terms, the paper does what it says: it extracts a definite, falsifiable consequence from a stated line element and points at data where it might show. Whether that data supports it is a question the paper answers more confidently than its evidence warrants.

See also

• C Johan Masreliez
• Apeiron
• Dark Matter
• Tired Light
• Steady State Theory
• Mach's Principle
• Cosmic Microwave Background
• Hubble Constant