Velocity-Dependent Inertial Induction: A Possible Tired-Light Mechanism
| Scientific Paper | |
|---|---|
| Title | Velocity-Dependent Inertial Induction: A Possible Tired-Light Mechanism |
| Read in full | Link to paper |
| Author(s) | Amitabha Ghosh |
| Keywords | inertial induction model, tired-light, redshift, cosmology, Mach's Principle, cosmic drag |
| Published | 1991 |
| Journal | Apeiron |
| Volume | 1 |
| Number | 9-10 |
| No. of pages | 25 |
| Pages | 95-119 |
Read the full paper here
Abstract
The tired-light interpretation of the cosmological redshift is as old as the discovery of the phenomenon itself, and a number of mechanisms have been proposed by researchers in cosmology. This article presents the basic ideas behind the author's recent proposal of an inertial induction model consisting of both velocity- and acceleration-dependent terms which can explain the cosmological redshift both quantitatively and qualitatively. A major difficulty with the various tired-light mechanisms is that no other reliable experimental verification of the proposed theories is possible, whereas the velocity-dependent inertial induction gives rise to a number of detectable astrophysical and astronomical phenomena. A few of these have been studied, and it has been shown that the predicted effects do exist.
Overview
Amitabha Ghosh, then in the Mechanical Engineering Department at IIT Kanpur, published this review in Apeiron in 1991 as a summary of a programme he had been developing since 1984. Its starting point is Mach's Principle in the quantitative form Dennis Sciama gave it: that the inertial resistance of a body is not intrinsic but is the gravitational interaction of that body with all the rest of the matter in the universe, expressed as an acceleration-dependent term added to the ordinary inverse-square attraction. Ghosh's move is to ask why the interaction should be confined to acceleration. He proposes that the same reasoning admits a velocity-dependent term as well, so that a body moving uniformly with respect to the mean rest frame of a quasi-static universe experiences a small universal drag.
The consequence he is chiefly interested in is that photons are subject to this drag, losing energy exponentially with distance travelled and so producing a cosmological redshift in a static universe — a tired-light mechanism. Ghosh's explicit claim for his version is methodological: unlike the many tired-light schemes tabulated in his opening section, this one is not a single-purpose hypothesis. The same drag coefficient, fixed once by the mean density of the universe, is applied without further adjustment to the secular slowdown of the Earth's rotation, the secular acceleration of Phobos, the excess redshift at the solar limb, the redshift of radio signals grazing the Sun, the flatness of spiral galaxy rotation curves, the transfer of the Sun's angular momentum, and the relaxation time of globular clusters. This departs from the standard account on two fronts at once: it removes the need for cosmic expansion and hence for the Big Bang, and it replaces the Equivalence Principle with a derivation.
The argument
From Sciama's inertial induction to a velocity term
Ghosh sets the historical frame briefly — Newton's absolute space, Berkeley's objection thirty years after the Principia, Mach's 1872 proposal that inertia depends on the presence of other matter — and notes that Mach's principle lacked a quantitative model until Sciama (1961, 1969). In Sciama's scheme the interaction between masses m1 and m2 at separation r contains, beyond Gm1m2/r2, a term Gm1m2a/c2r, so that resistance to acceleration against the whole universe is
- F = ma Σuniverse Gm2/c2r.
Sciama showed the sum is of order unity for the estimated mean density and observable radius, which makes the inertial law a manifestation of acceleration-dependent gravitational interaction and dispenses with the equivalence principle as a separate postulate — there being only one kind of interaction. Ghosh accepts this but presses the objection that Sciama cannot say why the sum should be exactly unity rather than merely of order unity; on his account it is "perhaps only by chance".
His proposed interaction between two particles is
- F = −(GmAmB/r2)ur − (GmAmBv2/c2r2) f(θ) uv − (GmAmBa/c2r) f(φ) ua,
where θ and φ are the angles between the position unit vector and the velocity and acceleration directions respectively, and f(θ), f(φ) are inclination factors. The first term is the static one, the third is Sciama's, and the second is the new velocity-dependent inertial induction. Ghosh notes the masses are strictly relativistic gravitational masses, negligible except near c, and that "little attention has been paid to the possibility of a velocity-dependent term, perhaps because of the fact that such a velocity-dependent drag is practically undetectable."
Fixing the drag coefficient self-consistently
Integrating the interaction of one particle with an infinite, homogeneous, quasi-static universe kills the static term by symmetry and leaves velocity- and acceleration-dependent resultants. To make the integrals converge Ghosh introduces a second assumption: that G is not constant but is proportional to the energy of the particles that transport the gravitational effect, and that these gravitons are themselves subject to the same drag. Writing the velocity resultant as −(k/c)mv uv, a graviton of energy E moving at c loses energy as dE/E = −(k/c) dr, giving
- E = E0 exp(−kr/c), and hence G = G0 exp(−kr/c).
Substituting this exponentially screened G back into the integrals produces k = G0χρc/k, i.e.
- k = (G0χρ)1/2,
and the total inertial-induction force becomes
- F = −(k/c)mv uv − ma ua.
This is the paper's most elegant result: the acceleration term comes out identically equal to −ma, with coefficient exactly one and no dependence on the density or the horizon radius, so "the exact equivalence of gravitational and inertial masses is explained" without the coincidence Sciama's version requires. Taking f(θ) = cos θ |cos θ| and f(φ) = cos φ |cos φ| gives χ = π, and with ρ = 7 × 10−27 kg/m3,
- k = 1.21 × 10−18 s−1.
Ghosh notes an asymmetry in where the two effects matter: velocity-dependent induction is dominated by local interaction near massive bodies, while acceleration-dependent induction is dominated by the universe as a whole.
The redshift
For a photon of energy E = hν the drag is −kE/c, so dE/E = −(k/c) dx and
- ν/ν0 = exp(−kx/c),
which for kx/c ≪ 1 linearises to Δλ/λ0 ≈ kx/c. Redshift is therefore proportional to distance in a stationary universe, and k is identified with the Hubble constant, whose estimated value Ghosh gives as approximately 1.6 × 10−18 s−1 — "very close to the calculated value of k". He notes two further qualitative agreements: the shift is proportional to wavelength and departs from linearity at large z, as observed; and because the drag is stronger where matter is denser, redshift should be enhanced along lines of sight through matter concentrations, which he attributes to Karoji and Nottale (1976). He also observes that the same universal induction gives a mechanism by which linear and angular momentum of moving systems is transferred to the rest of the universe.
Local tests
The bulk of the paper is a list of independent applications of the same coefficient.
Earth's spin-down. Tidal friction is the accepted explanation of the observed Ω̇ ≈ −6 × 10−22 rad s−2, but the torque required implies the Moon recedes at ṘM ≈ 1.3 × 10−9 m s−1, which traced backwards puts the Moon destructively close to the Earth about 1,300 million years ago — while the geological record shows no such catastrophe over 3,500 million years and shows tidal phenomena throughout. Ghosh's analysis of the Sun–Earth–Moon system gives a resisting torque of 4.75 × 1016 N·m from the Earth's spin, accounting for Ω̇ ≈ −5.5 × 10−22 rad s−2 and leaving only a small residue for tidal friction; on this account the Moon's distance is presently decreasing at −0.15 × 10−9 m s−1, dissolving the close-approach problem. "A prediction of almost the exact amount of required drag torque by the inertial induction model cannot be pure chance!"
Phobos. Phobos is observed to be accelerating in its orbit at 10−3 deg yr−2, difficult to explain on a Mars with no oceans. The model applied to the Sun–Mars–Phobos system yields 26.5 × 10−21 rad s−2, i.e. 1.5 × 10−3 deg yr−2, the residual difference attributed to neglected inclination effects and to assuming a terrestrial radial density profile for Mars.
Solar limb redshift. A photon leaving the solar surface at angle θ suffers, from gravity plus velocity-dependent drag,
- Δλ/λ ≈ (GMS/c2rS)[1 − (2/3) sin2θ],
which combined with granulation motions gives an equivalent recession velocity veq ≈ 0.636[1 − (2/3) sin2θ] − cos θ − 0.2 sin θ km s−1. Ghosh's point is that the observed limb redshift substantially exceeds GMS/c2rS, which granulation alone cannot supply.
Grazing photons. On the standard account the blueshift of approach cancels the redshift of recession for a photon passing a mass, leaving nothing. With drag, Ghosh obtains a residual
- Δλ/λ ≈ exp[(4/3)GM/c2r] − 1,
tabulated as 2.69 × 10−8 for Jupiter, 2.83 × 10−6 for a typical star, 2.26 × 10−4 for a white dwarf, 0.492 for a neutron star and 0.95 at a Schwarzschild radius. He cites two anomalies as support: Sadeh, Knowles and Yaplee's (1968) report of a 150 Hz shift in the 21 cm signal from Taurus A at five solar radii from occultation, and the unexplained redshift of order 10−7 in the 2292 MHz Pioneer-6 signal as it passed behind the Sun (Merat, Pecker and Vigier 1974), which was symmetric on both sides of the disc. He proposes deliberate grazing experiments as the cleanest direct test.
Flat rotation curves. Ghosh observes that a flat rotation curve requires a specific radial mass distribution, and that since flatness is universal among spirals "there must exist a servomechanism which distributes matter according to the required unique pattern". Applied to a self-gravitating rotating disc, velocity-dependent induction gives equilibrium when a star both satisfies a slightly modified Kepler law and has the inward pull of matter inside its orbit balanced by the drag from matter outside it — a condition he and co-workers showed (Ghosh, Rai and Gupta 1988) leads to nearly constant orbital velocity. "Until now no other acceptable servomechanism has been identified."
Solar angular momentum and globular clusters. The nebular hypothesis requires a mechanism to move angular momentum from the Sun to the planets, and the usual candidates act only during the short (~2 × 107 yr) pre-main-sequence phase. Induction acts throughout the main sequence; with L = 1044 kg m2 s−1 and a dislodged fragment of 0.023 MS, Ghosh's expression gives lS ≈ 1.4 × 1041 kg m2 s−1 at t = 4.7 × 109 yr, close to the Sun's present value, and predicts that newly born stars should be fast rotators — as observed — and that satellite systems should likewise hold most of their system's angular momentum. Finally, the anomalously long relaxation time of globular clusters drops to ~1017 s when the drag is included.
Assessment
The paper's genuine strength is structural rather than rhetorical, and Ghosh identifies it correctly: most tired-light proposals are unfalsifiable in practice because the photon-energy-loss law is their only observable consequence, whereas here a single coefficient k, fixed by ρ and G, is required to do work in seven unrelated places. That is the right shape for a physical hypothesis, and it is a fair criticism of the field that this discipline is rare. The self-consistency argument that gives k = (G0χρ)1/2 is the most interesting technical step in the paper, because it converts Sciama's numerical coincidence into an identity: the coefficient of the acceleration term comes out exactly −1, so the equivalence of inertial and gravitational mass is derived rather than postulated. Whatever one thinks of the premises, that is a real result within the model, and Ghosh is right that Sciama's version leaves the unity unexplained. The Earth–Moon argument is also better posed than it is usually given credit for: the lunar recession rate really does extrapolate to an uncomfortably close encounter well within the geological record, and this remains a live problem in tidal-evolution modelling.
The difficulties are substantial. Two of the model's central steps are assumed rather than derived. The inclination functions f(θ) = cos θ |cos θ| and f(φ) = cos φ |cos φ| are introduced "for the purpose of numerical computation" with no argument from any principle, yet they set χ = π and so directly set the value of k that the whole paper then compares with the Hubble constant; a different plausible choice would give a different k and the agreement would evaporate. Likewise the assumption that G is proportional to graviton energy, and that gravitons suffer the same drag, is what makes the integrals converge at all; the paper offers no independent motivation for it, and it amounts to an exponentially screened gravity whose consequences for solar-system dynamics — where G0 is measured to high precision — are never checked. The self-consistency loop is also worth noting: the first term is "assumed to be equal to" −(k/c)mv before k is solved for, so the derivation fixes a coefficient it has already presupposed the form of.
The numerical agreements are looser than the prose suggests. The computed k = 1.21 × 10−18 s−1 is compared with a Hubble constant of "approximately 1.6 × 10−18 s−1" — a 25 per cent discrepancy, presented as "very close" — and it depends on a mean density ρ = 7 × 10−27 kg/m3 which is itself uncertain by more than that factor and which the model does not predict. The Phobos figure of 1.5 × 10−3 deg yr−2 against an observed 10−3 is a 50 per cent overshoot, described as "surprisingly close". And the Earth–Moon result is in direct conflict with measurement in a way the paper does not confront: lunar laser ranging, operating since 1969 and by 1991 already accurate to centimetres, measures the Moon's recession at +3.8 cm yr−1, or +1.2 × 10−9 m s−1. Ghosh's model predicts −0.15 × 10−9 m s−1 — the wrong sign. This is the paper's clearest empirical failure, and it is the one place where the drag term makes a prediction that a direct, unambiguous measurement had already contradicted at the time of writing.
Two further conflicts with established measurement should be recorded, both post-dating the paper but bearing on the programme. Tired-light mechanisms generically predict no time dilation of distant transient sources, whereas the light curves of Type Ia supernovae are observed to be broadened by exactly the factor (1 + z), a result established from the mid-1990s onward and now measured to z > 1. Ghosh's mechanism attenuates photon energy along the path and offers no way to stretch the arrival times of a light curve. Second, a drag that removes energy from photons must deposit it somewhere; unless the deposition is precisely thermalised, the mechanism should blur distant images and distort the blackbody spectrum of the microwave background, which COBE's FIRAS measurement (1990–1996) constrains to better than 5 parts in 105. The paper does not address either issue, and neither is a peripheral matter for a static-universe cosmology.
The rotation-curve argument deserves separate comment because it is the most interesting and the most slippery. Ghosh is right that flatness is near-universal and that this cries out for a mechanism rather than a coincidence of initial conditions — that is the same instinct that motivates modified-dynamics approaches, and it is a better instinct than the paper's critics usually allow. But his equilibrium condition, that inward pull from interior mass is balanced by drag from exterior mass, is a statement about a steady state whose stability is not examined, and the balance is stated to "invariably" give constant velocity on the authority of an earlier paper rather than shown here. Nor is any galaxy's observed curve fitted; the reader is given a schematic figure. As with much of the paper, the claim is plausible in outline and unverifiable as presented.
What survives is a programme rather than a result: a Machian gravity with a velocity term, one free coefficient, and a genuinely admirable willingness to be tested in many places at once. Ghosh's own closing suggestion — measure the extra redshift when starlight grazes a planet or satellite — is exactly the right proposal, and it is to his credit that he names a decisive experiment rather than resting on the accumulated approximate agreements.