Action-at-a-Distance and Local Action in Gravitation
| Scientific Paper | |
|---|---|
| Title | Action-at-a-Distance and Local Action in Gravitation |
| Read in full | Link to paper |
| Author(s) | Toivo Jaakkola |
| Keywords | Action-at-a-Distance, Local Action, Gravitation |
| Published | 2007 |
Read the full paper here
Abstract
A new theoretical framework is presented by giving a summary of equilibrium cosmology (EC) recently developed by the author. In EC, gravitation is an equilibrium process providing energy balance in systems of baryonic matter, while electromagnetic radiation is the contrary effect. Gravitation on a body is a pressure effect of gravitational quanta (gravitons) conducted from the background field by the gravitation field of the body. The formation of the field is outlined. Gravitons and photons interact via electrogravitational coupling (EGC), which causes the redshift effect and an analogous weakening of gravity, as well as the cosmic background radiation which is a re-emission equilibrium effect. From pressure-induced gravitation and EGC, a dynamical theory (EGD) can be constructed which unifies the gravitation effects in systems on different scales; until now, numerous ad hoc hypotheses had been necessary to explain the effects.
When EGD is applied to the two-body problem, Newton's law is obtained directly. In it the force is a sum of two equal terms which are due to the two fields of graviton flow into the bodies, which are mutually screened by the second body. While gravitation is basically not an attractive but rather a repulsive pressure force, the two-body attraction results from the screening effect. The dilemma of a distant action versus a local action character of gravitation receives a simple but unexpected solution: both are true. While the momentum due to the pressure of gravitons flowing towards the second body has a distinctly local character, the momentum obtained due to the screening of the body's own field by the second body is an action at the distance of that body. Both are expressions of a single interaction between the mass systems and the background field.
Overview
The paper appeared in Apeiron Vol. 3 Nr. 3–4 (July–October 1996), written by the Finnish astronomer Toivo Jaakkola of Tuorla Observatory, University of Turku. Its full title is "Action-at-a-Distance and Local Action in Gravitation: Discussion and Possible Solution of the Dilemma," and it is part historical essay, part critique of general relativity, and part exposition of Jaakkola's own equilibrium cosmology. He organises the whole subject around three mutually exclusive answers to the question of how gravity acts: action-at-a-distance (AAAD), relativistic local action (RLA), and material field local action (MFLA). The first depends only on separation and its time derivatives with no reference to any medium; the second works through a metric field determined by the matter distribution; the third works through a material medium.
Jaakkola's thesis is that MFLA is correct, that AAAD and RLA are both untenable in their usual forms, and — the twist he says surprised him as much as the reader — that when Newton's law is derived from the MFLA picture it splits into two equal terms, one of which is genuinely local and the other genuinely a distant action. The dilemma is therefore dissolved rather than decided. He writes the paper deliberately as a detective story, calling gravitation "a three-pipe problem," and closes by describing AAAD and RLA as "two ghosts fighting about which of them is real."
The argument
Newton was not a Newtonian
The historical section makes a point Jaakkola thinks has damaged physics: Newton did not believe gravitation was action at a distance. He quotes the 1693 letter to Bentley calling such action "so great an absurdity that I believe no man who has in philosophical matters any competent faculty of thinking can ever fall into it," and notes that of 108 occurrences of "attraction" in the Principia, ninety are in the mathematical books, and that Newton warned he was "using familiar language so as to be more easily understood by mathematical readers." Newton's own preference was for an æther of variable density, and he suggested that what are called attractions "might more truly be called impulses." Jaakkola attributes the misattribution to Cotes's preface to the second edition. He assembles the hostile verdicts of Leibniz ("inexplicable, unintelligible, precarious, groundless and unexampled") and of Ernst Mach, who observed that Newtonian gravitation "no longer disturbs anybody: it has become common unintelligibility."
Velocity-dependent theories are really field theories
A section reviews the Weber school — Gauss (1835), Wilhelm Weber (1846), Riemann, Clausius, Gerber, Walter Ritz — and their gravitational analogues, writing the Weber-type law as F = −Gm1m2/r2 multiplied by a bracket containing (dr/dt)2/h and 2r(d2r/dt2)/h, which reduces to Weber's generalisation of Coulomb's law when h = c2. He surveys modern successors: Surdin's æther-based Weber theory, Andre K T Assis's Machian Weber potential (perihelia, Hubble's law, Olbers' paradox, the CBR, gravitational absorption), and Amitabha Ghosh's velocity-dependent inertial induction, which adds rather than subtracts terms and accounts for the Earth's secular spin retardation without a catastrophically close early Moon, the Phobos acceleration anomaly, and solar centre-to-limb redshift.
His distinctive claim is classificatory: these theories are conventionally filed under AAAD, but in pure AAAD there is "no rationale for the higher-order terms," nor indeed for the inverse square itself — "in place of F ∝ 1/r2 any other distance law could apply." Velocity dependence presupposes something with respect to which velocity is measured, so the Weber tradition belongs, on Jaakkola's reading, to MFLA.
Against relativistic local action
Conceptually, Jaakkola objects that general relativity re-absolutises space by absolutising one kind of motion, that of light: when light bends near the Sun space is said to curve, when it is delayed time is said to slow. He offers the parallel that if time were defined by terrestrial rotation, a large earthquake "would shake the whole Universe." Empirically he presses four points. The solar centre-to-limb redshift variation is not predicted by relativity at all, which gives a constant z = 2.12 × 10−8 across the disk; limb values exceed the prediction; redshifts appear symmetrically before and after occultation, as in the Taurus A 21 cm line and the Pioneer-6 2292 MHz signal, which at three solar radii showed z ≈ 5 × 10−8. All of this, he argues, is a redshift–distance effect, tying the solar case to the cosmological one. On light deflection he grants that data beyond five solar radii fit the 1.75 arcsec prediction but reports a 10% excess in some 200 closer optical deflections at the 4σ level. On Mercury he concedes GR predicts 43 arcsec per century well, while questioning whether an exact fit requiring perfect solar sphericity supports or embarrasses the theory.
The cosmological tests are his own specialty. Compiling published determinations of the deceleration parameter, he finds Hubble diagrams giving q0 = +0.93 ± 0.19 (closed), local density estimates q0 = +0.03 ± 0.08 (open), optical angular-diameter tests q0 = −0.9 ± 0.2, and radio angular-diameter relations falling outside the relativistic range entirely, with no sign anywhere of the predicted minimum in angular size near z ≈ 1. He calls the internal inconsistency "as bad as it could be" and the proliferation of evolution models a set of "epicycles" exceeding the Ptolemaic count.
Equilibrium cosmology, gravitons and electrogravitational coupling
The constructive part rests on the claim, argued in Jaakkola's earlier papers, that redshift is not Doppler but an interaction effect whose strength goes as the square root of density, supported by Arp's intrinsic quasar redshifts and Tifft's quantization. The universe is then not merely static but in equilibrium, indicated most directly by the blackbody spectrum of the cosmic background radiation — "precisely an equilibrium spectrum."
In this framework gravitation is carried by gravitons that form a gravitational æther paralleling the electromagnetic one, with a homogeneous cosmological component (a cosmic background gravitation, CBG) and localised components bound to hierarchically organised mass systems. Gravity on a body is the pressure of gravitons flowing in from the background, conducted by the body's own field — "pressure-induced gravitation" (PIG). Graviton–photon interaction, "electrogravitational coupling" (EGC), produces the redshift and an exponential weakening of gravity, with absorption coefficient α(r) whose cosmological value is αc = H/c. Energy conservation ties the strength of gravitation to it by G(r)α(r) = A, with A ≈ 4.22 × 10−35 cm2 g−1 s−2, giving a generalised force law a(r) = G(r)M(r)e−α(r)r/r2. Integrating over a uniform density yields a finite cosmic acceleration ac = Gcρc/αc, about 1.1 × 10−8 cm s−2 for ρc = 10−30 g cm−3, which he presents as an explicit formulation of Mach's Principle and as the resolution of the Seeliger–Neumann gravity paradox. Because G ∝ 1/α ∝ r on galactic scales, the law degenerates to F ∝ 1/r, which he offers as flat rotation curves without dark matter.
The two-body derivation and the dual solution
The key calculation is elementary. Two spheres B1, B2 of masses m1, m2 and radii R1, R2 sit at separation r. B2 blocks a fraction A2/2π of the graviton inflow onto B1, where A2 = πR22/r2, giving a net momentum change S1 = η1m2A2/2π; symmetrically S2 = η2m1A1/2π. Identifying the absorption coefficients with surface gravity, ηi = Gmi/Ri2, the two terms are each Gm1m2/2r2 and sum to Newton's law. Three consequences are drawn. The interaction is not direct: "the link runs via the Universe external to the system." The inverse square is no longer brute experience but geometry — the solid angle of the screening body times the 1/r2 falloff of inflow density. And the two equal terms differ in kind: S2 is a local push from the second body's field, while S1 is the shadow the second body casts on the first body's own inflow, which is action at that body's distance. Hence both answers to the centuries-old dilemma are true.
Jaakkola proposes tests: eclipse anomalies (Saxl and Allen's 1970 torsion pendulum, Newcomb's lunar longitude fluctuations, Majorana's absorption experiments) for the shadow term, and diurnal, monthly and annual variation of surface gravity for the pushing term. He also treats the Sagnac effect, Michelson–Gale, and satellite Sagnac experiments as evidence for an æther bound to the Earth.
Assessment
The historical scholarship is the strongest part and is not merely decorative. Jaakkola's demonstration that Newton rejected action at a distance, with the Bentley letter and the counted usages of "attraction," is accurate and well sourced (Cohen, North, Roseveare, Pais), and his argument that pure AAAD leaves both the inverse square and the higher-order Weber terms without rationale is a real conceptual point rather than rhetoric. The two-body derivation is genuinely elegant: from one assumption — that gravitons flow in proportional to mass and are absorbed with efficiency equal to surface gravity — the inverse-square law falls out geometrically, and Newton's third law is exactly satisfied term by term, which he correctly notes is a difficulty for field theories generally. The split of F into a pushing and a shadow term is a substantive claim because it is in principle testable through eclipse and screening experiments, and he says so.
The difficulties are serious and largely of the kind the paper does not confront. The identification η = GM/R2 is asserted, not derived; it is exactly the step that makes the answer come out Newtonian, and no independent account of graviton absorption fixes it. More damaging, the derivation makes gravity depend on R22/r2 — the geometric cross-section of the screening body — and only cancels because η1 carries a compensating 1/R12. This is the standard shadow-gravity problem that has dogged the tradition since Le Sage: bodies must be effectively transparent for mass proportionality to hold, yet effectively opaque for screening to produce the force, and Jaakkola never reconciles the two. Nor does he address the classical drag and heating objections, which he explicitly sets aside ("I leave the question here") after invoking Ghosh's results as a reinterpretation of drag.
The internal numbers are also uneven. Gc ≈ 10 G0 is inferred from redshift observations via the field equation Gα = A, but the same equation with the locally measured G0 and αc = H/c is what fixes A, so the factor of ten is a consistency requirement of the scheme rather than an independent result. The graviton velocity is left unspecified: at one point vg may satisfy Laplace's vg > 108c via Wesley's relation, at another it "may be of the order of c," and at another the screening effect is simply "instantaneous." A theory whose central claim is about the locality of the action ought to settle this.
Against measurement, the exposed claims are cosmological. The redshift-as-interaction reading must explain the (1+z) stretching of Type Ia supernova light curves, which is a timing effect no absorption mechanism naturally produces, and must avoid the image blurring that any photon–graviton scattering with a change of direction would cause — quasar imaging constrains this severely. His CBR argument, that a blackbody spectrum is "precisely an equilibrium spectrum," proves less than he needs: thermalisation in a static medium is exactly what is hard to arrange over cosmological path lengths without destroying the spectrum, and the observed anisotropy power spectrum, unavailable in 1996, is now a further constraint that equilibrium cosmology has not addressed. The deceleration-parameter table on which he rests the "empirical inconsistency" of standard cosmology reflects 1970s data with error bars that later work substantially revised. His reading of Hafele–Keating — that the westbound clock ran fast and that special relativity forbids direction dependence — omits the rotating-frame and gravitational-potential terms that the experiment was designed to include, and this is the weakest empirical passage in the paper.
Read as a programme rather than a finished theory, however, the paper is candid about its own status. Jaakkola says outright that the historical aim was not well fulfilled, that the actual form of the shadow term "is not known," and that "the way ahead will be shown by experiment and observation." He also declines the triumphalism common in this literature, calling general relativity "historically a completely justified and respectable theory" and "the best formulated theory yet presented" even while rejecting it. That combination of a concrete mechanical derivation with an explicit list of experiments that could refute it is what gives the paper its continuing interest.