Newton conceded his ‘pull’ was conjecture and based his law on a fortuitous correlation of inverse squares. No wonder it won’t fit into a unified theory, but there is an alternative that could.

A background note

Childhood illusions of sunrise and sunset are soon explained by the rotation of the Earth, but not so the illusion of a ‘pull’ of gravity to keep it in orbit. It is not a thing you can easily, or safely, experiment with, so Newton settled for a pull as an extension of Aristotle's `inherent tendency' of matter still current after two thousand years, making the idea a bit out of date. Advances in science may take a litle while to filter through, but this is absurd. Newton was eventually persuaded by Hooke of Galileo's argument for an outside force, but the theory stuck.

However, even while popular fascination with the unknown keeps the medieval notion of a pull alive, there is a move afoot to get us up to date by reviving the external force. Before the issue becomes clouded in mathematical wrangling over the small print, the physical argument for dumping an energyless pull needs an airing and, for the sake of science, the illusion dispelled.

The inverse square is not unique to the force of gravity. It crops up too in Kepler’s laws for elliptical orbits in planetary motion round the Sun, but they say nothing about why. But it was a Godsend as it enabled Newton to avoid ackowledging his debt to Hooke for his contribution, yet doing so obscured the crucial role of density in describing weight, which never appeared in his ‘law of gravity’. (The ‘rigorous scientific method’ requiring verification came about later.)

By ignoring the geometry of Hooke's version, Newton could adopt an analogy with a false notion of suction for his force, and scientists still naively quote it. A century and a half later a value was put on his co-efficient G, which incorporated Hooke's geometrical component for calculating relevant volume in combination with the inverse square. The other variable component for specific force was found empirically.

How it all started

Newton handed down his law in 1689, eight years after Hooke had used the reciprocal of the total area of a sphere to define the volume of two slender cones meeting at the centre as 2/3d², which can be recognised as a major element of the law. The mass within it depends on its density and a specific force of around 1 Nm per ten megatonnes applied across it yields a differential which is the force of gravity as given by the law. It gives no clue, however, to the strength of the gravitational field providing the force.

Hooke had solved Galileo's riddle from a century earlier by recognising that bodies in free fall were weightless. All Galileo had done was to ask whether two weights tied together would fall faster than either on their own, but it took far longer than he expected for ‘the penny to drop’ among the academics of his time and in generations to come. Logic is still no substitute for experimental verification.

Where the two theories differed was that Hooke’s `flux' passed clean through a body shedding a little of its energy on the way to account for a small differential in opposing forces. Newton's was much smaller, by many orders of magnitude, being totally absorbed in a body and dissipated from it in some unspecified way, simulating an illusory ‘pull’ of suction. Is that how people see it now? Crucially a weak force was an essential component of his calculations, allowing approximations to be made where convenient, so he was understandably reluctant to see his elaborately worked theory being so simply undermined.

Hooke’s theory scores by making gravity the equal and opposite reaction to ‘anti-gravity’, the cause of cosmic expansion, which is, like weight, a function of density and distance. There can be no danger, as some would have us believe, of similarly catastrophic results should either gravity or anti-gravity predominate. The greater likelihood is that both fail progressively as a critical density at the periphery can no longer support the release of energy needed for acceleration and cohesion. Now that would be a theme for science fiction!

Checking the maths

As yet inconclusive mathematical theories seek to resolve inconsistencies between the law and theory of gravity, yet Newton himself pioneered the technique of dimensional analysis which reveals the composite nature of the gravitational ‘constant’. It is compounded of a geometrical proportion of volume and a specific force applied to mass. There has to be an even distribution of density to convert volume to mass, as may be surmised for the Sun in the plane of the ecliptic, but not all over the Earth. Here elongation of its dense core along its polar axis upsets the calculation, and the Earth may not be alone in this. Other planets may have the same problem. An incidental result is that massive icebergs drifting towards the tropics (one nearly making it a few years ago but for grounding short of Rio) need no longer face a climb twenty kilometres high!

The nearest approach to a physical theory of gravity came from a nineteenth-century amalgam of Faraday’s conviction that inductance had a role in it, though he had the roles of electric and magnetic inductance reversed, and Bohr’s concern that Nature is too economical with its resources to squander the vast amount of energy in shoals of neutrinos hurtling about space in all directions. It could create a field in which gravity could manifest itself as a difference between opposing forces across massive bodies. A magnetic susceptibility is all that is needed for inductance among charged particles to create an effective ‘flux’, and that may occur in the nucleus with the decay of colliding pions.

Its multiple functions might include overriding the mutual repulsion of protons within the atomic nucleus, creating drag by distorting the orbits of electrons around it, and maintaining an electromagnetic field to act as carrier for radiation throughout space. The broad spectrum of background radiation may be evidence of it. There is a curious correlation between a plotted incidence of frequencies and the effects of gravity, the peak at 2.7K corresponding to that at the interface between weight and acceleration, so what significance could that have?

An algebraic correlation can be made between fields of gravitation and radiation, though without requiring equivalence. The energy involved in the process of magnetic inductance is given by E=HA², where H signifies inductance measured in henries, bearing a striking resemblance to Einstein’s E=mc² and implying a somewhat different interpretation of it from that usually given. Maxwell’s constant value of c was conditional, not absolute as Einstein proposed. Supposing the term c² to represent the exponential rate of expansion of a spherical wave of radiation (by analogy with the reciprocal of d² as a fraction of the surface area of a sphere), the specific energy required to keep it going in perpetuity is E⁄m.

Here m stands for the diffuse matter throughout space forming the vehicle for photons, radiating energy in a wave-form which can be manipulated in a number of ways, and continuously replenished by inductance from the output of nuclear fusion in myriads of stars, which cannot. This is the essential difference between them. The initial impulse setting off the radiation need take no further part in its spread, and the interdependence of matter and energy is conserved with no conversion between them.

Physical reality

A weak force of gravity is the result of a marginal imbalance between opposing forces. Conversely, a powerful local boost offsetting this drop, as in proximity to the Sun, could cause a momentary radial burst of speed of radiation to account for the early reappearance of a star from behind the Sun observed during the 1919 solar eclipse. It offers a more plausible explanation than ‘curvature of space’, particularly as it was substantially less than Einstein’s prediction. When Sir Arthur Eddington, who had given qualified support to the theory after making the observation, was asked to comment on the claim that only three people in the world understood the theory, it is said he was silent for a while before replying he had been trying to think who the third person might be!

Feynman gave a series of lectures on the theme that there were many times more theories in physics than demonstrable facts, which he illustrated by occasional reference to that of a gravitational pull. Many others besides him have had major reservations about its soundness, not least Newton himself. Theories continue to proliferate, all trying to confine natural forces within a set of mathematical laws, when it has long been clear they represent a statistical balance between alternative stable states of elementary particles in unstable equilibrium, allowing for the proverbial random input from a butterfly’s wings.

The self-limiting balance may be the product of a widespread interaction of inverse-square ratios among forces, in which none can ever reduce to zero or approach infinity, as it might then be either overwhelming or irrecoverable. Laws given by a ‘Great Architect’ turn out to be trends instituted by a Supreme Actuary, and they call for an altogether more sophisticated mathematical treatment which few if any would comprehend. Newton may have had a point in claiming that if he couldn’t explain the force of gravity it was ‘probably beyond the wit of man’!

Scientists, treating laws as axiomatic and relaying them with a quasi-religious zeal as dogma, should heed the advice (given in extravagant hyperbole for added emphasis) to remove the log from their own eye before presuming to pour scorn on others’ dogma as the speck in their’s. The credibility of physics depends on forgoing belief like some secular religion in mystical forces belonging to a world of make-believe.

A convincing physical explanation can’t come soon enough. The mathematics of it can follow at leisure.