The Unification of Macroscopic Physics

Scientific Paper
Title	The Unification of Macroscopic Physics
Read in full	Link to paper
Author(s)	Burniston Brown
Keywords	action-at-a-distance, retarded action, inertia, Mach's principle, electrodynamics, gravitation, relativity
Published	1958
Journal	Science Progress
Volume	46
No. of pages	15
Pages	15-29

Read the full paper here

Abstract

The ancient Greek atomists maintained that forces between bodies could only be communicated by pressure or impact, a view that was supported by Aristotle and St. Thomas Aquinas: it appears in the scholastic axiom that C matter cannot act where it is not. Duns Scotus and his followers did not agree; William of Ockham using his Razor to out any intermediate actions which were unobservable and saying that there was no reason to object to action-at-a-distance.

Overview

This is G. Burniston Brown's programmatic statement of a physics built on retarded action-at-a-distance rather than on fields, on an aether or on the postulates of relativity. Brown takes as his motto Newton's remark that "the whole burden of philosophy seems to consist in this — from the phenomena of motions to investigate the forces of Nature and then from these forces to demonstrate the other phenomena," and he means it methodologically: one starts from a physical picture of matter, extracts a force law from experiment, and then deduces the remaining phenomena. He explicitly refuses the opposite procedure, which he attributes to relativity theory, of beginning from postulates about what moving observers measure.

The physical picture is austere. All "stuff" is composed of unchangeable interacting material particles; all change is motion, never generation or annihilation; force is the cause of motion and matter is the cause of force. The theory is restricted to scales large enough that quantum considerations can be set aside — hence "macroscopic." Brown argues that the ether must go (the Michelson–Morley null result, together with Lodge's demonstration that light speed is not appreciably affected by the motion of nearby matter, leaves no room for a dragged ether), and that ballistic or emission transmission must go too, on the strength of Majorana's experiments, which he reads as showing that the interaction time is independent of the relative motion of source and receiver. What remains is action-at-a-distance — but not the instantaneous kind. The unification promised in the title is then the claim that gravitation and electrodynamics obey force laws of the same form, differing only in the substitution of −mm′ for qq′.

The argument

The law of retarded action

Brown lays down one physical hypothesis: all macroscopic action-at-a-distance has the same retardation constant c. From this follows his "law of retarded action" — every particle in the universe is continually acting on every other, but a particle at time t can affect a particle at distance r only at the later time t + r/c. He is careful to call c the retardation constant rather than the velocity of light, since on his view nothing travels: "the oscillatory forces of light do not pass through holes any more than the steady forces of gravitation do." Talk of rays, of light "passing through" an aperture, of something occupying successive intermediate positions, he dismisses as "thing-language" — a habit of ordinary speech that has been mistaken for physics.

To this he adds a principle of physical relativity: every particle acts on every other with a force depending only on the particles themselves (measured by mass and charge), their relative separation and motion, and the constant c. Superposition and the parallelogram of forces are carried over from Newton and Galileo as experimentally confirmed, and extended to cover relative motion and retardation.

Building the force formula from experiment

Because electrical forces vastly exceed gravitational ones and can be measured accurately, Brown derives the extra terms empirically from electrodynamics and then transfers them to gravity. The velocity terms come from Ampère's force law between current elements, converted to charges by way of Rowland and Hutchinson's result that a moving charge produces the same magnetic effect as a current when qv replaces i ds. The acceleration terms he takes not from induction experiments but from radio: at a large distance from a transmitting aerial every part of the aerial is effectively equidistant, so retardation only shifts the phase, and the induced force yields directly the acceleration contribution. Taylor's theorem then extends the result to the near field.

The outcome is an extended Coulomb force containing the electrostatic term, velocity terms in v²/c² (resolved along the line of centres and along the direction in question), and acceleration terms in f/c². An undetermined constant K appears, because any contribution that integrates to zero round a closed circuit is compatible with Ampère's experiments. Brown's first consistency check is that the velocity terms and the acceleration terms independently reproduce e.m.f. = −∂N/∂t, Neumann's formulation of Faraday's induction law — the first case for uniformly moving circuits with steady currents, the second for circuits at rest with changing currents.

The origin of inertia

The most striking section takes up Berkeley's suggestion, examined by Newton and later by Mach. Substituting −mm′ for qq′ gives the gravitational force between two moving particles, but a force law alone says nothing about the resulting motion. Brown therefore asks what a roughly uniform spherical distribution of surrounding matter — which is what observation shows — does to a particle near its centre. For uniform velocity the extra force integrates to zero at the centre and is negligible over most of the interior: hence no resistance to steady motion, which is Newton's First Law recovered rather than assumed. For acceleration f the surrounding universe exerts a force opposed to f and proportional to it, of the form (4/3)πρR²mf / c², where ρ is the mean density of matter and R the observationally estimated radius of the universe. Writing the coefficient of m as the "inertial mass" reproduces F = m_if, Newton's Second Law, as a derived result. The Third Law follows from force being mutual, existing only between two particles — "a force 'at a point in space' is a pure conception with no experimental evidence." Brown also gives the small position-dependent corrections for a particle displaced a distance ρ from the centre, radial and tangential, and notes they are unobservable locally. He offers a quantitative check: the relation fixes a mean cosmic density from G and R, and reports that the number agrees with contemporary estimates.

Perihelia, momentum and energy

The constant K is fixed here. Applying the extended gravitational formula to a planetary orbit gives a perihelion rotation per revolution that, for K = −3, coincides with the expression Gerber obtained in 1898 from a retarded gravitational potential propagating at c, and with Einstein's 1916 result — in good agreement with Mercury.

For collisions Brown reduces the formula to the radial case and argues that near molecular separations the acceleration term is negligible, leaving E = (qq′/r²)(1 − ½v²/c²). If one insists on charging the velocity dependence to the mass rather than to the interaction — as, he says, relativity does — one recovers, within present accuracy, the familiar momentum expression with the factor (1 − v²/c²)^−1/2. The same manoeuvre applied to the gravitational force between a particle at rest and one given velocity v converts the bracket into an apparent change of mass equal to the kinetic energy divided by c². He stresses that the ambiguity of which mass carries the bracket is precisely why he prefers to say the force changes: the force is mutual, so no decision about who is moving — and no reference frame, and no observer — need enter.

Assessment

The distinctive thing here is the direction of explanation. Brown does not postulate inertia and then look for its cause; he writes down a force law calibrated on laboratory electrodynamics, applies it to the observed matter distribution, and gets Newton's three laws out as consequences. That is a genuinely ambitious realisation of Mach's principle — closer in spirit to a calculation than to a slogan — and it is done with an economy of hypotheses: one retardation constant, one similarity assumption between gravity and electrodynamics, one undetermined coefficient. His insistence that c is a retardation constant rather than a speed of something, and his diagnosis of "thing-language" as a source of physical confusion, are sharp philosophical points that survive independently of the formalism. The recovery of Neumann's induction law from the velocity and acceleration terms separately is a real internal check, not a rhetorical one.

The difficulties are also real. The unification rests on an assumption Brown himself flags as chosen "based on simplicity" — that gravitational and electrodynamic forces vary identically with relative motion — and nothing in the paper independently tests it; the whole gravitational sector is an extrapolation from electrical experiments. The constant K is not determined by the theory: it is fixed at −3 precisely because that reproduces the Mercury perihelion, and Brown candidly admits no other phenomenon is available to check it. Fitting one datum with one free parameter is weaker than a prediction, and it makes the perihelion agreement a calibration rather than a success. The velocity terms are derived from conduction experiments where drift velocities are minute, so their extension to relativistic electrons is an extrapolation of many orders of magnitude; Brown concedes that experimental accuracy cannot then distinguish his formula from one containing higher powers of v². The inertia calculation depends on a mean density and a radius of the universe that were, in 1958, uncertain by orders of magnitude, so the "agreement with present estimates" carries little weight.

Against measurement, the paper's own conclusion lists the damage. Only the perihelion advance is claimed as satisfactory. The solar limb redshift gets "a value of the right order" from increased inertia near a large body, but Brown calls it unresolved. On light bending he is uncompromising: on an action-at-a-distance theory no bending in free space can occur, and the observed grazing-incidence deflection is attributed to terrestrial and coronal matter — an attribution the paper does not calculate, and one that later measurements of radio-source deflection and of gravitational lensing by galaxies and clusters, far from any solar corona, make very hard to sustain. His closing suggestion that relative velocities greater than c may occur, supported by the transit of cosmic-ray secondaries through the atmosphere, is the weakest passage: that is the classic muon-lifetime observation, and the time dilation reading of it has since been confirmed directly by the storage-ring measurements of muon lifetime at known γ. Brown's own framework, which contains no length or time transformation, must instead treat the particles as superluminal — a considerably heavier commitment than the one he is trying to avoid. The paper is best read as a coherent and honestly-stated research programme whose electrodynamic core is well-motivated and whose cosmological and optical extensions were asserted rather than established.