Centrifugal Force

Centrifugal force is the outward effect associated with rotation — the pull felt in a swung sling, the outward thrust in a centrifuge, the tendency of an orbiting body to recede from its centre. In modern textbook mechanics it is classed as a fictitious or pseudo force: an artefact of describing motion from a rotating frame of reference, with no physical cause behind it. A body in curved motion is held to experience only an inward centripetal force; what looks like an outward force is said to be nothing but inertia, the body's tendency to continue in a straight line.

That classification is the point of dispute in the literature archived on this wiki. Most of the papers collected here treat centrifugal force as a real outward force with a physical cause, and regard its demotion to a fictitious status as a twentieth-century error that severed classical mechanics from the medium in which the older physicists believed it operated. The topic is dominated by David Tombe, who has returned to it in paper after paper, and whose position — that centrifugal force is an aether pressure, and that the same pressure appears in electromagnetism — supplies most of the argument set out below. Other lines are represented by Charles William Lucas, who derives inertia and centrifugal force from an electrodynamic force law, by Nainan K Varghese, who denies that curved motion is a single motion at all, and by Nassim Haramein and Elizabeth A. Rauscher, who add the related Coriolis term to Einstein's field equations.

The mainstream account

The standard treatment is worth stating accurately before it is criticised. Newton's first law holds that a body free of net force moves uniformly in a straight line. Circular motion is therefore an accelerated motion, requiring a real inward force — gravity, tension in a string, the normal force of a wall — directed to the centre. When the motion is described instead from a frame rotating with the body, extra terms appear in the equations of motion: a centrifugal term directed outward, proportional to the square of the angular velocity, and a Coriolis term acting on radial motion. These terms are introduced to preserve the form of Newton's second law in a non-inertial frame, and on the orthodox reading they are bookkeeping devices rather than forces: they have no agent, no reaction partner, and vanish when the description is transferred back to an inertial frame. The felt outward pull, in this account, is the inertia of the body itself and the reaction it exerts on whatever constrains it.

The dispute: real or fictitious?

The papers here reject the last step of that argument rather than the mathematics leading to it.

Tombe's "The Centrifugal Force Paradox" (2011) states the objection most directly. It is commonly taught, he writes, that centrifugal force does not exist except as a fictitious force observable only from a rotating frame, and that curved-path motion involves only a centripetal force. But if the net zero force of straight-line motion at constant speed is resolved into polar components, one of those components is a centrifugal force — and that component can physically react against a constraint. Something that presses on a constraint is not a bookkeeping term; it reveals, on his account, an underlying pressure associated with inertia itself.

The companion paper "Centrifugal Force Denial" (2011) argues the same point from a practical case. A mooring line can be cast from ship to shore by swinging a weight in a vertical circle, building up angular speed, and releasing it: the swinging stores pressure, which is then released as kinetic energy in the projectile. Tombe calls the stored quantity centrifugal potential energy. One may of course deny that any such pressure exists and describe the whole episode as a body's tendency to move in a straight line — but the denial, he argues, explains nothing that the pressure account does not explain better.

"Double Centrifugal Force" (2011) presses further, examining a rotating system in which two separate centrifugal forces act at once: one relating to the rotation axis of the system, the other to the centre of the Earth and to horizontal transverse speeds within the system. The second, Tombe reports, has the power to raise an object vertically in defiance of gravity — an effect he takes to be inexplicable if centrifugal force is a mere frame artefact. In "Centrifugal Force Between Two Orbital Systems" he asks whether two coplanar orbits sitting side by side, the configuration found inside atomic and molecular matter but never on the astronomical scale, can repel one another with centrifugal force.

Nainan K Varghese arrives at a rejection of the textbook picture from a different direction in "Motion in a Curved Path (According to 'Hypothesis on MATTER')" (2010). On his Hypothesis on MATTER all natural inertial motions are straight lines; the rotation of a macro body is the resultant of simultaneous straight-line motions of its constituent 3D matter particles in different directions and at different speeds appropriate to their positions in the body. A body moving in a circle is under a constant inward effort, and simultaneously possesses two linear motions — one toward the centre, in the direction of the centripetal force, and one deflected outward from the tangent. Curved motion, in short, is not a single motion requiring a single force but a composite, and the outward tendency is a real component of it.

Charles William Lucas takes up the historical problem in "The Electrodynamic Origin of the Force of Inertia, Part 3" (2008). Newton, he observes, could account for inertia and centrifugal force only by leaning on his Existence Theorem for absolute space and time, framing both in absolute coordinates; Einstein's general relativity, on Lucas's reading, failed to deliver what Mach had envisaged, namely a basis for inertia and centrifugal force in relative coordinates. Lucas derives both from his universal electrodynamic force law, which is written in relative coordinates throughout: from that perspective the inertial force is an average residual electrodynamic force, and the centrifugal force with it. Neither absolute space nor curved spacetime is required.

Tombe's account: centrifugal force as aether pressure

Tombe's positive theory is set out most compactly in "The Cause of Centrifugal Force" (2008). Centrifugal force, he writes, is the outward radial expansion arising in connection with absolute rotation. He takes as his starting point Leibniz's demonstration that centrifugal force obeys an inverse cube law when angular momentum is conserved — not the inverse square of gravitation. Since the inverse cube law is the law of the electric dipole field, he reads this as evidence of the dielectric nature of space itself. Space, on his proposal, is densely packed with dipolar aethereal vortices acting like tiny Archimedes' screws, and centrifugal force is the aether pressure drawn up when those vortices are linearly stretched or angularly accelerated.

"Centrifugal Pressure in the Aether" (2008) gives the formal expression. Identifying the magnetic vector potential A with the electric current density J — both, in his scheme, representing a flow of aether — he obtains centrifugal force as the gradient of a term in aether density and velocity, and takes this to confirm a close link between centrifugal force, kinetic energy, and repulsion pressure.

The absolute-rotation question is addressed in "The Faraday Paradox and Newton's Rotating Bucket" (2008), which sets Newton's bucket experiment beside the Faraday paradox of the rotating magnet. Inertia, Tombe argues there, is normally understood in a very limited Cartesian way, as the tendency of a body to persist in uniform motion; understood generally, inertia is centrifugal force in irrotational fields. Centrifugal force is in turn one mutually perpendicular aspect of a more general convective force of the form v × Ω, which acts in magnetic fields and in the cyclonic phenomena of the oceans and atmosphere alike.

In "Centrifugal Congestion in the Gravity Sink" (2008) the same pressure is made the counterweight to gravity. Gravity, on Tombe's model, is a pull caused by tension in the aether as it is drawn into negative particles, which act as sinks; it is equivalent to a radial negative electric current. A universe of sinks alone would collapse, so a counterbalancing aether pressure is required, and this arises from positive charge sources. The balancing mechanism, he writes, involves dipolar vortices, Lenz's law, and centrifugal force. The physical medium behind all of this — a dense sea of electron-positron dipoles, each pair in mutual circular orbit — is described in "The Speed of Light" (2013, and again 2015) and in "Centrifugal Force and the Electron-Positron Sea", where the electric dipole with its inverse cube field is proposed as the primary physical cause of centrifugal force, and the inertial path and the Mach Principle as the compound effect of a dense multitude of superimposed dipole fields filling space.

A separate paper, "Centrifugal Force in the Schwarzschild Field", treats centrifugal force as an inertial effect induced by motion through the space-time continuum and argues that gravity, if strong enough, can destroy that centrifugal force and convert it into an electrostatic attraction augmenting the gravity.

Centrifugal force in electromagnetism

The distinctive feature of Tombe's programme is that centrifugal force is not confined to mechanics. He holds that it is the same pressure that appears in electromagnetic phenomena, and that this identity was visible in Maxwell's own work before it was edited out of the textbooks.

"Centrifugal Force in the Electric Circuit" (2009) states the claim plainly: centrifugal force is heavily involved in electromagnetism — in the magnetic force on a current-carrying wire, and in the electromotive force induced in a wire moving through a magnetic field. In the first case it is a simple centrifugal force of the kind that keeps planets in orbit; in the second it is a compound centrifugal force closely similar to the transverse Coriolis force acting in non-circular planetary orbits and in vortex phenomena generally.

The same mechanical-electromagnetic parallel is drawn in "Bernoulli's Principle and the Theory of Flight" (2007). When an aeroplane moves horizontally, the air pressure below the wings exceeds that above, producing lift at right angles to the motion; when a current flows through a wire in a magnetic field, a differential pressure acts on either side of the wire, producing a force at right angles to it. In the first case, Tombe writes, the pressure arises from centrifugal force exerted by air molecules; in the second, from centrifugal force exerted in the medium.

The historical argument is made in "Maxwell's Original Equations" (2011) and "The Significance of Maxwell's Equations" (2012). Maxwell, Tombe writes, worked within the context of a sea of tiny aethereal vortices pressing against each other with centrifugal force; the equations that bear his name have been removed from that physical context, and outside it their full meaning is lost. "The Double Helix and the Compound Centrifugal Force" (2012) addresses the standing objection that a dense particulate medium would produce friction in planetary motion: the double helix pattern, he argues, converts potential frictional effects into the ordered inertial effects recognised as the centrifugal and Coriolis forces.

Relation to the Coriolis force

The Coriolis Force is treated throughout this literature as the near relation of centrifugal force rather than as a separate phenomenon. Tombe's "The Coriolis Force" (2011) makes the point from the source: in his 1835 paper Gaspard-Gustave de Coriolis called it the "compound centrifugal force", and that, Tombe writes, is exactly what it is — a compound inertial force arising when a compound motion causes two opposing centrifugal pressures to press differentially on either side of an object. "The Coriolis Force in Maxwell's Equations" (2010) develops the same idea: the Coriolis force is induced by a compound motion of two independent but physically connected components, one linear and one rotatory, deflects an element perpendicular to its path just as centrifugal force does, and is mathematically exactly twice the simple centrifugal force. "The Centrifugal Force and the Coriolis Force" (2014) returns to Coriolis's 1835 derivation and to his treatment of these supplementary forces in the plural.

The most unusual application is "The Coriolis Force and the Rattleback" (2010), on the rattleback or Celtic stone, which Tombe calls the most mysterious phenomenon in classical mechanics: it reverses its angular momentum, he argues, by inducing a Coriolis pressure from the dense background sea of rotating electron-positron dipoles that serves as the medium for light.

Thierry De Mees makes the Coriolis effect fundamental in a quite different framework. In "Is the Differential Rotation of the Sun Caused by a Coriolis Graviton Engine?" (2010) he derives the fundamentals of gravitomagnetism from reciprocal graviton losses by particles defined as trapped photons, and finds that the gravity field is generated by a Coriolis effect exerted by gravitons upon particles — with inertial resistance generated by a Coriolis effect as well. Applying the graviton mechanics to the Sun, he reports an amplitude matching the Sun's rotation frequency.

Nassim Haramein and Elizabeth A. Rauscher approach rotation from within general relativity rather than against it. In "A Consideration of Torsion and Coriolis Effects in Einstein's Field Equations" (2003) and "The Origin of Spin: A Consideration of Torque and Coriolis Forces in Einstein's Field Equations and Grand Unification Theory" (2004) they treat torque and Coriolis forces as dynamic properties of the spacetime metric and the stress-energy tensor, amend the field equations with the corresponding terms, and solve for a modified Kerr-Newman metric — arguing that the inclusion of these rotational terms bears on novae and supernovae, galactic formation, central supermassive black holes, polar jets, accretion discs, spiral arms and halo formation. The same considerations of spacetime torque and Coriolis forces are carried into plasma physics in "Collective Coherent Oscillation Plasma Modes In Surrounding Media of Black Holes and Vacuum Structure - Quantum Processes with Considerations of Spacetime Torque and Coriolis Forces" (2004).

Positions of researchers on this wiki

The researchers collected here do not form a single school, and their disagreements are as instructive as their agreements.

David Tombe holds that centrifugal force is a real outward force, caused by pressure in a dense aether of dipolar vortices, and that it operates in electromagnetism as well as in mechanics. His is the most developed position on this wiki and the one that most directly contradicts the textbooks. It depends on the existence of the aether: if there is no medium, there is no pressure to be drawn up, and the mechanism fails.
Charles William Lucas agrees that centrifugal force is real and physically caused, but locates the cause in an electrodynamic force law written in relative coordinates rather than in an aether pressure. His objection is aimed equally at Newton's absolute space and at Einstein's failure to deliver Mach's programme.
Nainan K Varghese denies both the textbook account and the need for a medium-borne outward force, resolving curved motion into simultaneous straight-line motions of constituent particles. On his analysis the argument over whether centrifugal force is "real" is malformed, because rotation is not a primitive motion.
Thierry De Mees does not argue about the reality of centrifugal force at all; he makes the Coriolis effect the generator of gravity and of inertial resistance within a gravitomagnetic, graviton-based scheme.
Nassim Haramein and Elizabeth A. Rauscher retain Einstein's field equations and add rotational terms to them — a strategy the aether theorists here would regard as building on the wrong foundation, and which they in turn would regard as unnecessary.
Jovan Marjanovic treats centrifugal force not as a theoretical question but as an engineering one. In "The Secret of Free Energy from the Pendulum" (2011) he examines a pendulum with a movable pivot point, determines the maximal over-unity quotient obtainable under stated conditions, and analyses the influence of the critical angle at which the pivot begins to move.

The archive also holds a 2019 paper, "Reason for a Cyclone to Spin — Coriolis Force only Terminates It", which does not yet have a page here. It argues that cyclones all show converging movement about an eye whereas the Coriolis effect is framed on diverging movement, and that convergence and divergence being opposite concepts, more physics must be involved in producing the observed pattern.

External links

"Centrifugal Force" — the full paper, General Science Journal