True Explanation of Operation of Homopolar Engine
| Scientific Paper | |
|---|---|
| Title | True Explanation of Operation of Homopolar Engine |
| Read in full | Link to paper |
| Author(s) | Andrija Radovic |
| Keywords | homopolar generator, moving magnetic field, Maxwell's Equations, Lorentz Force, field strings, Inertia |
| Published | 2009 |
| Journal | Il Nuovo Cimento |
| Volume | 124 B |
| Number | 1 |
| No. of pages | 25 |
| Pages | 13-37 |
Read the full paper here
Abstract
Operation of Faraday's homopolar engine had crucial aftermaths to contemporary science. Most of misunderstandings of the machine's operation caused wrong acceptance of N hypothesis instead of M one. Although there were plenty of authors suspecting that physical fields are moveable, this fact is finally duly proven by the experiment depicted in the text. There are also analyzed classical string theoretical concept with fields' equations and the induction formula.
Overview
Andrija Radović's paper, published in Il Nuovo Cimento B in January 2009, takes the two-century-old puzzle of the Faraday disc — that spinning the magnet changes nothing, while spinning the disc generates a voltage — and argues that the standard reading of it is exactly backwards. Radović frames the question as a choice between two positions he labels the M hypothesis, in which physical fields have their own velocities that "mainly match the velocities of the fields' sources", and the N hypothesis, in which fields have no velocity at all and poles merely change the magnitude of eternally existing fields. He holds that Faraday's homopolar experiment was taken as proof of the N hypothesis, that this was "the first electric machine ever built and consequently it was a milestone for all subsequent physical theories", and that everything downstream — the need for an observer to anchor velocity, the Lorentz transformations, and ultimately Special Relativity — followed from a misreading.
His counter-argument is mechanical rather than mathematical. If the permanent magnet's rotation affects neither induction nor torque, the magnet cannot be the stator of the machine when it runs as a motor; and since nothing else is left to push against, the reaction must be taken by the outer part of the electric circuit, which requires that the magnetic field rotate with the magnet. He then reports a three-body version of the machine — freely rotating magnet, disc, and brush-carrying ring — in which the induced voltage depends on the difference between disc and ring angular velocities, and a Van de Graaff experiment in which a charged pendulum hung above a spinning homopolar magnet deflects. On this basis he rebuilds electromagnetism from a "field string" idealisation, recovers Maxwell-like equations with total rather than partial time derivatives, and extends the picture to inertia, missing galactic mass and chemical bonding.
The argument
The homopolar machine and the stator problem
Radović begins from the standard result for the Faraday disc, that with ω ⊥ r, ω ⊥ B and r ⊥ B,
- V = ∫ (ω × r) × B · dr = ωdisc B r2 / 2,
with the magnet's angular velocity entering nowhere. Faraday concluded that the field does not move; Radović's objection is that this makes the motor version unintelligible. "It is quite obvious that a permanent magnet cannot be a stator simply because its rotation affects neither induction nor torque at all." Overlapping the disc with the magnet to make a compact motor sharpens the point: the only remaining candidate for a prop is the external circuit, "otherwise the device will seriously violate the very basic law of angular momentum's conservation by repelling on itself".
The three-rotor experiment
His experimental centrepiece is a generator with three independently rotating parts — magnet, conductive disc, and a ring carrying the brushes and the outer circuit. The measured voltage obeys
- V = (ωdisk − ωring) B r2 / 2,
so that when the outer circuit rotates with the disc at the same rate no voltage appears, and the magnet's rotation remains irrelevant throughout. Radović reads this as proof that "the outer part of the electric circuit is also exposed to a rotating magnetic field which intersects both inner and outer parts of the electric circuit". The null result for magnet rotation is then explained rather than assumed: because the field lines are closed, any closed contour crosses a given region an even number of times with equal inner and outer intersections, so the rotating magnet induces equal and opposite potentials in the internal and external parts of the circuit, which cancel. This is presented as "the geometrical property of 3D space".
The charged pendulum
A second experiment hangs a small ball charged by a Van de Graaff generator above a spinning homopolar magnet. Radović reports that the tether's angle from vertical is "strongly affected by the angular speed of the permanent magnet regardless the magnet's conductivity and capacity", with the equilibrium condition
- Q1 ωM h B2 = m1 g (h/ℓ) √(1 − (h/ℓ)2),
which he says the measured inclination "almost perfectly matches". He calls this "the ultimate proof that magnetic field rotates altogether with its source, just as Tesla supposed", and notes that if electrostatic capacitance could be excluded but the effect remained, the alternative would be that the magnetic field is "only a catalyst" and the real interaction is with the ether.
Field strings and the Maxwell-like equations
Radović then idealises field lines as strings, motivated by a late nineteenth-century experiment in which two magnets immersed in a superconductive fluid interact with constant force irrespective of distance until the string's potential energy is exceeded and it snaps. Potential is defined as the rate at which strings cross a wire, U = dNB/dt; field strength as string concentration through a surface, B = dNB/dS and E = dNE/dS = (1/ε) dQ/dS. Assuming strings can neither appear nor vanish, a change in field magnitude must come from string migration, and he derives the general field-string equation
- d2N / (dt dS) = ∇ × (v × dN/dS), hence dB/dt = ∇ × (v × B),
with analogous forms asserted for the electric and, notably, the gravitational field. Combining with U = dΦ/dt and Stokes' theorem gives ∇ × E = dB/dt — "the first Maxwell equation", but with a total time derivative. The second is obtained from Biot–Savart, giving B = (E × v)/c2 and then c2 ∇ × B = −dE/dt. Radović claims a specific economy here: "there is no need for missing DC term with current density... This term was artificially added in official Maxwell equation just to keep its ability to handle appearance of constant magnetic field near DC conductors."
He then compresses the pair into a single complex field K = E + ic B, satisfying the recursive relation i c ∇ × Kj+1 = dKj/dt and the migration equation dK/dt = ∇ × (v × K), with force on a charge simply F = Q K, energy density P = ε K conj(K)/2, and a corresponding Poynting vector. A side argument, supported by an image-charge and Meissner-force calculation over a superconducting plane yielding a coefficient k = 1, concludes that the standard electric energy density "should not be halved at all".
Infinite conductors, inertia and gravity
Applying the migration equation to two infinite parallel conductors carrying AC — a case where no closed contour exists and Faraday's law cannot be applied — Radović extracts a field migration speed
- v = (r/I) dI/dt,
remarking that "the migration velocity can be superluminal too", and recovers E = (μ/2π) dI/dt along the conductor with the correct transformer polarity, plus V = (μℓ/2π) dI/dt. He calls this "a clear proof of the correctness of the whole concept". Differentiating B = (E × v)/c2 in time gives an induced field Eind ≈ V a/c2, from which he writes an inertial force F = Q1 V2 a/c2 and a gravitational analogue F = m1 a Vgrav2/c2, concluding that "inertia of charged particle is caused by the external potential that pervades it" — an explicitly Machian result, and he notes that Mach's Principle "could be proven within M hypothesis too because distribution of physical fields' string is not necessarily uniform". A parallel line gives B ≈ −V ω/c2 and the combined Eind = V(a + v × ω)/c2, from which he concludes "the magnetic field is a torsion electric potential".
He then speculates that if gravitational strings in the Galaxy are distributed over k dimensions with 2 ≤ k ≤ 3 rather than isotropically, the force law becomes G ∝ m/|r|k−1, which "may explain the missing mass in our Galaxy" — planar rather than spherical string distribution where neighbouring galaxies are distant. A brief chemical excursion computes the water molecule's bond angle as arccos(−1/4) = 104° 25′ 39″ from string saturation, and attributes metallic and van der Waals bonding to partial string interaction with multiple neighbours.
Consequences for relativity
Radović's correction to the Lorentz force is that the velocity must be taken relative to the field's source, not to an observer:
- F1,2 = Q1 (dr1,2/dt) × B2.
He states that this "makes Einstein first postulate invalid and there is also no more necessity for the existence of Lorentz transformations at all". His verdict on relativity is nonetheless partial rather than total: Einstein "decided to fix classical mechanics instead of classical electromagnetism", and the result is "a very good approximation" whose "partial legacy can still be using in engineering calculations". He offers an analogy: removing magnetic interaction from a set of moving charges while preserving the forces would require modifying the charges exactly as Einstein modified mass — which works approximately because "observer's velocity is usually very close to velocity of the one participant" — and suggests charge and mass should properly be tensors rather than scalars in the Coulomb and Newton force laws. He credits special relativity with the correct Čerenkov radiation formula.
Against relativity he cites stellar aberration, the measurability of absolute velocity against the background radiation by Doppler shift, and the BOOMERanG project. He presses a reciprocity objection — "if the one who is moving faster has slower passing of time, then there is the question who is the boss that should judge who is moving slower and who faster" — and argues that time dilation, if real, must be tied to acceleration, since metrology classes time and acceleration as absolute variables and velocity and potential as relative. Against general relativity he sets an inequality between the centre of gravitational mass, rG = √m ∫ (r/|r|3) ρ dV / |∫ (r/|r|3) ρ dV|3/2, and the centre of inertial mass, rm = ∫ r ρ dV / m, which he says "vigorously challenges Einstein's identifications of inertial and gravitational masses".
Origin of the blunder
The final section locates the root error in the reference frame implicit in F = ma. Defining acceleration as a1,2 = d2r1,2/dt2 makes the law F1,2 = m1 d2r1,2/dt2, in which one end of the radius vector sits on the mass and the other is undefined; defining the inertial frame as the one in which an accelerometer reads zero is, he says, "Petitio Principi" — a spring accelerometer in a rocket works perfectly well "even in open cosmos far away from any cosmic body". The undefined end is whatever causes inertia: a local gravitational field, an immovable ether, the centre of all mass in the universe, or the position at which the particle was created. He adds a technological corollary: if the cause of inertia could be identified it could serve "as prop for a new kind of propulsion which would not be a reactive one". He traces the dispute back to Aristotle's argument to Plato that all bodies must fall equally, noting in passing his own view that a heavier body falls marginally faster because it displaces the Earth's centre of mass more.
The conclusion urges that the M hypothesis "should replace officially accepted N hypothesis as soon as possible", and closes with a sober note against the free-energy expectations of the surrounding literature: "Contemporary science should stop giving us fake hope that there are plenty of technical opportunities ready to be effortlessly discovered or invented and that these are not happening just because there is some economical conspiracy which suppresses them all. Actually, the cold reality is completely different: it is extremely difficult to make any breakthrough in science and technology."
Assessment
The paper is at its strongest where it is most concrete. The three-rotor generator is a real and well-chosen experiment, and the result — voltage proportional to ωdisk − ωring, with the magnet irrelevant — is worth having stated plainly, because it makes explicit something the textbook treatment usually leaves implicit: that the flux rule alone does not tell you which parts of the circuit are doing the work, and that the "unipolar induction paradox" survives a century of confident dismissals. Radović's angular-momentum argument for the motor case is likewise a genuine physical question rather than a rhetorical one; a machine that appears to have no stator is a fair thing to worry about, and his answer — that the external circuit is the stator — is at least the right shape of answer. The closed-line cancellation argument for why magnet rotation produces no net EMF is elegant and, unlike most of the paper, follows from something rather than being asserted.
The difficulties begin where the paper generalises. Several central steps are stated rather than derived. The identification of field lines with conserved "strings" that can migrate but not be created or destroyed is the load-bearing assumption of the whole reconstruction, and it is introduced by analogy to an unnamed nineteenth-century superconductive-fluid experiment for which no citation is given; no argument is offered that a mathematical construct with an arbitrary density of lines can bear a conservation law. The step from the string-migration equation to "the first Maxwell equation" quietly changes what is being claimed: ∂B/∂t = −∇ × E with a partial derivative is Faraday's law, while dB/dt = ∇ × (v × B) with a convective derivative is the ideal-MHD induction equation for a field frozen into a moving conducting medium. These are different statements about different situations, and the paper treats the second as a correction of the first. The claim that the displacement-current term "was artificially added... just to keep its ability to handle appearance of constant magnetic field near DC conductors" inverts the history: Maxwell introduced it for charge conservation, and without it the equations do not yield electromagnetic waves at c — which the paper elsewhere relies on. Relatedly, the derived relation B = (E × v)/c2 is the low-velocity field transformation, valid to first order in v/c; using it as an exact identity is what permits the later result that field migration "can be superluminal too", so the superluminal conclusion is an artefact of the approximation rather than a discovery.
There are also internal inconsistencies in the paper's own commitments. Radović invokes the ether as a candidate anchor for inertia in the final section while stating parenthetically, earlier, that its existence "was disproved by Michael-Morrison experiment" — and he never resolves which he holds. The claim that "magnetic field rotates with its source" is asserted for a permanent magnet whose field is axially symmetric, so that a rotation of the source produces no change in the field configuration at all; the paper does not explain what physical quantity is supposed to be rotating, and the charged-pendulum result is presented without the control that would matter most — the same measurement with a non-rotating magnet and a spinning conductive shroud, or with the charge and magnet co-rotating. Given that a spinning magnetised conductor develops a real surface charge distribution (the unipolar generator's own electrostatics), an electrostatic origin for the deflection is precisely what needs excluding, and the paper excludes it by a capacitance estimate that is cited to another work rather than shown. The galactic-mass proposal, likewise, is a one-paragraph dimensional suggestion; a fractional-dimension force law with 2 ≤ k ≤ 3 is not tested against any rotation curve, and the paper's own figure is said to show "regions with negative masses... allegedly denoted as measuring errors" without saying whose data these are.
Finally, the objections to relativity are of uneven quality. The reciprocity complaint ("who is the boss") is the standard misreading of the twin problem, answered in every textbook by noting that only one twin accelerates; and it sits oddly beside Radović's own, better, observation that time effects should be tied to acceleration rather than velocity — he arrives at the orthodox resolution while presenting it as a refutation. Stellar aberration and the CMB dipole are not evidence against special relativity: the first was derived relativistically by Einstein in the 1905 paper, and the second establishes a preferred cosmological rest frame, which special relativity permits and general relativity requires. The inequality between the centres of inertial and gravitational mass is more interesting, but it is an inequality between two integrals that are simply different functionals of the same density, and showing that they differ for an extended, inhomogeneous body does not touch the equivalence of inertial and gravitational mass for a test particle — the quantity that Eötvös and, later, the lunar laser-ranging and MICROSCOPE results constrain to parts in 1015. What the paper does not do anywhere is confront that measurement, or accelerator data on the velocity dependence of mass, both of which its programme would need to accommodate.
That said, the concluding pages are unusually honest for the genre. Radović explicitly refuses the suppression narrative, insists that "it is extremely difficult to make any breakthrough in science and technology", and states plainly that relativity yields "pretty correct results" and should be treated as "an excellent set of formulas for variation of mass on subluminal velocities". A reader who discounts the reconstruction of electromagnetism is still left with a well-posed experimental question about where the reaction torque in a homopolar motor goes.