The Marinov motor: A skeleton in the closet of physics Thomas E. Phipps, Jr.a) 908 S. Busey Avenue, Urbana, Illinois 61801, USA (Received 22 December 2013; accepted 2 March 2014; published online 26 March 2014) Abstract: The Marinov motor (MM) is a device whose operation has been verified by several independent investigators. This fact is an embarrassment to physicists, since their accepted Lorentz force law is unable to account for it. Full understanding of the MM seems to require (1) a more robust interpretation of the relativity principle, (2) recognition that first-order physics has never been right (in view of the Galilean noninvariance of Maxwell’s equations), (3) acceptance of force action by vector potential A, and (4) willingness to abandon covariance in favor of invariance. CV 2014 Physics Essays Publication. [http://dx.doi.org/10.4006/0836-1398-27.2.183] Re ́sume ́: Le moteur Marinov (MM) est un dispositif dont le fonctionnement est confirme ́ par nombre d’investigateurs inde ́pendants. Ce fait est un embarras pour les physiciens, puisque la loi de force de Lorentz qu’ils acceptent n’a pas moyen de le justifier. Il semble que, pour une compre ́hension totale du MM, il faudrait: (1) une interpre ́tation plus de ́veloppe ́e du principe de la relativite ́, (2) une reconnaissance que, en conside ́ration de la noninvariabilite ́ Galile ́enne des e ́quations de Maxwell, la physique du premier ordre n’a jamais e ́te ́ juste, (3) une acceptation de l’action de la force par le vecteur potential A, et (4) un consentement d’abandonner la covariance pour accepter l’invariance. Key words: Marinov Motor; Electrodynamic Force; Galilean Invariance; First-order Physics; Relativity Principle; Invariance Versus Covariance. I. INTRODUCTION One of the many frustrations of Stefan Marinov’s life was that he never could account theoretically for the working of the motor he had invented1 (which he called “Siberian coliu”). All he knew was that it did work. One of the many associated ironies was that within weeks of Marinov’s (possibly unrelated) suicide, James P. Wesley, in Germany, came up with an answer.2 That answer proves important for a number of aspects of physics, particularly for our understanding of relativity. A typical demonstration form of the Marinov motor (MM) is shown in Fig. 1. A toroidal solenoid or permanent magnet is held fixed, and a direct current 2i from an external source is led into a surrounding horizontal conductive ring (supported in bearings not shown) through brushes on opposite sides that permit the ring to rotate freely in place. The current divides, so that i flows in each half of the ring. If the angle / between the two vertical planes containing the magnet and the ring-current entry–exit points vanishes, / 1⁄4 0, as shown, a torque is observed to be exerted on the ring, which causes it to turn azimuthally. Alternatively, the ring may be fixed (brushes replaced by solid contacts) and the magnet suspended so that it can turn. In that case, when / lies in the interval 690, torque of a given sense is exerted. If the magnet’s turning then continues past those angular limits, the torque sense reverses, so that, to get continuous rotation (motor action), commutation of the current (direction reversal each half-turn) is necessary. There are many variants of these designs. For instance, the vertical members of the toroid may be either inside or outside the ring,3 torque may be multiplied by use of multiple rings in series,4 each split at the current entry and exit points and wired so that full current flows in each half-ring, etc. II. FAILURE OF THE LORENTZ FORCE LAW What was it, then, that puzzled Marinov about the operation of his motor? In brief, it seems quite impossible that the motor work according to the “known” laws of physics. The accepted Maxwell theory of electromagnetism, which should govern, recognizes only one way in which ponderomotive electrodynamic force can be exerted, and this is in accordance with a semi-empirical supplement to the field equations known as the Lorentz force law, namely, F 1⁄4 qðE þ vd  BÞ: (1) Equation (1) expresses the only known linkage of the fields to observability. In the MM, there are equal amounts of plus and minus charge present; hence, E  0. Only the “magnetic” part of the force law, qvd  B, can be effective. The detector or field-sensor charge velocity qvd refers to current in the ring. Leaving aside all questions of magnitude of the leakage B-field outside the toroid, we see from the cross product nature of the Lorentz magnetic force term that the force exerted by any stray magnetic field external to the toroid acts in the radial or vertical direction, transverse to the ring current, i.e., in the plane normal to vd. [Identically, vd  ðvd  BÞ 1⁄4 0 for all B.] So there is no predicted a)tephipps@sbcglobal.net 0836-1398/2014/27(2)/183/8/$25.00 183 CV 2014 Physics Essays Publication PHYSICS ESSAYS 27, 2 (2014) azimuthal driving force action or reaction (no motor force parallel or antiparallel to vd acting on either the ring or the toroid). Like the bumblebee, the MM cannot work; yet it does. I shall discuss the empirical evidence for that in Section V. III. THE INVARIANT TOTAL TIME DERIVATIVE OF VECTOR POTENTIAL So, what is wrong with the Lorentz force law? That is the puzzle confronted and solved by Wesley. The key recognition is that whereas B-flux is largely contained within the permanent magnet or closed toroidal solenoid, there is also an “A-field” of the vector potential A, which, owing to proximity, is of appreciable magnitude at the ring. Conventional electromagnetic theory concedes to this A-field no ability to exert ponderomotive force. But conventional theory could be wrong! It is worth entertaining that possibility, which will require thinking outside the relativity box. In such willingness to look beyond orthodoxy lay Wesley’s genius. Among 10 000 physicists, there is bound to be one like him who is able to question what he was taught. The scientific and technological progress of our species depends on that one in ten thousand. Wesley’s challenge was to quantify what Marinov had discovered. His reasoning may have gone somewhat as follows. First let us review what we know about the electromagnetic potentials ðU; AÞ. They are conventionally thought to be related to the magnetic field by B 1⁄4 r  A and to the electric field by E 1⁄4 rU  @A @t : (2) However, there is a serious flaw in the latter expression. We note that motors in general are first-order devices (that is, they depend on v/c, not on higher powers), so we need to focus attention only on first-order physics, which means that it will suffice to treat inertial transformations by the Galilean transformation (GT), r0 1⁄4 r  vt, t0 1⁄4 t, under which, if the relativity principle holds in its strictest interpretation, we must demand genuine formal invariance of observables such as field quantities. In fact, there is reason to consider each order of approximation as defining its own “physics,” because effects at each order are independently observable. We suppose that no observation ever violates the relativity principle. (It would be big news if it did.) That being the case, we are justified in demanding separate invariance of field-related quantities at each order of approximation, beginning with the first, where covariance is not an option. [For field quantities under the GT, E0 1⁄4 E; B0 1⁄4 B (proven in Ref. 7 for first-order invariant field equations, wherein @=@t is everywhere replaced by d=dt and also at higher orders for replacement by d=ds), which express unqualified invariance.] At low speeds, we have first-order validity of the Galilean velocity addition law, v0 d 1⁄4 vd  v; (3) v being the constant velocity of the primed with respect to the unprimed inertial frame (and d-subscripted velocities being arbitrary detector velocity relative to the indicated frame). Why do I emphasize literal invariance of field quantities, when all the world accepts covariance5 as a perfectly good substitute? Simply because true invariance is an attainable expression of form preservation, and I can see no reason to settle for less. Even the wisest of us is in no position to know (although conventional wisdom asserts) that nature settles for less. Covariance does not leave unchanged the field quantities whose form it “preserves.” It redefines those quantities as linear combinations of the old quantities. Does redefinition sound to you like honest form preservation? That, to be sure, is what you have been taught, but would you have thought it without the teaching? The universal covariance dodge is both sly and clever. It beautifully illustrates the principle that the best way to hide an error is to universalize it. A real physicist should be able to sense the impermanence of a physics built on such tricks. Physics is going to need real physicists if progress is to be more than a catch-word. Now, what we observe about Eq. (2) is that the vector E it defines is not Galilean invariant. The reason is that the partial time derivative operator @=@t spoils invariance. Thus, under the GT, we have ð@=@t0Þ 1⁄4 ð@=@tÞ þ v  r 61⁄4 ð@=@tÞ. This could be a point of weakness in the whole established conceptual structure, so let us direct our attack there. How to fix it? Well, with little effort, we find that the total time derivative is Galilean invariant. That is, given the commonly accepted definition of the total time derivative, FIG. 1. Schematic of a typical form of the MM. 184 Physics Essays 27, 2 (2014) d dt 1⁄4 @ @t þ vd  r; (4) where vd is the arbitrary velocity of a charge that acts as “field detector” or field sensor (the same parameter as in the Lorentz force law, not to be confused with the constant relative velocity v of two inertial frames). Observe that there is much physics in Eq. (4); e.g., it destroys spacetime symmetry and all the ratiocinations that go with it. Using Eqs. (3) and (4) and the fact that under the GT r0 1⁄4 r, we verify first-order formal invariance d dt  0 1⁄4@ @t þ vd  r  0 1⁄4@ @t0 þ v0 d  r0 1⁄4@ @t þ v  r  þ ðvd  vÞ  r 1⁄4@ @t þ vd  r 1⁄4 d dt : (5) Therefore, we boldly propose to make all electromagnetic theory first-order invariant by replacing the invariancespoiling @=@t wherever it appears in the field equations or elsewhere by the invariant d/dt. Thus, Eq. (2) yields a modified (Galilean invariant) force law,6 F 1⁄4 qE 1⁄4 q rU þ dA dt  : (6) This law, F 1⁄4 qE, being formally of an “electric” character, is simpler in structure than Eq. (1), inasmuch as it lacks an overtly magnetic B-field part. Observe, moreover, by virtue of Eq. (4), that something exciting has happened to the magnetic part of this electric qE force law. Suddenly, we have acquired a new force term of motional induction. From Eqs. (4) and (6), the new term is Fmotional induction 1⁄4 ðq=cÞðvd  rÞA; (7) where I have thrown in a power of c, the light speed, to conform to conventional units. (Elsewhere c is understood to be unity.) Recall that we said the A-field extends outside the magnetic toroid and thus impinges on the near-by currentcarrying ring. So, in Eq. (7), we have the means of describing a ponderomotive force action on the ring or a reactive-force action on the toroid. This was Wesley’s resolution of the puzzle. To be sure, the whole discussion has been limited to the first order, but that is the order needed to describe motor action. Further, it is more or less apparent that higher order physics cannot be right unless the first order is right. That there could be a first-order mistake or omission in the Maxwellian formulation of electromagnetic physics will strike orthodox physicists as ludicrous. But the MM speaks for itself. When an observed violation of the laws of physics occurs, what gives ground? The laws or the facts? Or do we just hide our heads and hope the whole thing will go away? To be true to history, the latter course has marked the reaction of the physics community so far. This suggests that physics as a science is at an end. From here on, it will be just a taught doctrine. Trust to the academies for that. It is what they do. How is Eq. (4) to be generalized to higher orders, consistently with our theme of invariance instead of covariance? This remains a topic for research. One plausible suggestion7 is to replace the noninvariant t wherever it occurs in such relations as Eq. (4) and the electromagnetic field equations (wherein @=@t has already been replaced everywhere by d/dt) with the higher-order invariant proper-time parameter s associated with the field detector; whence @=@t ! d=dt ! d=ds. This, by the accepted definition of proper time, ensures time dilation at second order, via the famous ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1  ðv=cÞ2 q factor, but not Lorentz contraction; spacetime symmetry having already been renounced in view of its violation by Eq. (4). [That is, ð@=@x; @=@y; @=@z; @=@tÞ is spacetime symmetrical; whereas, by Eq. (4), @=@x; @=@y; ð @=@z; d=dtÞ is not. From this, we see that the homogeneous spacetime manifold concept underlying both the special and general theories of relativity is falsified by the empirical evidence of the MM.] Clearly, true invariance is an attainable ideal at all orders. It is a myth that covariance is the best we can hope for. Further study is evidently needed, but it does not concern our present first-order considerations on motor action. There are several other ways of arriving at something resembling the basic force law of Eq. (6). For instance, starting from the vector identity8 rða  bÞ 1⁄4 ða  rÞb þ ðb  rÞa þ a  ðr  bÞ þ b  ðr  aÞ; (8) if we take b to be our vector potential A, and a to be a velocity vd that is constant or at any rate not explicitly dependent on spatial coordinates, this simplifies to vd  ðr  AÞ 1⁄4 rðvd  AÞ  ðvd  rÞA: (9) Then, since B 1⁄4 r  A, the Lorentz force law, Eq. (1), with Eqs. (2), (4), and (9), yields FLorentz 1⁄4 qðE þ vd  ðr  AÞÞ 1⁄4 q rU  @A @t þ rðvd  AÞ  ðvd  rÞA  1⁄4 q rðU  vd  AÞ  dA dt  : (10) Superficially, this resembles a gauge transformation of the scalar potential U in Eq. (6), the transformation function being Ð vd  Adt. But since there is no matching transformation of A, it is not a true gauge transformation, hence does not leave the force gauge-invariant. This unfamiliar form of the Lorentz force law, Eq. (10), is equivalent to what we are assuming to be the valid force law, Eq. (6), provided we are willing to modify Eq. (10) by subtracting from it the term qrðvd  AÞ. This simple result holds rigorously, however, only under the stipulated conditions on vd. In any case, our claim is confirmed that the unmodified Lorentz force law is not equivalent to the presumably correct Eq. (6). It should be Physics Essays 27, 2 (2014) 185 remarked, though, for purposes of possible experimental inquiry that the discrepancy is a gradient term that integrates to zero around any closed curve. Since experiments involving current require closed circuits, the physical effect (presence or absence) of this extra gradient term is not easily demonstrated experimentally. However, in general, when two rival candidate laws of nature differ in their predictions only by an exact differential quantity, so that their difference vanishes when integrated around any closed curve, an experimental method7,9,10 which I have termed “inertial modulation” allows them to be distinguished. (The basic idea is to spoil the exactness of the differential by a suitably varied distribution of mass around the circuit. Such a mass distribution can serve formally as a Green’s function in the integrand, thereby altering the dynamics enough to reveal the desired distinction of laws.9) Thus, there is an empirical way to distinguish the candidate laws of Eqs. (1) and (6). The method has not been applied to that particular problem; but it has been applied11 to the related rivalry between the Lorentz force law and the original Ampe`re law of force between current elements, with the empirical decision in favor of the latter. This experiment,11 like the MM, rates as one of the turning points of modern physics that is completely ignored by modern physics. IV. SO, WHAT’S NEW? If there is anything fundamentally new in the above, it is that the relativity principle must be more broadly and insightfully interpreted than has been the custom among physicists. Thus, the principle must be seen as implying true invariance at each order of approximation, independently of the other orders, because, if the principle is about anything, it is about what can be observed, and each order of approximation can offer physical effects that are independently observable. In contrast, Einstein’s procedure implies that the first order will take care of itself. Whatever may be wrong there is magically corrected by second-order applications of the relativity principle. Further, to clinch this, he substituted Lorentz covariance (second-order mathematics differing intrinsically from true invariance) for genuine invariance, as his means of expressing form preservation at all orders. By this stratagem, he took the whole world of physics with him, trembling in a stunned ecstasy of admiration. On two counts he was wrong: (1) Covariance is no substitute for invariance. (2) First-order physics demands first-order (low speed) invariance, regardless of what is happening at higher orders. The first order constitutes a physics of its own, divorced from all higher-order considerations and entitled to its own (firstorder) relativity principle. The first order will not take care of itself; it needs to be analyzed like any other physics. That is what a full understanding and application of the relativity principle implies. Anything less is a swindle. Evidence of the MM shows that for a century, physicists have been easily swindled. No wonder they prefer to ignore the testimony of fact. Continuing ignoration of the MM will demonstrate that they like things the way they are and mean to keep them that way—to keep the “relativity” ecstasy rolling. In our youth, indeed, we all rolled in the sheer ingenuity of its contrivance. The trouble is (a) most of us never had the second thoughts that are supposed to come with maturity, (b) from among external nature’s many attributes, ingenuity was conspicuously left out. Successful description of nature we know must be beautiful; that means it cannot be contrived. In connection with first-order questions, it may be worth noting the remarkable first-order limiting form of the Lorentz time transformation, namely, t0 1⁄4 t  vx=c2. Although the difference between this and the GT appears subject to empirical testing over either very long distances or very short time intervals, I am not aware that any such tests have been made. The fact is that none of Einstein’s theories cleared up or even addressed the manifest problems of electromagnetism at first order. From start to finish, there was no first-order (Galilean) invariance of Maxwell’s equations or of the equations that defined the electromagnetic potentials. One was left to infer, if one chose, that the relativity principle did not hold at first order. Indeed, strictly construed as a true invariance principle, the relativity principle did not hold at any order. From that standpoint, the second-order swindle was an all-order swindle. The relativity principle, in its debilitated Einsteinian form, was a delicate conception that originated and lived only at second order, where spirits refined in subtlety could best appreciate it. And the resulting covariance (ersatz invariance) was a parallel test of the physicist’s capacity to appreciate the subtlety of the almost-as-good, this time on the side of mathematics. V. WESLEY’S TORQUE FORMULA AND THE EMPIRICAL EVIDENCE Let us first see qualitatively why the motional induction force specified by Eq. (7) must produce an azimuthal torque that turns the magnet or the ring, whichever is free to rotate. We may begin by recalling Ampe`re’s model of a permanent magnet. This pictures the bulk material as filled with tiny current loops lying in planes transverse to the magnetic flux lines, each loop enclosing a flux line. In the interior of the material, adjacent coplanar current loops cancel each other, but around the periphery of the magnet, there is no cancellation, so a closed loop of virtual current flows around the magnet’s outer surface. Alternatively, if the magnet is replaced by a solenoid, a real (electronic) current flows around the outer surface, producing a similarly contained bundle of magnetic flux lines that constitutes the internal B-field. In the case of either the magnet or the solenoid, the important thing to note is that the surface “magnetic current” flows azimuthally. The vector potential A is produced by current and is directed in the same way as the current that produces it. This turns out to be just as true for the virtual current responsible for permanent magnetism as for the real current in a solenoid. So, the A-vector circulates azimuthally, just as the ring current does, and we see that the force predicted by Eq. (7) is indeed such as can exert ponderomotive torque on the mobile portion (“armature”) of the motor. Wesley performed the necessary integration2 and given that (a) the ring is free to rotate and (b) the vertical planes containing the magnetic 186 Physics Essays 27, 2 (2014) toroid and the ring-current exit–entry points coincide (/ 1⁄4 0, as in Fig. 1) obtained an approximation for the ring torque2,3 as dTb