21st Century Science & Technology


The Suppressed Electrodynamics of Ampère-Gauss-Weber

From the Spring 2001 issue of 21st Century Science & Technology (full text)

The Ampère Angular Force

The Fundamental Electrical Law of Weber

The Weber Constant


Limiting Velocity and Critical Length


An iron curtain divides the subjects of gravity and electrodynamics, in today’s academically accepted versions of physics. Those attempting to cross it will risk the intellectual equivalent of machine-gun fire. Beyond, lie even more serious obstacles which come, not from outside, but from within the mind of the investigator. To get at the source of those self-imposed shackles, requires that we go beyond the bounds of what is today defined as “physics,” into matters usually classified as philosophical, or metaphysical. In doing so, we cannot avoid noticing that there are two schools in physical science, each one so distinct from from the other as to constitute two entirely different domains. It is the unfortunate aspect of our modern legacy that most, even among well-educated scientists, are unaware even of the existence of such a distinction. Yet, if the real history of physics of the 19th century were known, most of what passes as teaching of fundamental topics in that discipline today, would be shown to be, in the best of cases, misdirected, in the worst, willful fraud.

We know of no better way to correct this deficit than to present this review of the conceptual history of 19th Century electrodynamics. We have two purposes. First, to provide the reader with an introduction to the mostly unknown electrodynamic theory of André-Marie Ampère, and his successors—this, as a necessary aid to understanding our feature article on the subject of anti-gravity by the distinguished French research scientist, Dr. Rémi Saumont. Second, by exposing a crucial aspect of the suppressed history of gravity, electricity, and magnetism, to address the deeper problem of method holding back science today.

The heart of the matter before us, begins with the hypothesis and experimental validation of the Ampère angular force. Before the discovery by Oersted and Ampère of the effective equivalence of a closed current and a magnet, it appeared that the pairwise forces between bodies were governed by the same law of universal gravitation, which Johannes Kepler had first noted in his 1609 New Astronomy.1 At the time in question, 1819-1821, three known phenomena appeared to behave according to the assumption that the force between two bodies was determined according to the inverse square of their distance of separation. Apart from gravitation, these were the phenomena of electrostatic, and magnetic attraction and repulsion, investigated especially by Coulomb and Poisson.

In all three cases, there was some question as to the perfect validity of the inverse-square assumption. In the case of magnetism, the impossibility of separating the two opposite poles, made exact measurement of the pairwise relationship of one magnet to another always inexact. This problem of the existence of a “third body” did not entirely go away, even in the case of the most carefully observed of these phenomena, gravitation.

The Ampère Angular Force
In 1826, André-Marie Ampère published a groundbreaking study, summarizing the work of five years of research into the laws of the new science that he had named electrodynamics. The results showed, that in the case of the pairwise interaction of two infinitesimally small elements of direct current electricity within conductors, the force between the elements was not simply dependent on the inverse square of their distance of separation, but also depended on the angles which these infinitesimal, directional elements made with the line connecting their centers, and with each other. (Included among the effects of the angular force was the result that successive elements of current within the same conductor would tend to repel one another—the longitudinal force.)2

Ampère’s discovery did not escape the attention of Carl Friedrich Gauss at Göttingen University, the foremost mathematical physicist of the age. Within two years of the publication of Ampère’s results, Gauss turned his attention to the matter of firmly establishing their validity. His program, which was not to reach complete fruition until 1846, required, first, the establishment of an absolute measure for the force of the horizontal intensity of the Earth’s magnetism (a measure of the deviation oft he compass needle from true North). Up to that time, all measure of the strength of the Earth’s magnetism was relative, determined by counting the frequency of vibration of a particular magnetic needle. Gauss, a masterful experimentalist as well as the leading mathematician of the age, determined to apply the precision techniques of astronomical measurement to the task. The result was the instrument known as the magnetometer. In his paper of 1832, Gauss created a revolution in geophysics, showing how to determine the Earth’s magnetic force at any given location and time.3

One methodological aspect of the paper on magnetism proved defining for physics to this day. As also for his later work with Wilhelm Weber, in connection with electrical measurement, Gauss determined that the measure of magnetic force must be consistent with the units of measure of mass, length, and time, already in use in other branches of physics. Owing to the philosophical and historical illiteracy of most contemporary physics teaching, however, Gauss’s intention is nearly always misconstrued, to assume that these units are meant to be self-evident scalar quantities. Rather, as a familiarity with Gauss’s immediately preceding work on the subject of curvature would show (and, as was made perfectly explicit in the famous 1854 Habilitation thesis of his leading student, Bernhard Riemann,4) Gauss had already introduced a fully relativistic conception into the framework of experimental physics. His 1828 description of the attempt to use state-of-the-art surveying techniques to measure the angular defect of a large terrestrial triangle should make this point evident5: As elaborated 26 years later by Riemann, it is the principal task of physics to determine the nature of the non-constant curvature of the non-Euclidean, multiply-connected geometric manifold which defines the action of physical processes.

We will shortly see how, in the joint work with Weber on the determination of the fundamental electrical law, Gauss again introduces an actually relativistic conception, this time in connection with the measure of force.

The reader must be warned, at this point, against a probable misinterpretation of the import of statements made so far: That would be to assume, that, were my perfectly accurate historical statements to be proven valid to his satisfaction, it would only be necessary to correct some names and dates to make the accounts in existing textbooks more or less valid. The reader’s persisting error would involve, among other things, a confusion over our use of the term relativistic. From Kepler’s rejection of a reductionist treatment of the inverse square law of gravitation discovered by him, through the work of Leibniz, Huygens, and the Bernoullis on the common isochronic principle governing falling bodies and light propagation in an atmosphere, to Gauss’s devastating proof of Kepler’s planetary harmonics, in his discovery of the orbit of Ceres, there prevailed a conception of the foundation of physics entirely different from that taught in today’s respectable institutions of learning. Today, the term relativistic, means a formulaic correction to a system of equations and other formalisms premised on an assumed, self-evident notion of three-fold extension in space and one-fold in time. Up to, approximately, the 1881 seizure of power by Hermann von Helmholtz at Berlin University’s Physics Department, the leading minds of European continental science rejected such an underlying assumption as sophomoric.

Again, the problem is present-day historical illiteracy. It is essential that the reader grasp that the history we sketch here, is not some “alternative current” in physics. The early 19th Century discoveries, originating in Paris, and spreading into Germany through the influence of Gauss and his students at Göttingen University, were not some alternative current in physics. They remained, throughout most of the 19th century, the central line of thought. Today’s academically acceptable physics is built on a radical deviation from that line of thought, imposed, not by reason, but by political maneuverings. (Attempts to provide alternative explanation, rarely represent more than the sort of bureaucratic maneuvering which the advocate supposes to be necessary to maintain job and position.) The proximate source of the errors can be traced to the imposition of the Maxwell electrodynamics and the flawed doctrine of thermodynamics associated with Clausius and Helmholtz. The deeper differences go to the fraudulent representation of the Leibniz calculus by Euler and Maupertuis, and its effect in suppressing the earlier breakthroughs of the French Scientific Academy, as exemplified by the work of Huygens.

Second Equilibrium Experiment

Ampère constructed many different electrical apparatuses to deduce the relationship of current elements that went into his angular-dependent force law. Here, a reproduction from his 1825 work of the Second Equilibrium Experiment, in which a movable conductor, GH, is suspended between parallel vertical beams, PQ and RS, one containing a straight wire, one a sinuous wire. The experiment shows that GH does not move when current passes through all the wires.

The Fundamental Electrical Law of Weber
The experimental validation of the Ampère force was accomplished over the period 1832-1846, by Gauss’s assistant and leading experimental collaborator, Wilhelm Weber. Weber’s discovery made a revolution in physics, the full implications of which are still unrealized. Worse, today, the underlying discovery itself is almost buried.

Ampère’s experimental conclusions drew on a series of brilliant geometrical deductions, derived from the observation of configurations of current-carrying wires in which the forces, presumably, cancelled each other, producing no observable motion. To validate the Ampère Law, one needed to be absolutely sure that the lack of motion was not due to friction in the joints of the apparatus, or related effects. Gauss and his young assistant, Wilhelm Weber, devised a new apparatus, the electrodynamometer, which could directly measure, to within fractions of a second of arc, the angular displacement produced in a multiply wound electric coil by another electrical coil perpendicular to it. By reducing the effects of each of the two coils to that of circular current loops, Ampère’s simple law for the force exerted by a current loop could be applied. Placing the coils in different positions, and at different distances from each other, allowed for determinations of the electrodynamic force, geometrically equivalent to those which Ampère had deduced form his null experiments.

The results of a rigorous program of instrument building and experimentation, interrupted by Weber’s expulsion from Göttingen University as a result of the political events of 1837, were finally published at Leipzig in 1846.6 These results completely confirmed the deductions of Ampère, and also introduced a new physical principle.

The discovery of the phenomena of electrical and magnetic induction had introduced a new element into the considerations of electrical law, not taken up in Ampère’s 1826 work. There thus existed, side by side, three seemingly valid descriptions of the electrical interaction: (1) the Coulomb-Poisson law, describing the interaction of two electrical masses at rest; (2) the Ampère law, describing the interaction of elements of moving electricity, and: (3) a description of the laws of induction, elaborated by Emil Lenz and Franz Neumann. In his Fundamental Electrical Law, stated in 1846, Weber achieved the unification of these various phenomena under a single conception.

Instead of the mathematical entities, described as current elements by Ampère, Weber hypothesized the existence within the conductor of positive and negative electrical particles. He assumed that the presence of an electrical tension caused these particles to move at equal velocities in opposite directions. If one regards an Ampère current element as containing, at any given instant, a positive and a negative electrical particle, passing each other, then in the pairwise relationship of two current elements, there are four interactions to be considered. By the Coulomb law, these interactions, consisting of two repulsions and two attractions, cancel each other. However, the elementary experiments of Ampère had shown that a motion is produced between the wires, implying the existence of a force not described by the Coulomb law.

For example, two parallel conducting wires attract each other when the current in the two wires flows in the same direction, and repel each other when the opposite is the case. The situation is perfectly well explained under the Ampère force law, when one takes into account the angular relationship of the respective current elements. However, Weber’s unifying approach was to assume that the relative velocities of the electrical particles produced a modification in the Coulomb electrostatic force, to produce the resultant force between the wires. Considering all the configurations which Ampère had examined, as well as those arising from the phenomena of induction, he was able to formulate a general statement of the Fundamental Electrical Law. This showed that the general law describing the force of interaction of two electrical particles, depends upon the relative velocities and the relative accelerations of the particles.7 The Coulomb electrostatic law thus becomes a special case of Weber’s general law, when the particles are at relative rest.

It is not too difficult to see that Weber’s Fundamental Electrical Law, almost unknown today, is a statement of a relativistic law of physics, long predating the statement of relativity we are accustomed to.8 Here it is the force, rather than the mass, which varies with the relative motion. But, not only does it predate the Einstein formulation, it is methodologically far superior. One can, in various ways, attempt to show an equivalence of the two statements, but the usefulness of such efforts is doubtful. The problem lies elsewhere. The two statements lie in two entirely different domains. One is a continuation of the Leibnizian current of physics; the other, whatever the intentions, serves to hide errors embedded in the assumptions underlying the Maxwell equations.

Schematic magnetometer

Left, a schematic diagram of the magnetometer designed by Carl Friedrich Gauss in 1831, to measure, for the first time, the absolute intensity of the Earth’s magnetic force. Needle 1 tends to produce an angular deflection in the second, oscillating needl«, while the Earth’s magnetism attempts to realign it with the magnetic meridian. The resulting deflection is measured by reflection of the meter stick into the telescope. By comparing this deflection of needle 2 to the oscillation of the same needle, when acting solely under the influence of the Earth’s magnetism, the absolute intensity of the magnetic force is determined.

At right is a portable magnetometer built for Wilhelm Weber in 1839.

portable magnetometer


Historical Collection of Göttingen University I. Physical Institute
The electrodynamometer, constructed in 1841, which Wilhelm Weber used in the final determination of the validity of Ampere’s electrodynamics. It consists of two perpendicular electrical coils. The outer coil is suspended in such a way that its rotation, under the influence of the inner coil, can be precisely determined by observing the deflection of the mirror image of a meter stick in a telescope, as in the Gauss-designed magnetometer. The inner coil can be removed, and placed at various distances.

The Weber Constant
In the Weber Electrical Law, there is a relative velocity, corresponding to the constant c in his formula, at which the force between a pair of electrical particles becomes zero. The Weber-Kohlrausch experiment, carried out at Göttingen in 1854, was designed to determine this value. It was found to be experimentally equal, in electrodynamic units, to the product of the velocity of light, in vacuo, with the square root of 2. That value, became known as the Weber constant. In electromagnetic units, it was equal to the light velocity. Bernhard Riemann, who participated in the experiment, soon wrote up the obvious conclusion of a deep connection between light and electrodynamic, or electromagnetic phenomena. What was not obvious, was the answer to a question which Gauss had insisted, in his 1845 correspondence with Weber, be a prerequisite to further progress. That was to find a constructible representation of how the propagation of the electrodynamic interaction occurs.9

What Maxwell is famously celebrated for, unifying the representation of light and electromagnetic phenomena using a wave conception, was precisely what Gauss—and Ampère before him, had rejected as an oversimplification. Ampère had been so close to the development of the modern wave theory of light, that its founder, his good friend Augustin Fresnel, lived in his Paris apartment at the same time that Ampère was carrying out his electrical researches. To suppose that Ampère, and later Gauss, did not consider a wave representation for electromagnetic propagation is absurd. In order to establish his theory, Maxwell had to disregard the most crucial questions and anomalies that had arisen in the decades-long study of these phenomena by the greatest minds before him. Foremost among these were the angular (or relative velocity) dependency of the electrodynamic force, and the little problem of where gravitation should fit in.

The possibility of subsuming the phenomenon of gravitation under electrodynamics, came up for serious discussion early in this history. One of the more widely discussed contributions was a memoir of about 1830 by O.F. Mossotti, a French physics teacher at the University of Buenos Aires.10 Mossotti proposed to account for gravitation in the following way: If matter is assumed to be constituted of equal amounts of positive and negative electricity, then, by the usual interpretation, there would be a cancellation of the attractive and repulsive forces. However, if it be assumed that the attractive forces between particles of opposite electrical charge, slightly exceed the repulsive forces of the like particles, a universal tendency for attraction would result.

Weber gave serious consideration to the Mossotti hypothesis. In a posthumously published manuscript on the relationship of electricity and gravitation, he discussed the extreme difficulty of experimentally determining whether such a small difference between attractive and repulsive forces exists.11

In the same memoir, Weber reviews the work of several astronomers, who attempted to apply his Fundamental Electrical Law to correct the law of gravitation, by including terms for the relative velocities and relative accelerations of a pair of bodies. One of the glaring anomalies in the Newton-Laplace theory of gravitation was its inability to accurately predict the advance of the perihelion of the planets, of which Mercury’s is the largest. (The phenomenon is famous as being one of the foundational proofs for general relativity.)

In 1864, the Göttingen astronomer C. Seegers proposed to examine the advance of the perihelion from the standpoint that the gravitational force be represented in the same way as the Fundamental Electrical Law.12 Thus, the relative velocities and accelerations of the bodies of the solar system would have to be taken into account, and the factor 1/c2 introduced as a correction. Eight years later, Prof. Scheibner in Leipzig determined a secular variation of 6.73 arc-seconds for the perihelion of Mercury, attributable to the application of the Weber law. In 1872, Tisserand found the value 6.28 seconds for Mercury, and 1.32 seconds for Venus, by applying the Weber law.13

Another approach to the unification of gravitation with the Ampère-Gauss-Weber electrodynamics, was taken at the beginning of the 20th Century by the Swiss mathematical physicist, Walther Ritz. After brilliant successes in spectroscopy at Göttingen, Ritz launched an attack on the electrodynamics of Maxwell and Lorentz, and attempted to revive the abandoned approach of Gauss, Weber, and Riemann. In a short paper on gravitation, he suggested that the net effect of the electrodynamic forces between two electrically neutral bodies would be an attraction. His approach was not that of Mossotti; rather, he seems to be considering the internal motions of the electrical particles in the atoms as generating such a net effect. The paper is all too short; Ritz died in 1909 at the age of 31. (Deviations in the gravitational force, detected at eclipses, and other anomalous effects suggesting the need for radical revamping of accepted theory continue to make themselves known. The recent work of Maurice Allais, Benedetto Soldano, and Shu-wen Zhou is notable.14)

Ritz was not alone in his dissatisfaction with the oversimplification of the Maxwell electrodynamics. From the first 1820 breakthrough hypothesizing the origin of magnetism in microscopic electrical currents, the Ampère electrodynamics was seen as a means of gaining insight into the microphysical domain. The enormously complex task of adducing the atomic structure from such indirect evidence as that provided by spectroscopy, came to an abrupt, abnormal halt about the time of the 1927 Solvay conference, where Bohr’s great oversimplification of atomic structure was imposed by political thuggery of the worst sort. Here again, we come to the importance of a virtually unknown aspect of Weber’s work.

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Limiting Velocity and Critical Length
As for electrodynamics, so for the history of atomic theory, the modern teaching is largely a fairy tale. A brief look at two crucial matters will establish this point beyond contradiction, and may help orient the reader to finding a way out of the present impasse. If it appears, at first, that we have “dug him in deeper,”by making matters more complicated than they might have already seemed, we are confident the feeling will be only temporary.

The point here is best summarized by reference to the last two of the memoirs, published in Weber’s lifetime, under the title Elektrodynamische Maassbestimmungen (Determinations of Electrodynamic Measure). The 1870 memoir, available in English, was the first to come to this writer’s attention, about a decade ago.15 The immediate topic is Helmholtz’s objection, that Weber’s Electrical Law could lead to the possibility of infinite work arising from a finite amount of work. Weber shows that for Helmholtz’s fears to be realized, electrical particles would have to move at enormous relative velocities, exceeding the constant c. He thus arrives at a concept of a limiting velocity, quite similar to that found 35 years later in the Special Theory of Relativity, yet arrived at by an entirely different process than that which leads Einstein to this assumption. (Again, the usual warnings apply: Any attempt to find an equivalence or interpolation, as by algebraic means, between the Ampère-Gauss-Weber electrodynamics, and today’s Brand X, is fruitless. To achieve any useful understanding, the reader must relive the original discovery as if it were his own).

More startling than the immediate answer to Helmholtz’s objection, are the conclusions Weber is led to in his preliminary summary of the Fundamental Electrical Law. Here, he introduces for the first time the consideration that the electrical particles possess not merely a quantity of electricity (the magnitude we today call charge), but also mass. When the consideration of mass is introduced into his velocity-dependent electrical force equation, it results that there is a critical length below which the force of repulsion between two electrical particles is changed to attraction, and vice versa! The Weber critical length has the value:


It is among the delightful ironies of the official cover-up known as modern scientific historiography, that the expression for the classical electron radius (a concept which is not supposed to come into existence for another 30 or more years), falls out of Weber’s expression—indeed, as a trivial case!

It gets more interesting. Weber has already dared, in the 1870 paper, to conceive the notion we know today as the proton-electron mass ratio, which leads him to wonder as to the possible motions of the different configurations of particle pairs. It turns out that, according to his relativistic electrical law (one which was never considered in the accepted, modern formulations of atomic theory), it is possible to develop an orbital system for the case of a lighter electrical particle of one sign, orbiting a heavier particle of the opposite sign! It is also possible for two similar particles of the same sign to develop a closed system of oscillations along the straight line connecting them.

We leave to a future time, the treatment of the last major accomplishment of Weber, the refutation of Clausius’ thermodynamics and the Helmholtz Energy Principle.16 The problem with the fraud known as modern, academically accepted science, is not merely that credit has not been given for these prior discoveries. Far more devastating is that, in the modern formulation of notions similar to those that Weber had derived far earlier, there is no lawful derivation. We fly, rather, by the seat of our pants, hoping to reach the destination intact.

—Laurence Hecht

Notes ____________________________________

1. Johannes Kepler, New Astronomy, William Donahue, transl. (Cambridge: The University Press, 1992) p. 395

2. André-Marie Ampère, “Memoire sur la théorie mathématique des phénomenes électrodynamiques uniquement déduite de l’experience,” in A.M. Ampère, Electrodynamiques, uniquement déduite de l’experience,” (Paris: A. Hermann, 1883). A partial English translation appears in R.A.R. Tricker,5Early Electrodynamics: The First Law of Circulation (New York: Pergamon, 1965) pp. 155-200. ”A review of the Ampère-Gauss-Weber electrodynamics appears in Laurence Hecht, “The Atomic Science Textbooks Don’t Teach,” 21st Century, Fall 1996, pp. 21-43.

The law of force which Ampère derives is:


3. Carl Friedrich Gauss, Die Intensität der Erdmagnetischen Kraft auf absolutes Maass zurükgeführt, ed E. Dorn, Ostwald’s Klassiker der Exakten Wissenchaften, Vol. 53 (Leipzig: Wilhelm Engelmann, 1894). English translation in 21st Century Science archive (The Intensity of the Earth’s Magnetic Force, Reduced to Absolute Measure).

4. Bernhard Riemann, “On the Hypotheses Which Lie at the Foundations of Geometry,” in David Eugene Smith, ed., A Source Book in Mathematics (New York: Dover Publications, 1959) pp. 411-425.

5. Carl Friedrich Gauss, General Investigations of Curved Surfaces, transl. Adam Hiltebeitel and James Morehead (Hewlett, N.Y.: Raven Press)

6. Wilhelm Weber, “Elektrodynamische Maasbestimmungen: über ein allgemeines Grundgesetz der elektrischen Wirkung,” Werke (Berlin: Julius Springer, 1893) Bd. 3, pp. 25-214. English translation in 21st Century Science archive (Determinations of Electrodynamic Measure: Concerning a Fundamental General Law of Electrical Action).

7. equation

8. More than a decade before the publication of Weber’s 1846 paper, one can find an 1835 entry in Gauss’s Notebooks, showing a hypothesized form of the electrodynamic force law, dependent on relative velocity and acceleration, that is essentially equivalent to that which Weber used in the 1846 publication. Interestingly, the Gauss formulation appears on the same page as an alternative formulation, which was the one James Clerk Maxwell chose to use in his text Treatise on Electricity and Magnetism to falsely imply a difference in electrodynamic views among the three collaborators, Gauss, Weber, and Riemann.

c. “Text of the Gauss-Weber 1845 Correspondence,” (in “The Atomic Science Textbooks Don’t Teach,”) 21st Century, Fall 1996, pp. 41-43.

10. O.F. Mossotti, “On the Forces which Regulate the Internal Constitution of Bodies,” in R. Taylor, ed. Scientific Memoirs, Vol. 1, pp. 448-469.

11. Wilhelm Weber, “Elektrodynamische Maassbestimmungen, insbesondere über den Zusammenhang des elektrischen Grundgesetzes mit dem Gravitationsgesetze,” Werke (Berlin: Springer, 1894), Bd. 4, pp. 479-525. English translation in 21st Century archive, (Determinations of Electrodynamic Measure: Particularly in Respect to the Connection of the Fundamental Laws of Electricity with the Law of Gravitation).

12. C. Seegers, “De motu perturbationibusque planetarum secundum legem electrodynamicum Weberianam solem ambientium,” Göttingen, 1864

13. Tisserand, “Sur le mouvement des planètes autour du Soleil d’apres la loi electrodynamique de Weber, Compt. rend. Sept. 30, 1872.

14. Maurice Allais, “Should the Laws of Gravitation Be Reconsidered,” 21st Century,jFall 1998, pp. 21-33. Benedetto Soldano, “Space Probe Acceleration Anomalies Suggest Nonequivalence,” 21st Century, Summer 1999, pp. 66-69, 75. `hu-wen Zhou, “Abnormal Physical Phenomena Observed When the Sun, Moon, and Earth Are Aligned,” 21st Century, Fall 1999, pp. 55-61.

15. Wilhelm Weber, “Elektrodynamische Maasbestimmungen, insbesondere über das Princip der Erhaltung der Energie,” (1871), Werke (Berlin: Springer, 1894), Bd. 4, pp. 247-299. English translation in Philosophical Magazine, 4th series, Vol. 43, No. 283, January 1872, pp. 1-20, 119-149 (“Electrodynamic Measurements—Sixth Memoir, relating specifically to the Principle of the Conservation of Energy”).

16. Wilhelm Weber, “Electrodynamische Maasbestimmungen, insbesondere über die Energie der Wechselwirkung,” Werke, Bd. 4, pp. 362-412.

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