The Fraud Of The Inverse Square Law

by Hunter Cobb

Conference speech, Schiller Institute Conference, February, 1997. Printed in The American Almanac, April 7, 1997.

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Oersted's Discovery What Ampere Did What Ampere Discovered Weber Invented ... A Significant Irony Figures

What I want to do in the next thirty minutes is destroy one of the most sacred cows in all of physics--the inverse square law. I've made a quick survey of the audience and I suspect I may not completely succeed in this in thirty minutes. I don't see anybody over two hundred years old, so you probably haven't escaped indoctrination in the Enlightenment school of physics. But what I hope to do, at least, is provoke a little bit of doubt in your mind about the idea of a mathematical formula being a fundamental law of the universe.

So what is the inverse square law? There are actually two of them in your standard physics textbook. Here's what they look like.

Oersted's Discovery

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In 1819, the Danish scientist Hans Christian Oersted made a very important discovery, which clearly demonstrated a connection between electricity and magnetism, which we will demonstrate here. (Fig. 2) What you see is a compass, which has a magnetic needle, and we have a wire, that right now has no current going through it, right next to the compass. Now, we'll connect the circuit. As you can see, the needle is deflected.

So that's what Oersted did, and news of this discovery created quite a stir throughout the scientific community, particularly in France. Many scientists of the empiricist school made measurenents of this deflection of the compass needle and made calculations of the forces involved. But they didn't make any new hypotheses about what was going on.

That remained for Andre-Marie Ampere, who did make a hypothesis. He said, ``If electric current creates a magnetic effect, maybe what a magnet is, is simply a form of electric current.'' That is, he proposed a revolutionary conception: that a bar magnet consists of an amalgam of microscopic current loops, lined up in the same direction. This is essentially the model of a magnet we have today, with the current loops the orbits of electrons. (Fig. 3) The top picture shows a bar of iron that is not magnetized, and you see the little circuits going around in a disordered way, and at the bottom, you see a magnet with the little circuits all lined up. So this was Ampere's hypothesis about what was going on in a magnet.

Now, how do you test such a hypothesis? What Ampere was proposing was the existence of what he called a magnetic molecule, something on a scale that was too small to be seen, even with a microscope.

Ampere conducted a number of ingenious experiments to test this hypothesis. One configuration he devised was a helical coil of wire, which he called a solenoid, which he figured would behave like a bar magnet. That is, while his hypothesis said a bar magnet consists of many tiny current loops, all lined up in the same way, a helix of current on a macro scale--large enough to see and construct--should behave like a magnet, as we'll see in the next demonstration. First we'll demonstrate with a bar magnet, and we'll use just a simple nail which is magnetized. As you can see, one end of the nail attracts the north pole of the compass and the other end of the nail repels the north pole. So in the magnet, one end is a north pole and the other end is a south pole. Now we'll show what happens with the solenoid, which we will now hook up. (Fig. 4) It's a fairly weak solenoid, so you have to get it pretty close. O.K. There you see an attraction--I think. Sometimes these experiments don't work the way they're supposed to. Is the current on there? All right, I think you can see a little bit of an attraction there. Now flip it over and show the other end [of the solenoid] and see what that does. We may have a loose connection there somewhere. [After a few more tries, the compass needle deflects away from the other end of the solenoid.]

This actually points out one of the real problems of scientists. You have really be committed to what you're looking for or you're not going to find it! There are so many variables that come in. And it's a lot easier if you know what you're looking for, than if you're a scientist investigating something new.

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What Ampere also did is measure the force between two parallel wires. Here I have a device to show the force between currents in parallel wires. (Fig. 5) You can see the two parallel loops of wire. When I turn on the current, it will flow through both loops, and in the same direction. I have this hooked up to the equivalent of a car battery. It's a fairly hefty current source, so I won't leave it on very long. When I connect up the circuit, you can see that the wires are attracted to each other. Now with the switch on top of the box, I can change the direction of the current in one of the loops, so the current will go in opposite directions in the two loops. Now you can see the wires repel each other.

Ampere made a further hypothesis concerning this interaction, which gave a lot of headaches to Helmholtz, Maxwell and others. He asserted that the force between two wires can be viewed as the sum of the forces between infinitesimal current elements. Normally, those of the Newtonian school do not mind breaking up the world in this way and looking at action in the universe as a simple summation of pairwise interactions. But what Ampere discovered was that the force between two current elements depended not only on their distance, as in the inverse square law, but also on their angular position. (Fig. 6)

The diagram shows current elements in different relative positions. One word about this diagram. What we're looking at now is current elements all in one plane. The line between A and C is not meant to imply a third dimension. Think of two current elements: one is fixed at position A; the other can be at B or D or anywhere in between. If we keep the distance between the two elements the same, we find that the force between the elements depends not just on distance, but also on angular position.

Realize that what Ampere is measuring here is not something which can be measured directly. Electric current doesn't exist in isolated elements--you have to have a complete circuit. So what Ampere did is design experiments out of complete circuits, but arranged geometrically so that the magnetic effect of part of the circuit would be cancelled out by another part of the circuit. Thus he was able to measure indirectly what cannot be measured directly.

What Ampere Discovered

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What Ampere discovered is that the force between elements in positions A and D, which he called the longitudinal position, is one half the magnitude and in the opposite direction compared to the force between A and B, the parallel position. In other words, if the force between A and B is an attraction, the force between A and D will be a repulsion of half the intensity. At a certain position in between, the force would be zero. From these studies Ampere worked out a general formula for the force between two current elements in any positions relative to each other.

The Enlightenment physicist Hermann Grassman called Ampere's formula ``highly improbable.''

For a decade, Ampere's work, including his highly disturbing discovery that force between current elements does not obey a simple inverse square law, was either ridiculed or ignored.

In 1832 what began was a very fruitful collaboration between the young scientist Wilhlem Weber and the old man of the Leibnizian tradition at Gottingen University, Carl Friedrich Gauss. They did a number of experiments including inventing an electromagnetic telegraph. Then Weber began a long series of experiments on his own to confirm Ampere's discoveries.

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Weber invented a device called an electrodynamometer to accurately measure the force between very small currents, using two coils of current- carrying wire. By creating coils of hundreds of turns of wire, the magnetic effect of a very small current would be magnified. The electrodynamometer utilized an ingenius principle, developed earlier by Gauss, for measuring the earth's magnetic field, where one magnet was suspended by a thread in a north-south orientation. A second magnet, brought into proximity with the first, would cause the first magnet to rotate. Here is a diagram viewed from above. (Fig. 7) At the the top left is the magnet hanging by a thread. At the right is the second magnet.

The scientist observes the motion of the first magnet by means of the device at the bottom--a telescope and meter stick. (Fig. 8) A small mirror attached to the rotating magnet faces the telescope, so that the scientist looking at the mirror will see the image of a point on the meter stick. A slight rotation of the magnet will register as a significant shift in the point on the meter stick seen by the scientist.

Weber used a similar device, with a rotating coil of wire, suspended from above, instead of the rotating magnet. I'll demonstrate with a crude model. (Fig. 9) What you can see is two coils of wire, one fixed to the bottom of the box, and a second, moveable coil, inside the fixed coil and at a right angle to it. The moveable one is hanging from the top of the box, suspended by the two wires carrying current to the coil. Attached to the hanging coil is a small mirror. For this demonstration, rather than using a telescope and meter stick, I have a small laser shining on the mirror, so that the beam is reflected onto the ceiling.

Understand: the purpose of the light beam and mirror is simply to greatly magnify the effect of a small rotation of the coil. What I have here is two small c-cell batteries and a switch to connect the circuit. I recommend you watch the spot on the ceiling as I connect the switch. [The spot on the ceiling jumps about a foot.] I'll just point out, the current is fairly small from these two batteries; if I hooked them up to the other device [the parallel loops], you wouldn't have seen a thing.

With equipment similar to this, Weber was able to measure with much greater accuracy the forces between two current-carrying wires, and to confirm Ampere's force law. He then proceeded to formulate a more general law, based on a unified conception of force between two charges, in effect combining the static force law (the inverse square law; also known as Coulomb's law) with the force from the motion of the charges (also known as the magnetic force).

Rather than conceiving of electric current as a flow of fluid, as Ampere had, Weber used the model of his associate Gustav Fechner, who proposed that an electric current consists of charged particles moving through a wire, with positively charged particles moving in one direction and negatively charged particles moving in the opposite direction. Today the general model is that the positive charges are relatively stationary and only the negative charges move. Actually, it was Weber who proposed this modification.

A Significant Irony

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Consider now the earlier demonstration with the two parrallel loops. It's a simple experiment, but with a significant irony. Think of the wires hanging there with no current passing through them. There are positive and negative particles in each wire, but there are equal numbers of each, so there is no attraction or repulsion. Then we connect the circuit; the particles move. There are still equal numbers of positive and negative particles, but something has changed. A moving charge is fundamentally different from a static charge. One could say a new dimension has been added to the curvature of space when the charges move. That's the view that Weber tended toward. On the other hand, one could simply tack the label ``magnetism'' on the phenomenon and be done with it. James Clerk Maxwell did the latter and became the darling of the British Royal Society.

At one point, Weber had doubts about his approach, and it was the crucial intervention of Gauss which kept him on track. With renewed confidence, he pursued the implications of his formula and he arrived at some startling conclusions:

  1. Perhaps most startling is that under certain conditions, like-charges would no longer repel, but rather attract each other. This reversal of the Coulomb force would occur only at a very small distance of separation between the charges, on the scale of subatomic particles. Today's textbooks posit the existence of a new force, ``out of the blue,'' in order to explain why the atomic nulceus doesn't fly apart. They call it, creatively, ``the strong force.'' Somehow in the nucleus, positively charged particles sit peacefully right next to each other, at least according to the accepted model of the atom, so a ``strong force'' had to be invented to counteract the Coulomb force of repulsion between the positively charged particles. This is the trouble physicists have gotten themselves into by ignoring the work of Weber a century and a half ago.

  2. Weber's formula also predicted a limiting or maximum velocity for charged particles, related to the speed of light.

  3. Extending Ampere's hypothesis of minute current loops, Weber worked out the laws of motion for electrons orbitting an atomic nucleus. This was a couple of decades before the so-called ``discovery of the electron.''

  4. He even considered the likely connection between the oscillations of atomic particles and the frequency of light--a crucial conception in solid state physics today, utilized, for example, in the design of lasers.

Consider this remarkable work! With equipment only somewhat more refined than what I've domonstrated here today, Weber was making discoveries on the scale of sub-atomic particles, many orders of magnitude smaller than anything we can see. Like Eratosthenes' measurement of the unseeable circumference of the earth, Weber was measuring the unseeable in the microscopic realm.

Crucial to his success was the method of hypothesis. As Nicolas of Cusa put it, there is no measurement without hypothesis. Even in a simple task of measuring a length we are faced with a question: where does the yardstick come from?

We may fool ourselves, saying four-dimensional space-time is self-evident and that it's frivolous to ask where the yardstick comes from. But throughout history the scientists who did ask that question were the ones who made the breakthroughs.

Gauss understood this principle. He also understood that the fundamental lawfulness of the universe resides at this level of hypothesis, not at the level of a mathematical formula.

Consider the use of the term ``force.'' We tend to think of force as a cause of motion. But for Gauss, as for Kepler before him, speaking of forces of attraction and repulsion was a kind of limited shorthand for describing aspects of a higher level of ordering in the universe. This higher order lawfulness was the basis for Gauss's critical intervention with Weber when his confidence faltered.

Also intimately related to the method of hypothesis is the matter of the scientist's passion to pursue an investigation into the unknown, sometimes over many years and with hostility from academic authorities. The confidence comes from the scientist seeing himself, not as a passive observer watching from the outside, but rather as a necessary participant in the one ongoing universal experiment.

While Weber was making these remarkable discoveries, he was pelted with criticism. Helmholtz and Clausius said his formula would violate the law of conservation of energy. Maxwell formulated his famous four equations to impose an algebraic straightjacket on electromagnetism in the same way Newton did to Kepler's planetary mechanics. One of Maxwell's equations was called Ampere's law, but it is not what Ampere developed! It explicitly eliminates Ampere's longitudinal force, and thus conveniently gets rid of all the messy singularities which result from it.

All of Weber's critics insisted that a scientific law must be of the form of a simple algebraic formula--uniformly applicable over all ranges from the infinitesimal to the astronomical. This Enlightenment parody of scientific lawfulness is the unquestioned dogma of academia today. That's what you and I were taught. Perhaps this presentation has opened a small window on the real universe.

Let me conclude by saying that the person who should have been here giving this presentation couldn't make it because he is being held prisoner by the state of Virginia on a fraudulent 33-year sentence. Larry Hecht asked me to do this presentation after I read his article in 21st Century Science and Technology and got excited about it enough to write him a letter, asking him a bunch of questions. I for one, am very greatful to Larry, for keeping his mental faculties aggressively alert despite his unhospitable circumstances. I would urge all here to help further the cause of science by stepping up our efforts to bring about the early release of Larry and the other LaRouche prisoners.


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Fig. 1 [ Inverse square laws]
``The inverse square 'laws' in a standard physics text. The top one is for electrostatic force, the bottom one for gravitation.

Fig. 2 [ Two pictures, one with needle parallel to wire, the second with needle deflected.]
``Oersted's experiment for the first time showed the connection between electricity and magnetism.''

Fig. 3 [Diagram of current loops in non-magnet and in magnet]
``Ampere's hypothesis was that a permanent magnet is composed of many microscopic current loops. The top diagram shows a non-magnetized bar of iron, the bottom diagram a magnetized bar.''

Fig. 4 [Picture of solenoid and compass.]
``Ampere believed a helix of current on a scale large enough to see would behave like a bar magnet. Here we see a coil of wire, which Ampere called a solenoid. It deflects the compass needle just like a bar magnet.''

Fig. 5 [Two pictures of box with current loops, one with loops attracted, the other with loops repelling.]
``Flexible loops of wire are attracted to each other when current flows through them in the same direction. They repel when the current flows in opposite directions.''

Fig. 6 [Diagram of current elements in different relative positionsl]
``Ampere demonstrated that the force between current elements depends not only on their distance and the intensity of the current, but also on the angular position of one with respect to the other. If the force between elements at A and B is an attraction, the force between elements at A and D will be a repulsion of half the magnitude. (The line to C is in the same plane as the other lines.) This deviation from a simple inverse square relation was considered ``highly improbable'' by Enlightenment physicists.

Fig. 7 [Diagram of Gauss magnetomenter]
``View from above of a magnetometer, developed by Gauss to measure the earth's gravitation. The magnet at the top left is suspended by a thread, so it can rotate when another magnet is brought nearby. At the bottom of the diagram is a telescope and meter stick device used by the scientist to view the motion of the suspended magnet. He looks at a small mirror attached to the magnet and sees reflected a point on the meter stick. A small rotation of the magnet will register as a significant shift in the point on the meter stick seen by the scientist.

Fig. 8 [Picture of telescope and meter stick (p. 23 in Fall '96 21st Century) ``Telescope and meter stick device used with Gauss magnetometer and with Weber's electrodynamometer.''

Fig. 9 [Picture of electrodynamometer]
``A simple electrodynamometer. The larger coil is fixed to the bottom of the box. The smaller coil is suspended from the top of the box by the wires that conduct electricity to it. A small mirror is attached to the suspended coil. When current flows through both of the coils, the suspended coil is slightly deflected. The motion is made more visible by using a laser beam shining from the mirror onto the ceiling.


[Photo of Hunter Cobb]
EIRNS/Stuart Lewis [photo of L. Hecht]
Laurence Hecht, author of "The Significance of the 1845 Gauss-Weber Correspondence" in 21st Century Science & Technology, Fall 1996, and the inpiration for this speech; currently a political prisoner in Virginia.

[statue of Gauss & Weber]
Wilhelm Weber (standing) and Carl Friedrich Gauss are memorialized in this statue at Göttingen Univeristy.

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The preceding article is a rough version of the article that appeared in The American Almanac. It is made available here with the permission of The New Federalist Newspaper. Any use of, or quotations from, this article must attribute them to The New Federalist, and The American Almanac.

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