ěrsted's Missed Opportunity
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In 1820 Hans Christian ěrsted produced one of the purest examples of the empirical-inductive Scientific Method that we all learned in school. Even better, he performed the key task of the method, the hypothesis-testing experiment, as a classroom demonstration for his students. That demonstration astonished all who saw it or heard of it because it provided the first solid verification of the long-held suspicion that electricity and magnetism share an intimate relation of each to the other. But ěrsted could have gone on to achieve something even more spectacular: he could have taken an abstraction of his experiment and deduced Michael Faraday's law of electromagnetic induction, eleven years before Faraday discovered it more or less by accident.
That assertion may surprise some people: it certainly would have astonished me many years ago. A certain folklore has it that ěrsted made his discovery entirely by accident, that he benefitted from one of the purest examples of serendipity in modern science. But ěrsted's own account of the matter, backed up by his students, leaves no doubt that he planned his discovery in advance, as a good scientist should attempt to do.
K°benhavn Symphony: The Apothecary's Apprentice
Four steps comprise the standard Scientific Method, named as the classical Observation, Hypothesis, Experiment, and Theory that we learned in grammar school. We call that procedure inductive because it involves researchers drawing general conclusions about phenomena from limited sets of examples of those phenomena while ignoring the possibility that a counterexample might exist in some as yet unexamined case. For all the uncertainty that caveat implies, the Scientific Method has provided solid information on the nature of Reality and ěrsted used it to good effect.
First Movement: Observation
Before Europe had a network of well-marked roads, travelers carried navigational aids, including a magnetic compass. Among the tales that travelers would tell to astonish and delight their listeners were accounts of compasses going mad during thunderstorms. As lightning flickered overhead and thunder boomed off the mountainsides, they would say, a compass needle, instead of pointing steadily in one direction, would twist and turn. Even more curiously, compass needles only danced for thunderstorms and not for common rainstorms. Sailors would add their own variation on such stories: whenever lightning struck a ship's mast, the ship's compass jumped. Such anecdotes comprised the first set of observations that ěrsted presented to his students.
ěrsted's second set of observations originated in June 1752, when Benjamin Franklin applied the Scientific Method to a few observations of his own. In the 1740's Franklin had been studying static electricity (a study that was quite popular at the time) and had noticed that electric sparks resembled nothing so much as miniature lightning. That resemblance led him to hypothesize that lightning is, in fact, a giant electric spark. He contrived an observation to test that hypothesis by flying a kite into the leading edge of an approaching thunderstorm. When he saw that touching the key dangling from the kite's string to the charging knob on a Leyden jar made the jar's metal-foil leaves spread apart, he inferred that the indicated electric charge had come from the approaching storm. Having thus tested and verified his hypothesis into theory, Franklin could state with confidence that thunderstorms carry electric charge and, because they move, electric currents. He could also pull in his kite before he got blasted by lightning.
Second Movement: Hypothesis
In June of 1820, while giving an evening lecture on electricity, ěrsted presented the above observations to his audience and then drew what we would regard as the obvious inference: thunderstorms exert magnetic forces; thunderstorms carry electric currents; therefore, something associated with electric currents exerts magnetic force (at first ěrsted believed it was the incandescence associated with the most intense currents, those involved in lightning). In making that inference ěrsted acted out one of the primary functions that Francis Bacon attributed to the Bensalemite House of Solomon in his novel "The New Atlantis".
Bacon described the people of the undiscovered island of Bensalem sending Merchants of Light out into the world to gather observations and facts and to bring them back to the House of Solomon. In that great research institute, the model for England's Royal Society, natural philosophers would organize the information into lists and then wreak new knowledge from correlations among the lists. One list, for example, might comprise accounts of compass needles dancing during thunderstorms, another might comprise reports of experiments confirming the existence of electricity in thunderstorms, and so on.
Making correlations does not occur in a mental vacuum. You may well ask why ěrsted chose to correlate the magnetic disturbances associated with thunderstorms with those storms' electric currents. Why didn't he hypothesize, let's say, the thunder as the source of the magnetic effect? ěrsted's own reason, which he gave in his own report, was that he had in mind a preconceived notion that electricity and magnetism are related to each other. That notion was not unique to ěrsted: it had been current in European scientific circles for over two hundred years. As far back as 1600 William Gilbert, in his book De Magnete, speculated that electricity and magnetism might be two aspects of a single phenomenon. That speculation is reasonable given that what was known of electricity and magnetism at the time was that they are rare, mysterious, both repulsive and attractive, and obtained by stroking things (iron on lodestone for magnetism and glass on fur for electricity). By ěrsted's time that knowledge had not changed enough to dispel the suspicion, so it served as a template onto which the relevant observations accreted by simple association to generate ěrsted's hypothesis.
Up to this point ěrsted had not done anything that other truth-seekers had not done in the preceding millenia in devising stories aimed at explaining the workings of Reality. It was the next step that ěrsted took that sets the Scientific Method well apart from older myth-making techniques.
Third Movement: Experiment
We use hypothesis as a fancy Greek name for an educated guess. We hope that it is a well-educated one, but it is nonetheless a guess. In order to go beyond by guess or by Golly ěrsted had to put his hypothesis to a potentially fatal test. He had to arrange to compare what his hypothesis said to what Reality actually does.
Contriving an observation that would put his hypothesis to a proper test was easy for ěrsted. All he had to do was to put a wire near a compass, pass an electric current through the wire, and turn the current on and off to see whether the presence of the current affected the compass. Well, easy to conceive, not so easy to accomplish, however simple it was. Remember that line in "Back to The Future", in which a scientist in 1955 starts out by saying, "Maybe in 1985 you can buy plutonium at your corner drugstore,..."? Actually, you can go into your corner drugstore (or its modern supermall equivalent) today and buy something, for only a few bucks, that would be the envy of ěrsted and his contemporaries - an electric battery.
Prior to 1800 no one could have made ěrsted's discovery, because prior to 1800 no one could have performed ěrsted's experiment. All that natural philosophers knew about electricity in 1800 they had obtained from experiments involving static electricity or brief pulses of current, either the little ones that could be had from laboratory accumulations of static electricity or the big ones of Jove's arrows, drawn from darkling skies with kites (with sometimes fatal results). But ěrsted's experiment required the use of a strong, sustained electric current and that only became available in 1800.
Let's not discount the value of serendipity here. In 1791 Luigi Galvani published an account of experiments that he had performed on frogs' legs. He had conducted experiments aimed at elucidating the "animal electricity" that he and his contemporaries had inferred from their observations that discharging a static electric charge from a Leyden jar through animal muscle made the muscle twitch. Galvani had noticed that his frogs' legs also twitched when he touched them with an instrument made from a metal different from the metal in the hooks supporting the frogs' legs. Alessandro Volta took the inference that dissimilar metals contain electric fluid under different pressures and invented the electric pile in 1800. By alternating zinc and copper discs, with cloth or thick paper soaked in electrolytic solution between them, he created the first electric battery and gave Nineteenth Century scientists one of their most powerful tools for their examination of Nature.
Shortly after Volta's invention became known, ěrsted devised his own version of it. Nearly twenty years later he put it to good use. He mounted a thin platinum wire between two posts, laid a compass near the wire, and connected the wire to a convenient Voltaic pile. Electric current flowed and the compass needle swung away from north, a simple motion that would have flabbergasted anyone seeing it for the first time. Even better, when ěrsted interrupted the flow of the electric current, the needle swung back to its original orientation.
Fourth Movement: Theory
Here ěrsted put it all together. Here ěrsted analyzed the facts that he had gathered from his experiments and drew from them his statement of new knowledge:
"It is sufficiently evident from the preceding facts that the electric conflict is not confined to the conductor, but dispersed pretty widely in the circumjacent space. From the preceding facts we may likewise collect that this conflict performs circles; for without this condition it seems impossible that the one part of the uniting wire, when placed below the magnetic pole, should drive it towards the east, and when placed above it towards the west; for it is the nature of a circle that the motions in opposite parts should have an opposite direction."
From Bern Dibner "Oersted and the Discovery of Electromagnetism" (New York, Blaistell Pub. Co., 1962) page 21 translating from the original Latin "Experiments on the Effect of a Current of Electricity on the Magnetic Needle", Annals of Philosophy (1821 July 21), pages 71-76.
That reads truly weird. What does ěrsted mean by an "electric conflict"? And why has he not mentioned the magnetic field that the electric current generates? Electric conflict seems to have denoted some part of the electricity that leaked out of the wire and swirled around it to push on the magnetic poles in the compass needle. The concept of a magnetic field, a kind of stress in space that comes from magnets and electric currents and exerts force upon magnetic poles or electric currents, did not exist yet.
We may note that at this time scientists were still teasing apart what was to belong to chemistry and what was to belong to physics. They didn't know the components of matter and how they associated with each other. They didn't know how to separate composition of matter from activity of matter. But ěrsted's discovery gave them a giant step forward in learning how to make that separation. He could easily have parlayed that discovery into another discovery that would have doubled that giant step.
Rhapsody on a Theme of Newton
Symmetry provides the leitmotif for this piece. Once ěrsted demonstrated that electric charges can be made to exert a magnetic force, a general belief that Reality manifests symmetry led scientific thinkers of the time to infer that it should be possible to make magnetic poles (or their electric-current equivalents) exert an electric force. But nobody was able to figure out how to do that, even though it seems to us that it should have been obvious.
Reimagine ěrsted's experiment as he might have done. Stripped down to its simplest form the experiment comprises an electric current moving along a thin line past one pole face of a long bar magnet. The electric current itself must be the purest manifestation of electric current and this is where ěrsted would have had to be clever. The current that ěrsted actually used, the flow of conduction electrons through a platinum wire, is not pure and ěrsted would have known that fact, even if he didn't understand it exactly as I described it (he would have thought of it as a negative charge moving in one direction and/or a positive charge moving in the opposite direction, but he would not have thought of those charges as being associated with specific particles). A pure current, one that would not confuse his reasoning, would comprise an electric charge deposited onto a thread that is then moved rapidly in a straight line, perhaps by being unspooled from a reel and spooled up onto a takeup reel. In actuality such a current would have been far too weak to produce a discernible effect in ěrsted's experiment, but in concept it was just what ěrsted needed.
Symmetry again. Newton's third law of motion tells us that if A exerts a force on B, then B exerts an equal and oppositely directed force on A. Thus ěrsted knew that when his electric current exerted a force upon the magnetic poles in the compass needle, those poles exerted an equal and oppositely directed force upon the current.
ěrsted himself noted that in his initial experiment various effects were confused. He was obliged to conduct additional experiments to clarify his discovery. In conceiving those experiments he could have easily imagined the experiment that I described above. In his imagination he might have seen the speeding, electrically charged thread exerting a force upon the magnetic poles on the pole face nearer the thread and a much weaker opposing force upon the poles on the other, distant pole face. If the magnet were prevented from moving, the charged thread would, at equilibrium, be bowed away from a straight line by the net reactive force that the magnet exerts upon it.
Symmetry yet again. This is where ěrsted would have had to be especially clever. The basic concept of Relativity was known at the time (both Galileo and Newton had covered the subject in their seminal works) and ěrsted, who had been lecturing on physics for nearly twenty years, would certainly have known of it. It would not have been an immediately obvious concept to apply, but the idea of representing an electric current by a moving, electrically charged thread does carry a hint to look at the scene from the viewpoint of an observer moving with the thread. That observer would also see the thread bowed away from a straight line and, moreover, would see the bowed part moving along the stationary thread with a moving magnet. That's when the Eureka! moment comes.
Oh, what a grand symmetry this is! ěrsted stares in breathless wonder at what his two imaginary observers have reported to him and infers this: as an electric current (moving electric charges) exerts a magnetic force, so a magnetic current (moving magnetic poles) exerts an electric force.
Even more beautiful is the special irony that we see here. The content of ěrsted's imaginary experiment is essentially identical to the imaginary experiment that Albert Einstein described in the introduction to "On the Electrodynamics of Moving Bodies", the paper in which he first laid out the theory of Special Relativity.
The experiment to put that notion on trial in the court of Reality is of straightforward design. Basically, a collection of magnetic poles must be moved rapidly past a wire in a direction perpendicular to the direction in which the wire is oriented. ěrsted should have wanted that passage to be prolonged or, at the least, repeated frequently so that the electromotive force would build up an electric current for a long enough time to register on his detector. A bar magnet spinning end-over-end would have provided the rapid repetition and the axle on which it turns would support the sliding contacts that would rectify the alternating current generated in the wire by successive passages of the magnet's north and south poles (a problem that ěrsted would have seen and solved rather quickly, I believe). The addition of a hand crank and suitable gearing would have completed the initial design of a simple electric generator.
And how would ěrsted prove and verify his new hypothesis, that the generator produces an electric current when someone turns the crank? Why, simply by passing the presumed current through a wire laid over a magnetic compass, of course. ěrsted would use his earlier experiment as a means of testing his new idea.
Interlude: Ampere and Faraday
In 1820 electric batteries, then called Voltaic piles, were as rare as atomic piles, now called nuclear reactors, were in the late 1940's. As a consequence conducting experiments involving the use of strong electric currents was still a rare activity. Nonetheless, for all its expense, people insisted on conducting such experiments.
Andre-Marie Ampere discerned something special in ěrsted's discovery. An electric current exerts a force upon a magnet, so, in accordance with Newton's third law of motion, a magnet must exert a force upon an electric current. But then, Ampere reasoned, we don't need the magnet: two current-carrying wires will exert magnetic forces, each upon the other. That thought led Ampere to design and conduct experiments (using borrowed Voltaic piles) aimed at enabling him to work out the algebraic description of the exerted forces in terms of the strengths of the electric currents and the geometric descriptions of the wires.
Michael Faraday seems to have taken Ampere's idea a little too seriously. He believed that placing two coils of wire in proximity to one another would enable an electric current in one to induce the flow of electricity in the other. Apparently he believed that the magnetic force exerted by the initial current would compel the electric fluid in the other wire to move. He saw the problem as one of finding the right geometry for the coils and only found out the truth of the matter when he noticed that the galvanometer that he had set up to detect the induced current twitched whenever he opened or closed the primary circuit: his primary coil, he saw, only induced an electric current in the secondary coil when the electric current in the primary coil changed, causing a changing magnetic flux to sweep over the secondary coil. From that observation he deduced his law of electromagnetic induction.
In the course of his study of magnetism Faraday made one other very important contribution to modern physics. Self-confessed as having a poor grasp of mathematics, Faraday employed what he called "aids to the imagination". One of those was what we call a forcefield. Inspired by the patterns formed by iron filings sprinkled on paper in the presence of a magnet, patterns suggestive of a plowed field, Faraday conceived the idea that the magnet permeates the space around it with an influence that carries the magnetic force and he called that influence the Magnetic Field of Force.
Maxwell: Fantasia on a Theme of ěrsted
Once they had electromagnetic induction in mind, the scientists of the mid-Nineteenth Century had an almost complete theory of electromagnetism. In the early 1860's James Clerk Maxwell found an unsuspected missing piece and completed the puzzle of electricity and magnetism and then found that the puzzle covered more phenomena than many people had suspected.
Ampere's law tells us that a closed loop drawn about a wire entwines with a magnetic field whose strength is determined by the amount of net electric current passing through the loop. That loop also forms the boundary of a surface, so we can say that the magnetic field on the loop coordinates with the electric field penetrating the surface. The law of continuity applied to electric currents authorizes us to deform that surface in any way we see fit without violating Ampere's law.
James Clerk Maxwell took that authorization and parlayed it into new knowledge. He imagined a wire carrying electric current through a flat surface bounded by a circle centered on the wire. He then imagined breaking the wire and attaching the broken ends to a pair of flat metal plates that had a narrow gap between them. The current in the wire would then, for a time at least, build up an electric charge on each of the plates, negative on one plate and positive on the other. He then imagined so stretching and pushing the surface bounded by his magnetic circle that it slipped into the gap between the plates.
In that image a magnetic field still ran on the circle, but no electric current penetrated the surface. Instead, the electric field between the plates penetrated the surface. As current flowed in the wire, electric charge built up on the plates and the electric field between the plates grew ever stronger. When Maxwell carried out the relevant calculations, he discovered that the rate at which the electric field's flux through the surface changed coordinated with the magnetic field paralleling the circle. On that basis he added the rate at which the flux of an electric field changes to the electric current term in Ampere's law. Thus, in much the way that ěrsted had shown that an electric current generates a magnetic field, Maxwell showed that an electric field can also generate a magnetic field.
When Maxwell contemplated the four fundamental equations of electromagnetism (which now bear his name) as they would describe electric and magnetic fields in vacuum, he found himself on a path that led him to a wonderful conclusion. Faraday's law told him that an electric field would exist in otherwise empty space only if a changing magnetic field coincided with it and his contribution to Ampere's law told him that a magnetic field would exist in empty space only if a changing electric field coincided with it. In that picture he discerned the possibility of an electric field and a magnetic field that would each support the other indefinitely. But that indefinite support would only happen if the fields satisfied certain criteria:
A. Their intensities had to vary from place to place in the manner of a curve known as a sinusoid;
B. They had to move in a direction perpendicular to the directions they themselves pointed; and
C. They had to move at a speed determined as a function of the electric permittivity of vacuum and the magnetic permeability of vacuum, a speed that Maxwell calculated and found to come close to the value that Armand Fizeau had measured for the speed of light.
Knowing the crudity of measurements available at the time, Maxwell made a leap of faith and declared that electromagnetic waves did move at the speed of light and that light was very likely an electromagnetic wave.
But Maxwell left a question hanging fire. Electromagnetic waves must move at the speed of light, but the speed of light relative to what?
The physicists of the time took the Šther whose stresses Maxwell himself had imagined as being the electric and magnetic fields and postulated that those stresses could propagate through the space-filling superfluid as light, much as mechanical stresses can propagate through matter as sound. Indeed, Hendrik Antoon Lorentz devised his eponymous transformation, which appears so prominently in Special Relativity, as a description of how the Šther wind alters rulers and clocks. Physics had reached a new level of abstraction.
But one man took Occam's Razor to mad-slasher extremes. Seeing no compelling evidence for the existence of the luminiferous Šther, Albert Einstein assumed that it does not exist and devised the theory of Relativity. Without an Šther to serve as a reference frame, he had to ask the Maxwellian question anew - the speed of light relative to what?
He already had the principle of Relativity in mind, thanks to Galileo and Newton. In accordance with that principle he knew that if a ray of light passed two observers, then both observers must see it. And if the ray passed one observer without diminution, then it must pass the other observer without diminution. And those inferences must remain true to Reality, even if the observers move relative to each other. And that means that the ray must pass both observers at the same speed, that space and time must so differ for the two observers that both observers will measure the ray crossing 299,792.458 kilometers or 186,234.709 miles in the elapse of one second. And that fact leads us directly, as we have seen in the previous essays, to the Lorentz Transformation.
Strangely, we are still in territory that I believe ěrsted could have imagined, even if there's little chance that he would have imagined it if he had gone on to deduce electromagnetic induction. Imagine the effect that this project would have had on him if he had managed to reason out this far. He had set out to explore the relation between electricity and magnetism, a simple down-to-Earth scientific investigation, and here he stands, having parlayed his original experiment into knowledge of the structure of space and time, staring at the foundations of Reality Itself. But here we enter the realm of psychology and that realm lies beyond the scope of these essays.
Empiricism or Rationalism
In that title I have tacitly encoded a failing of the English language, the fact that the word "or" has two different meanings. We have the more commonly used meaning, the exclusive or, that separates the terms completely: it gives us the basis for dividing the world into mutually exclusive pairs, such as male-female, positive-negative, up-down, etc. Less commonly we have the inclusive or, which we sometimes write and/or, meaning that we may have one or both of the terms true to whatever realm we have under consideration. I have used the "or" in my title in that latter sense.
Whether ěrsted made his discovery accidentally or by design, he made it in the purest spirit of Empiricism. He observed a situation and the events that occurred in it and then abstracted from his perceptions a law that governed one of the phenomena present in that situation. He drew knowledge from direct experience. In so doing he paid tribute to a statement of Friedrich Schelling:
"The assertion that natural science must be able to deduce all its principles a priori is in a measure understood to mean that natural science must dispense with all experience, be able to spin all its principles out of itself - an affirmation so absurd that the very objections to it deserve pity. Not only do we know this or that through experience, but we originally know nothing at all except through experience, and by means of experience, and in this sense the whole of our knowledge consists of the data of experience. These data become a priori when we become conscious of them as necessary." Einleitung zu dem Entwurf eines Systems der Naturphilosophie - 1799.
I must certainly agree with the part of that statement that Schelling himself emphasized (the part in italics). I have no memories from my first few years of life because in those years I did not yet exist as a conscious being. In those years I merely accumulated experiences from which I would construct a consciousness that could later become rational. But at first I gathered my experiences in accordance with their emotional value and only later began the more sophisticated process of abstracting general concepts from collections of experiences that shared common features. I cannot doubt that my origin as a particular personality came from the empirical-inductive method acting upon my animal nervous system, so I cannot doubt that Schelling got it right when he said as much.
Nonetheless, like ěrsted and many of his contemporaries, I also agree with Immanuel Kant, who said, "a rational doctrine of nature deserves the name of natural science only when the natural laws at its foundation are cognized a priori, and are not mere laws of experience" (Metaphysical Foundations of Natural Science - 1786). My originating in an empirical-inductive process does not forbid me from embracing the idea that we can, in theory at least, deduce all of the laws of Nature from a handful of self-evident axioms, even if, by some necessity, we must obtain those axioms from an empirical-inductive process like the one that created us individually.
When we think of formal logic we usually think of the syllogism as its fundamental expression. Now I want to take a brief look at that concept through the four syllogisms that ěrsted would have used to deduce the law of electromagnetic deduction.
We may think of the basic syllogism as an expression of Euclid's first Common Notion: Things equal to the same thing are also equal to one another. In constructing a syllogism we devise two statements (the premises) with a common term and then construct a third statement (the conclusion) by deleting the common term and thereby equating the remaining terms.
First syllogism: we might call this ěrsted's syllogism:
1. Lightning is an electric current;
2. Lightning is something that exerts force upon magnetic compasses; therefore,
3. An electric current is something that exerts force upon magnetic compasses.
We can also construct a syllogism in which one premise instructs us to reverse the subject and object. Classical physics gives us two good examples of such logical reciprocity and ěrsted could have used them both.
Second syllogism: we take the generalization of the conclusion of the previous syllogism and apply Newton's third law for predicate reversal:
1. An electric current exerts force upon a magnet;
2. If A exerts a force upon B, then B exerts a force upon A; therefore,
3. A magnet exerts force upon an electric current.
Third syllogism: we take a generalization of the conclusion of the previous syllogism and apply the principle of Relativity for predicate reversal:
1. A stationary magnet accelerates a moving electric charge;
2. An observer stationary with one of two interacting bodies must observe the same interaction observed by an observer stationary with the other body; therefore,
3. A moving magnet accelerates a stationary electric charge.
1. A moving magnet can accelerate an electric charge;
2. Only that which exerts an electric force can accelerate an electric charge; therefore,
3. A moving magnet exerts an electric force.
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