Like I was saying last time, a major goal of physics is “to unify the various fundamental forces” in a theory that offers “a more elegant understanding of the organization of the universe”. This is called a grand unified theory or GUT if it doesn’t include gravity, and a theory of everything or TOE if it does:
Image from Sten Odenwald’s astronomy cafe
Personally I don’t understand why anybody doesn’t include gravity. Gravity is easy. Einstein explained most of it in his 1920 Leyden Address. A concentration of energy in the guise of a massive star conditions the surrounding space, making it “neither homogeneous nor isotropic”, this effect diminishing with distance. As a result the speed of light varies. So light curves downwards like sonar waves curve downwards in the sea, because there’s a vertical gradient in wave speed. Then matter falls down because of the wave nature of matter. That started with Louis de Broglie’s 1923 letter to Nature on waves and quanta, where he said “the wave is tuned with the length of the closed path”. Just think of the electron as light going round a closed path. The horizontal component bends downwards, so the electron’s position changes. In other words, it falls down.
The History of Electricity and Magnetism
The other forces are easy too, provided you’ve read enough stuff to get a handle on it. As for where to start, that’s tricky. But see for example the 2014 book Faraday, Maxwell, and the Electromagnetic Field by Nancy Forbes and Bill Mahon. It starts with a chronology, giving the principle events in the story of the electromagnetic field:
1600 William Gilbert publishes De Magnete and proposes that Earth acts as a giant magnet.
1687 Isaac Newton publishes Principia Mathematica.
1733 Charles du Fay distinguishes between vitreous and resinous electricity.
1745 Pieter van Musschenbroek and Ewald von Kleist independently invent the Leyden jar, a device that stores electricity.
1747 Benjamin Franklin puts forward the idea of positive and negative electric charge.
1750 John Michell demonstrates the inverse-square law of magnetism.
1766 Joseph Priestley demonstrates the inverse-square law of electricity.
1785 Charles Augustin Coulomb carries out precise experiments to confirm the inverse square laws of electricity and magnetism.
1800 Alessandro Volta invents the voltaic pile, or battery, thereby making it possible to generate continuous electric currents.
1820 Hans Christian Oersted shows that an electric current in a wire deflects a compass needle.
1820 André Marie Ampère begins to formulate a combined theory of electricity and magnetism based on action at a distance.
1821 Michael Faraday discovers the principle of the electric motor.
There’s more, much more, and other books too. See for example Electromagnetism from Ampère to Einstein by Oliver Darrigol, A History of the Theories of Aether and Electricity by Sir Edmund Whittaker, and The History of Electricity and Magnetism by Herbert Meyer. There’s also a whole pile of web pages on electromagnetic history including the Wikipedia article on the history of electromagnetic theory.
A vortex-like, circular distortion existed around the wire
For myself, I like Hans Christian Oersted’s 1820 Experiments on the Effect of a Current of Electricity on the Magnetic Needle. He mapped out the magnetic field around the current-in-the-wire. See the Princeton article on Oersted’s Theory. It says “Oersted proposed that a vortex-like, circular distortion existed around the wire”. Then see Ampère lays the foundations of electrodynamics by Christine Blondel and Bertrand Wolff . Note this: “Rare were those physicists who accepted Oersted’s vortex explanation, but Ampère was one of them”. Perhaps that’s why André-Marie Ampère noticed that a solenoid had a magnetic field like a bar magnet. He said “if the spirals acted like magnets, it was because magnets owe their magnetism to electric currents in planes perpendicular to their axes”. See Ampère’s researches in the science of electrodynamics and note this: “Is it not evident, then, to all how memorable would that discovery be that would rigorously establish the fact that to magnetize a needle is to excite, to put in motion around each molecule of the steel, a small, circular, electrical vortex?”
Image from Oersted fields and current density profiles in spin-torque driven magnetization dynamics by Riccardo Hertel
Ampère knew how a magnet works. That’s why a later section of the Princeton article says “Ampère’s model is startlingly close to the truth. There are no circular molecular currents after all, but the spinning electrons act just like loops of current”. James Clerk Maxwell’s didn’t call his 1861 paper a theory of molecular vortices for nothing. Einstein and Johannes de Haas didn’t perform their experiment for nothing either. See a simple experiment to demonstrate Ampere’s molecular currents. This was the Einstein-de Haas effect, which “demonstrates that spin angular momentum is indeed of the same nature as the angular momentum of rotating bodies as conceived in classical mechanics”.
Geometry of electromagnetic systems
There’s lots more like this. See chapter1 of the 1996 book Geometry of electromagnetic systems by Daniel Baldomir and Percy Hammond. They give a nice potted history of electromagnetism. They start with William Gilbert, who wrote a book called De Magnete in 1600. They tell us how according to Gilbert “the magnetic force was not a simple attraction but a ‘coition’ which involved rotation”. They also tell us that Gilbert “explored the region surrounding a magnet with a small magnetized needle and observed the curvature of the force”. They later talk about René Descartes, saying he put forward the view that all forces had to be transmitted by contact, which led him to conclude that space must be occupied by a material called the ether. Descartes is of course famous for his vortex theory. People tend to dismiss this sort of thing as archaic, but don’t forget that an accretion disk is a vortex of sorts, and a spiral galaxy looks like a vortex. Search the arXiv for vortex images and there’s lots of interesting papers:
Images by various authors
Baldomir and Hammond talk about lots of other people including Michael Faraday, saying he thought of particles as parts of space where forces converged. “Thus the particles were not embedded in a system of mutual forces, but they were aspects of the forces”. They also say that in a famous speculation, Faraday put forward the view that light itself might be due to transverse vibrations of the lines of force, and that this in turn suggested experiments that led to the discovery of the magneto-optic effect and diamagnetism. I think it’s amazing stuff for the early 19th Century.
The ability of a dynamic cause to create a static effect
Faraday was of course the inventor of the electric motor and the dynamo, and the guy who discovered electromagnetic induction. His experimental researches in electricity are fascinating. Check out his biography on the Encyclopaedia Britannica. Leslie Pearce Williams tells how in 1820 Ørsted announced the discovery that a current in a wire produced a magnetic field around the wire, and Ampère “showed that the magnetic force apparently was a circular one”. No such circular force had ever been observed before, and Faraday was the first to understand what it implied: “If a magnetic pole could be isolated, it ought to move constantly in a circle around a current-carrying wire”. Later on you can read about Faraday’s interest in powder on vibrating plates: “Here was demonstrated the ability of a dynamic cause to create a static effect, something he was convinced happened in a current-carrying wire”. That’s interesting, especially if you know how pair production works. Something else that’s interesting is that it was William Thomson, aka Lord Kelvin of vortex atom fame, who tipped Faraday off on using magnetic force to detect Faraday rotation. That’s because magnetic force could be produced at a much greater strength than electrostatic force. And of course, there’s this: “Since the very beginning of his scientific work, Faraday had believed in what he called the unity of the forces of nature. By this he meant that all the forces of nature were but manifestations of a single universal force and ought, therefore, to be convertible into one another”. If that isn’t grand unification I don’t know what is.
Sources and sinks
Which of course brings me on to James Clerk Maxwell. He used to be known as Clerk Maxwell, but for some reason, they don’t call him that any more. He wrote a paper in 1855 called On Faraday’s Lines of Force. I took note of something Maxwell said early on: “The results of this simplification may take the form of a purely mathematical formula or of a physical hypothesis. In the first case we entirely lose sight of the phenomena to be explained”. How true that is. I utterly empathise with his later sentence: “We must therefore discover some method of investigation which allows the mind at every step to lay hold of a clear physical conception”. Well said Clerk. I also empathise with not being “carried beyond the truth by a favourite hypothesis”. Unfortunately that’s what happened in this paper. It’s all sources and sinks and fluid analogy. The focus is on force rather than field. It’s all about effect, not cause. But Maxwell was only 24 when he wrote this. I can cut him some slack, especially since Faraday focussed on effects because he was the experimentalist.
The theory of molecular vortices
Baldomir and Hammond also tell us about Maxwell’s 1861 paper On Physical Lines of Force. There’s a lot of talk of vortices in this paper. As you’d expect, since the subtitle is the theory of molecular vortices. Baldomir and Hammond say “Vortices are essentially dipolar and Ampere’s equivalence of magnetic dipoles and current loops showed that magnetic vortices were associated with current while Faraday had shown that current vorticity was associated with magnetic flux”. This is the paper where Maxwell talked about the propagation of transverse vibrations through an elastic medium, He said the wave velocity was V =√(m/ρ), wherein “m is the coefficient of transverse elasticity, and ρ is the density”. There are issues of course, like “Maxwell decided that there must be particles between the vortices which behave like the idle wheels in a gear train”. There are no idle wheels. Maxwell got his vortices and his particles back to front. But he was spot on with these famous words: “The velocity of transverse undulations in our hypothetical medium, calculated from the electro-magnetic experiments of MM. Kohlrausch and Weber, agrees so exactly with the velocity of light calculated form the optical experiments of M. Fizeau, that we can scarcely avoid the inference that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena”. Maxwell was also spot on with this: “a motion of translation along an axis cannot produce a rotation about that axis unless it meets with some special mechanism, like that of a screw”. Sadly elastic space the screw nature of electromagnetism doesn’t seem to get much attention these days.
A Dynamical Theory of the Electromagnetic Field
Baldomir and Hammond then tell us about Maxwell’s 1865 paper A Dynamical Theory of the Electromagnetic Field. That was peer reviewed by Thomson aka Kelvin. In part 1 Maxwell refers to Faraday and says light can be thought of as undulations in an elastic ether. He also talks about “a motion of the ethereal medium going on wherever magnetic effects are observed”, saying “we have some reason to suppose that this motion is one of rotation, having the direction of the magnetic force as its axis”. In part 2 he likens electromagnetic induction to the momentum of a flywheel. In part 3 he’s cagey. He says when he uses “such words as electric momentum and electric elasticity” he’s directing the reader “to mechanical phenomena which will assist him in understanding the electrical ones”. And that “All such phrases in the present paper are to be considered as illustrative, not as explanatory”. However in the next sentence, he says this: “In speaking of the Energy of the field, however, I wish to be understood literally”. He went on to say “The energy in electromagnetic phenomena is mechanical energy. The only question is, Where does it reside?” Then he said “it resides in the electromagnetic field, in the space surrounding the electrified and magnetic bodies, as well as in those bodies themselves”. That’s the birth of field theory, right there.
Part 6 is where Maxwell talks again about the speed of light, repeating material from his previous paper. Again he talked of “an elastic medium through which the vibrations of light are propagated”. People tend to think of this elastic ether as something that’s been discredited, but it hasn’t. Yes, Einstein dispensed with the ether when he did special relativity, but he resurrected it when he was doing general relativity. Take a look at the Wikipedia aether theories article where Robert B Laughlin said this: “it is ironic that Einstein’s most creative work, the general theory of relativity, should boil down to conceptualizing space as a medium when his original premise [in special relativity] was that no such medium existed”. Laughlin also said the modern concept of the vacuum of space is a relativistic ether. So, what with LIGO, I think it’s a shame that people don’t pay more attention to Maxwell’s displacement current. Maxwell spoke of light in terms of a real displacement of elastic space. A lot of people think that’s naïve, but I don’t. When an ocean wave moves through the sea, the sea waves. When a seismic wave moves through the ground, the ground waves. So, what waves when a light wave moves through space?
There are virtually no depictions of the electromagnetic field
In 1871 Maxwell wrote a paper entitled Remarks on the Mathematical Classification of Physical Quantities. He talked about physical vectors, referring to “those which are defined with reference to translation and those which are defined with reference to rotation”. Then he said “the most remarkable illustration of them is derived from the two different ways in which it is possible to contemplate the relation between electricity and magnetism”. There’s the translation and rotation again. Push the current up the wire and the motor turns. Turn the dynamo and the current goes up the wire. Maxwell referred to Descartes, to Helmholtz and “his great paper on vortex motion”, and to Thomson and Tait. And to Ampère. Maxwell said this: “According to Ampère and all his followers, however, electric currents are regarded as a species of translation, and magnetic force as depending on rotation. I am constrained to agree with this view, because the electric current is associated with electrolysis, and other undoubted instances of translation, while magnetism is associated with the rotation of the plane of polarization of light, which, as Thomson has shown, involves actual motion of rotation”. This is the paper where he came up with convergence and curl and drew this picture:
Image by James Clerk Maxwell
It’s also where he said this: “when there is both convergence and curl, it will point in a spiral”. The electric field has the convergence. The magnetic field has the curl. Curl is also known as rot, which is short for rotor. You can combine them to depict the electromagnetic field. Like this:
For some strange reason there are virtually no depictions of the electromagnetic field. It’s a great pity, because a picture is worth a thousand words. When you see this picture, you can see immediately why charged particles move the way that they do. But sadly it sometimes feels like Maxwell’s unification never happened.
Maxwell never did abandon his vortices
Maxwell wrote his famous treatise in 1873. The title is A Treatise on Electricity and Magnetism. Google on Maxwell treatise vortex and you can read that this is where he abandoned his vortices. However look closer, and you can see he’s reverting to Ampère’s vortices. In Part IV Chapter III, Maxwell says this: “The experimental investigation by which Ampère established the laws of the mechanical action between electric currents is one of the most brilliant achievements in science. The whole, theory and experiment, seems as if it had leaped, full grown and full armed, from the brain of the ‘Newton’ of electricity. It is perfect in form, and unassailable in accuracy”. In Part IV/Chapter XI he says we must give up the old theory of magnetism, and adopt that of Ampère, which admits of no magnets except those which consist of electric currents. He also said we must also regard both magnetic and electromagnetic energy as kinetic energy. I am reminded of Ampère lays the foundations of electrodynamics: “Rare were those physicists who accepted Oersted’s vortex explanation, but Ampère was one of them”. Maxwell was another. Maxwell never did abandon his vortices. He was still talking of vortices in 1873. When Einstein was asked if he stood on the shoulders of Newton, he said “No, I stand on the shoulders of Maxwell”. And Maxwell stood on the shoulders of Ampère.
On vortex atoms
Sadly it was all ahead of its time, along with other theories of the day. Such as William Thomson’s 1867 paper On Vortex Atoms. They didn’t know about subatomic particles back then. It was the same for Peter Guthrie Tait’s related work on knot theory. See the MacTutor biography of Tait by John O’Connor and Edmund Robertson. They tell us that the vortex atom idea “led Tait, Thomson and Maxwell to work on knot theory since the basic building blocks, in Thomson’s vortex atom theory, would be the rings knotted in three dimensions”. They also say Tait, Thomson, and Maxwell exchanged letters in which they invented many topological ideas. Also see Topology and Scottish mathematical physics, again by John O’Connor and Edmund Robertson. They say we “now know that Thomson was completely wrong”. He wasn’t. Something else to take a look at is the remarkable story of Maxwell and Tait by David Forfar and Chris Pritchard. They say Thomson aka Kelvin never accepted Maxwell’s electromagnetic theory, which I think is pretty amazing. Is that why we are where we are? Anyway, it was Tait who came up with the knot zoo:
CCASA knot zoo image by Rodrigo Argenton, see Wikipedia
Not the particle zoo. The knot zoo. Knots have chirality. Google on positron chirality, and you’ll find that particles have chirality too. You may also turn up topological quantum field theory, which is related to knot theory. Or just take a look at the Wikipedia article on chirality. Note the section on physics. It says this: “In physics, chirality may be found in the spin of a particle”. That’s good. What’s not so good is that it says “chirality is a purely quantum mechanical phenomenon like spin”. That stems from the way quantum field theory went wrong in the late 1920s. If only Maxwell had lived longer.
Nothing else takes place
(1) That small portions of space are in fact of a nature analogous to little hills on a surface which is on the average flat; namely, that the ordinary laws of geometry are not valid in them. (2) That this property of being curved or distorted is continually being passed on from one portion of space to another after the manner of a wave. (3) That this variation of the curvature of space is what really happens in that phenomenon which we call the motion of matter, whether ponderable or etherial. (4) That in the physical world nothing else takes place but this variation, subject (possibly) to the law of continuity”.
People tend to dismiss this sort of thing, even though they’re quite happy about gravitational waves. If people understood the relationship between electromagnetism and gravity, I don’t think they would dismiss this sort of thing. Sadly Clifford died before his time too. In 1879, the same year as Maxwell.
A worble embracing itself
If only they’d lived. See The fluid dynamics of James Clerk Maxwell by Henry Keith Moffat. He talks about Kelvin’s 1867 paper On Vortex Atoms. He says “It was in this paper that he mentions his visit to Peter Guthrie Tait’s laboratory in Edinburgh, where he witnessed Tait’s demonstration of the production of vortex rings by ejection of air from an orifice, the rings being visualised by smoke”. He then tells of Maxwell’s letter to Tait of 13th November 1867. That’s where Maxwell said this: “But I fear that the simplest indivisible whorl is either two embracing worbles or a worble embracing itself”. The simplest indivisible whorl is a worble embracing itself? Now where have I heard something like that before? In a paper by John Williamson and Martin van der Mark called Is the electron a photon with toroidal topology? Google on Maxwell worble, then replace the word worble with photon. The embrace is strong. You know, sometimes being the physics detective is like uncovering the lost secrets of the ancients. Maxwell was ahead of his time, because the electron wasn’t discovered until 1897. We don’t call them molecular vortices any more. Or optical vortices. We call them spinors.
Image from the physorg article Magnetic nanoknots evoke Lord Kelvin.
PS: the “whorl” labelled (a) has the topology of an electron, (b) has the topology of a pion, and (c) is like an electron linked with an electron. As for (d), start from the bottom left and trace around it calling out the crossing-over directions: up, up, down. Now where have you heard something like that before?