The Electromagnetic Field

Historical Background

Following a discussion on another thread, I said I'd explain the electromagnetic field in outline terms. IMHO it's very important to get a conceptual grasp of electromagnetism in order to get to grips with light and the quantum of quantum mechanics, and how it relates to relativity. I'd say there's rather more synergy here than is commonly appreciated. Or at least more than I appreciated. Maybe you guys have always known about it. But in case some don't, here's a little history to get it across:

Einstein won his Nobel prize primarily for his 1905 photoelectric paper "On a Heuristic Viewpoint Concerning the Production and Transformation of Light". This established the quantum nature of light. Another paper in this his mirabalis year was "On the Electrodynamics of Moving Bodies". This is electrodynamics and refers to Maxwell, but is considered to be Einstein's special relativity paper. Another important paper was "Does the Inertia of a Body Depend Upon Its Energy Content?" concerning mass and energy. This is of course where Einstein refers to a body losing mass via radiation, and where E=mc² comes from. He’s mainly remembered for gravity and The Foundation of the General Theory of Relativity (3.6Mbytes), and there's a tendency to overlook the fact that that he was in on the ground floor of quantum mechanics in 1905, and a tendency to overlook the electromagnetism content. People tend not to hear about things like his 1920 Leyden Address where he said this:

Some people even think he was against quantum mechanics, but he wasn't, he was against the "spooky" Copenhagen Interpretation, that's all. He was still centre stage at the 1927 Solvay Conference, which discussed the Copenhagen Interpretation. Einstein essentially lost the argument:

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After this he was still lauded by the media and public, but became somewhat detached from quantum mechanics, which then morphed into quantum field theory, quantum electrodynamics, and so on. Anyhow, Einstein ended up as "trophy" at Princeton, largely out of the mainstream, still trying to unify electromagnetism and gravity to come up with a unified field theory. Electromagnetism was always very important to Einstein. He had pictures of Faraday and Maxwell on the wall of his study. They, along with Newton, were his "heroes".

All this came as something of a surprise to me when I found out about it. It seems to be an example of how reading the history and the original material sometimes puts a different slant on things. Things like Minkowski’s Space and Time paper from 1908. Most people know that this constituted an important development for special relativity. However very few people pay much attention to this little paragraph two pages from the back:

It isn't online as far as I know, but see page 73 of The Principle of Relativity: A collection of Original Memoirs on the Special and General Theory of Relativity. I scratched my chin and wondered about this, then read some original Maxwell. I have to say it's very different to what is described as Maxwell's Equations. That's because "Maxwell's Equations" aren't Maxwell's equations, because Heaviside rewrote them in vector form. Maxwell wasn't talking about vector fields. His seminal paper is On Physical Lines of Force. On page 53 he says this:

He's talking about a screw mechanism, which is what Minkowski's wrench was all about: a wrench turns a bolt, which has a screw thread. And the page heading is The Theory of Molecular Vortices. Maxwell was suggesting that the electromagnetic field was a sea of vortices, and particles moved through it. This picture is a reproduction of one in On Physical Lines of Force:

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If you're anything like me you're saying Huh? What? Then you read things like A Circular History of Knot Theory mentioning Kelvin's theory of vortex atoms. After a while it sinks in what Maxwell was talking about, and then you realise he missed a trick. He got it back to front. Here's why.

 

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Visualizing a slice through a cylindrical electromagnetic field

Look at the right-hand rule on English wikipedia. For a current in a wire, your thumb points in the direction of the current flow, and your fingers “are curled to match the curvature and direction of the motion or the magnetic field”.

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But note it’s one field, it’s the electromagnetic field, not separate electric fields and magnetic fields. Maxwell knew it, Minkowski knew it, and Oleg Jefimenko knew it. Jefimenko's equations are a useful reminder in this respect.

The electromagnetic field is a dual entity, there’s only one field there. Moving through an electric field doesn’t cause a magnetic field to be generated, because as Minkowski said, it’s the field, and it exerts force in two ways. What does it look like? It doesn’t actually look like anything, but iron filings on a piece of paper tells you that you can visualize a field, even if it's just a flat slice through it. And to visualise the complete electromagnetic field, you need a drill bit or a reamer:

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If I look at it from the top it reminds me of an electric vector field, like this one from Andrew Duffy’s PY106 physics course material at http://physics.bu.edu/~duffy/ :

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When I then look at the rotational magnetic vector lines of the right-hand-rule, I'm searching for a combined visualisation. So I grab a reamer in my right fist, put my left thumb on the bottom of it, and push upwards. It turns. I'm emulating the right-hand rule for the current in the wire. The reamer is giving an analogy of the cylindrical electromagnetic field around a vertical column of electrons.

(Continued)

 

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Pushing upwards is emulating the current flow, and the rotation I can feel is the magnetic curl or rot. The current flows, and the result is rotation, as demonstrated by Faraday way back in 1844:

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See this http://son.nasa.gov/tass/content/electromagnetism.htm]NASA electromagnetism page for a little more history. Minkowski referred to a wrench and Maxwell referred to a screw because the electromagnetic field really is like this. It’s essentially a “twist” field. Motion through it results in “turn”. Or vice-versa. Start with forward motion like with a pump-action screwdriver, and you get rotation, turn. Turn a screw with a screwdriver and the twist results in forward motion, so you can induce a current up the wire. This is why we have dynamos and generators, because this is how the electromagnetic field is. It's a "twist/turn field", as borne out by the physical evidence of say galactic jets, where two streams of charged particles moving at different velocities spiral around each other. The magnetic field is the "turn" aspect of this, that's why we talk of curl or rot. Because rot is short for rotor, and it really makes things turn:

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The reamer depicts the electromagnetic field for a column of electrons, at an imaginary cylindrical surface some distance round the wire. You have to use a fatter reamer to visualize the electromagnetic field for a larger cylindrical surface. Then to match the way the field diminishes with distance, the degree of twist has to reduce. So imagine a continuous series of fatter and fatter reamers, all occupying the same space, all with the twist diminishing. Now take a horizontal slice through this set of reamers. You’re also taking a horizontal slice through an electron’s electromagnetic field, and it's going to be something like this:

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That’s what the electron’s electromagnetic field would "look like" if you sliced through it from any direction. Let your eyes linger on it. It looks rather like a vortex, but at the heart of it is an electron. The electron is the vortex. That's was Maxwell's mistake. The vortex is in the particle, not in the intervening space. If only he'd got that right or somebody had fixed it! A slice through the electromagnetic field looks spiral because it combines the radial electric field lines with the concentric magnetic field lines.

 

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A very useful fluid analogy

To really "get it" in a visceral way, I urge you to try out Falaco solitons. These offer a fluid analogy that demonstrates a vorticial pair production, attraction, repulsion, and annihilation. For some reason people have difficulty accepting this until they've had some form of demonstration. The fluid analogy is by no means perfect, but I really do recommend it. You dip a plate into a pool, then stroke it gently forward while lifting it clear. You make a U-tube double whirlpool which moves gently forward through the water:

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That's something like pair production. Now create another Falaco soliton aimed towards the first, and repeat with various aims. Watch carefully. When the left-hand-side of one double whirlpool is near the left-hand-side of the other, the two similar whirlpools steer clear of one another. When the left-hand-side of one double whirlpool is near the right-hand-side of the other, the two opposite whirlpools move together. That's essentially attraction and repulsion. If you aim two double whirlpools straight at one another, face on, they meet and merge and disappear. This is best in a shallow pond with muddy bottom, when you see a surprisingly energetic kick-up. That's essentially annihilation. There's even something that looks as if it might be akin to low-temperature superconduction. Make two Falaco solitons in quick succession, and watch how the second one daisy-chains through the first, moving forward more rapidly than when it's on its own. It's all just a fluid analogy and it's by no means perfect, but it gets it across very well. Something else it gets across is that there's this round thing there in the water that's made out of movement. it isn't some point-particle, it isn't some billiard-ball, but nevertheless it's there. This is how you should think about a particle like an electron. It isn't some point-particle, and it isn't some billiard ball, it's just spinning stress-energy. Take away that spin, and the electron isn't there any more.

But note that neither a Falaco soliton nor an electron is a whirlpool. There's rotation, but there's nothing flowing inwards towards the centre. And for the electron, there's nothing rotating once you move away from the centre. The electron works more like an office floor polisher on a rubber sheet. Only there is no floor polisher, just the rotation, like a ripple in the rubber sheet going round and round. The rotation twists the rubber sheet round. If you're riding one of these kiddies and I'm riding another, then if the rotations are both clockwise or anticlockwise, we move together. If they're opposite, we move apart. Hence attraction and repulsion. And as you can imagine, if we were scooting around, there might be a bit of pirouetting going on.

 

The electromagnetic field in three dimensions

But what does the electromagnetic field "look" like for a single electron? It’s isotropic, apart from a minor issue with magnetic dipole moment. It looks the same from all directions. So how do you get an electromagnetic field that has this spiral feature in three dimensions? It's quote simply really, instead of twisting a rubber sheet, it's like you stick your hand into a spring-steel cubic lattice representing space, grab it firmly, and twist. Then you reach in with the other hand from the side, and give it another, orthogonal, twist. Then you take your hands away and imagine the distortion remains, and there's a little rotor in the middle causing it. I don't know if you can picture this, but there a type of "frame dragging" going on here. Your lattice lines were straight, now they're curved. The electromagnetic field is curved space. Not curved spacetime, like a gravitational field, curved space, with a chirality. It's curved in two directions, that's why it's "curled".

But anyway, you've got this rotor in the middle. Now drop in a second similar rotor. This will move away from the first in a straight line as if it's following an electric field line. If the first rotor is however moving upwards closely followed by a whole load more, like the current in the wire, the second rotor will move in a circular path as if it's going round magnetic field lines. If you make the first rotor and a whole load more travel in a helical path like in a solenoid, then if you chuck the second rotor through the middle, it doesn't fly straight. Instead it follows a helical path. It's still going around the magnetic field lines, but these now run straight inside the solenoid:

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Another way to picture it is via a Fibonacci spiral. You can make one by bending a wire so that the curvature diminishes with distance from the centre. Imagine you've just done it. Now lay this wire spiral flat on your desk, and bend it again upwards, again so the curvature diminishes with distance from the centre. But now it isn't so much curved as curled, because it's curved in two orientations. Now repeat with a thousand similar wires, and stick the curlier ends into a plasticine sphere to get the general idea. But not quite, because this would be like a head of hair with a "crown". To avoid this anisotropy, you need to stick them into a plasticine torus. A torus studded with doubly-curved Fibonacci spiral wires is more like it. The plasticine represents spatial stress-energy travelling in a rotational path, with the rotation in two orientations, frame-dragging the surrounding space. If we took away the wires, it would look something like this:

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Of course it doesn't really look like anything, and there's no actual surface, because all you're really seeing is stress-energy contour lines and arrows indicating direction of motion. But note that it's something like a "moebius doughnut". There's two rotations present, one like a turning steering wheel, one like a rolling smoke-ring. However it takes two turns per roll, which is why the electron exhibits spin ½. And this is a real rotation, with real angular momentum. You make an electron along with a positron from a +1022keV photon. Via pair production. It has to be a pair to conserve angular momentum. That's why you can't make an electron on its own.

Quite a few people have worked something out along these lines. There's the Williamson / van der Mark paper Is the electron a photon with toroidal topology? which appeared in Annales de la Fondation Louis de Broglie, Volume 22, no.2, 133 (1997). A somewhat similar paper The nature of the electron by Qiu-Hong Hu appeared in Physics Essays, Vol. 17, No. 4, 2004. Another similar paper is Rotating Hopf-links: a realistic particle model by E Unz 2006 which appeared in Physica D 223 2006. I imagine there's more, see google for other instances, such as this undated Electron Ring Vortex Model by William Hamilton.

 

Spin is classical

I don't know if you appreciate the significance of this, but it means spin is isn't "intrinsic" after all. It's classical. See the wiki Stern-Gerlach article which says:

If the particles are classical, "spinning" particles, then the distribution of their spin angular momentum vectors is taken to be truly random and each particle would be deflected up or down by a different amount...

The experiment shows that this doesn't happen, so we know the particles aren't spinning spheres. However the article, which is in line with the current consensus, goes on to say:

Electrons are spin-1⁄2 particles. These have only two possible spin angular momentum values, called spin-up and spin-down. The exact value in the z direction is +ħ/2 or −ħ/2. If this value arises as a result of the particles rotating the way a planet rotates, then the individual particles would have to be spinning impossibly fast. The speed of rotation would be in excess of the speed of light, 2.998×108 m/s, and is thus impossible.

There's actually nothing wrong with that, but here comes the non-sequitur:

Thus, the spin angular momentum has nothing to do with rotation and is a purely quantum mechanical phenomenon. That is why it is sometimes known as the "intrinsic angular momentum."

Whoa! We've established that the particle isn't rotating like a planet, but why can't it be rotating in some other fashion? There is no justification here for asserting that spin angular momentum has nothing to do with rotation, particularly since the electron exhibits magnetic dipole moment. And particularly since the Einstein-de Haas effect demonstrates that "spin angular momentum is indeed of the same nature as the angular momentum of rotating bodies as conceived in classical mechanics". It's easy to see what's happening in the Stern-Gerlach experiment, especially if you've played football and practised your free kicks. Imagine a whole bunch of spheres, like this:

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Now give them an earth-style spin to give yourself a set of "classical particles". Next, jumble them around so that the spin axes point in a variety of directions, then throw them through the inhomogeneous magnetic field. You'd see a line on the screen as per the classical prediction:

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Now collect all your still-spinning particles together again, and set them down on the table like a bunch of spinning globes. Now give them another spin in another orientation. Spin the spin axis. You have two choices as regards this new spin direction, this way: ↓O↑, or that way: ↑O↓. Now throw them through the inhomogeneous magnetic field and ask yourself what you'd see. Two spots, because there are two chiralities to the two compound spins. Apart from that, you can't say which way they're spinning. Spin a glass clock like a coin, and the rotation of the hands is clockwise when its face-on, anticlockwise when its rear-on, clockwise when its face-on, and so on. It's spinning both clockwise and anticlockwise. Spin the glass clock with your other hand and the compound rotation is different, but you can only describe the difference by using terms like spin-up and spin-down.

 

Discussion

All of this hopefully provides a coherent picture of the electromagnetic field as a "twist/turn" field. Charged particles are like doubly-spinning rotors which move both linearly and rotationally, because they curve or curl the surrounding space and interact with other charged particles doing the same. If anybody can point out any obvious flaws I'd be grateful.

But otherwise: what's an electromagnetic wave?

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The electromagnetic field variation rises to a positive maximum then descends to a negative maximum. And if an electromagnetic field is spatial curvature, with an electric "twist" aspect and a magnetic "turn" aspect, that means the photon is some kind of pulse of spacewarp. I'm not sure of the exact geometry or why it persists, but that's what it seems to be.

 

Haven't we been down this road before where others point out the flaws and you get belligerent in your woo-woo beliefs?

 

{Q} is right.

My opinions of this work haven't changed.

 

That said, it should be easy for someone to read this and find a flaw.

I'm currently busy learning about pricing options, so I don't really have the heart.

If no one finds a mistake by Sunday, I'll find one myself.

 

I can top that, I'm learning network analysis in R

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Though I imagine you're being paid more than I am.

Why bother, Farsight is doing what he did a year or two ago, deluding himself into thinking that because he can post pictures and drop the name of physicists whose work he doesn't know then he's doing science. He's the internet version of people who think they are a scientist because they have a white lab coat on. His previous "[Something] explained!" work got him nothing but ridicule across a multitude of forums and journals and he wasted some of his childrens' inheritance on vanity publishing his 'work'. Obviously he learnt nothing from the last time his 'work' was laughed off a dozen forums, what makes you think he'll do anything better now?

Regardless of whether someone does or doesn't slap Farsight for being a muppet this thread is worthy of pseudo.

 

Not yet

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That's certainly my initial reaction, but I want to give it a fair shake, at least.

 

What's the problem? This pays serious attention to the original Maxwell and provides good references and scientific evidence. If you think it's somehow flawed, find the flaws and elucidate them. If you can't, and if nobody else can, accept that there aren't any. Don't instead permit certain posters here to stifle discussion and damage what is, after all, a discussion forum.

 

Then, your flaws are found, you wave your arms around saying they aren't flaws and claim your victory stating emphatically no flaws were found, yes? Just like before?

 

I doubt entering this thread is a good idea, but:

Well that's the point. Technically you've only provided evidence that Maxwell originally thought of electromagnetism a certain way. So what? There's a reason those ideas were eventually dropped: from a scientific perspective they don't add anything to electromagnetic theory. I'm not an expert on the early history of electromagnetism, but from what I gather the issue was simply that the notion of a "field" was a novel concept at the time, and Maxwell was simply trying to relate electromagnetic behaviour to behaviour he was already familiar with. That page in Maxwell's paper you linked to is filled with allusions to fluid mechanics for instance. Nowadays we just prefer to take the idea of a field on its own merits, and we'd view descriptions of the electromagnetic field in terms of fluids and vortices (and luminiferous aethers, while we're at it) as unneeded and basically untestable baggage. Most people who've studied electrodynamics will see things this way.

 

Are you seriously that oblivious to all the comments you had about your work last time? Didn't you take anything anyone said on board?

Your naivety about what actual physics involves is stunning, though not unexpected given your past. If you had bothered to open any book on Maxwell's work which actually examines Maxwell's equations then you'd realise just how little attention you work really pays to them. Hell, you haven't even stated them anywhere in your couple of posts! You've written 3 or 4 A4 pages of pictures and text and not once actually justified your claims or used anything specific which Maxwell's work covered. The level of content and discussion in your posts isn't very high, anyone whose state a course in EM could knock up something as long in part of an afternoon and they'd at least bother to state Maxwell's equations! If I were to see a paper on ArXiv which had in its abstract or title something like "A serious analysis of Maxwell's work" I'd expect dozens of pages examining the details of his work, not 4 pages of arm waving where the author doesn't demonstrate any knowledge or understanding which can't be gleaned from a casual read of particular Wikipedia pages. If you'd bothered to open a book or paper on electromagnetism you'd have seen just how far short your 'serious attention' really falls.

You have no idea what 'good references' and 'scientific evidence' is. In saying that you've shown you haven't done any real reading around or made any real attempt to understand the scientific method or the level of detail and attention expected in serious work.

Before I brushed off such comments from you as just a result of naivety but now its clear you haven't learnt anything from your last round of "I've explained [something]!" 'papers' which were critically panned on all forums you posted them. Either you're being deliberately obtuse or you seriously lack the ability to learn from your mistakes.

You didn't listen to anything anyone said last time, when you made repeated mistakes on even the most basic of things. Why should we bother again?

Flawed reasoning. Absence of evidence is not evidence of absence. If I showed university level work which was wrong to a 10 year old they'd not be able to spot the mistakes, despite there being some. Of course in that analogy the material is completely over the 10 year olds head, while your work is laughably basic and devoid of anything which requires beyond high school level ability. The reason why few or no people will reply about your mistakes is that we all know its wasted on you, you have either no wish or no capacity to understand your mistakes.

If you wanted an honest informed discussion I'd be all for it, but you don't. You never do. If and when someone bothers to point out mistakes you just ignore them. Do you know the difference between a mathematical axiom and a physical postulate yet? I commented on your misunderstanding of the distinction between them dozens of times on PhysOrg and you ignored any attempt at a discussion. I tried to engage you in discussion, you refused. So trying the "This is a discussion forum, don't just slag me off" is a little hypocritical, you only want to talk to people who agree with you, you'll find some excuse to ignore everyone else.

 

The Maxwell reference shows the pedigree, but isn't evidence. The evidence is in the observable phenomena. Electrons move linearly in what we call an electric field, and rotationally in what we call a magnetic field. We know that these are two aspects of the electromagnetic field. The right hand rule is a representation of how we experience the field for a moving column of electrons. Pair production is real, electron magnetic dipole moment is not disputed, the Einstein-de Haas effect demonstrates that spin angular momentum is of the same nature as classical angular momentum, the homopolar motor demonstrates the macroscopic results, and so on.

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Alphanumeric offers only a diatribe of allegations, as ever. If you can find any flaws I'd be grateful. I value your sincerity.

 

I'm not sure why there's so much hostility - I'm happy to go through this.

Hi Farsight. I'm afraid, from a scientific point of view, I'm not too interested in the history and prefer the actual science. So I'll start at a point where I feel the science begins (ish).

I'm lost here. Heaviside just wrote the equations in different notation (considerably simplifying them). The scientific predictions made by those equations are unchanged, whether you choose to write them in vector form, write them in component form, write using the language of differential forms, write them in ancient Hebrew... and so on.

I think perhaps you're confused when a physicist says "an electromagnetic field is a vector field", when really they should say "the observable phenomena produced by an electric field can be accurately described with the use of a vector field". But the latter option is so OTT it's bordering ridiculous - so we abuse the language and just say they're the same thing. The same thing happens all over physics.

Does that help at all?

 

I imagine you're aware of it but for other people I feel I should point out that up to and including Newton's day 'scientific theories' were expressed entirely in terms of words. Newton found this clumsy and wanted a better way and that partly motivated his development of calculus.

For instance "The acceleration experienced by a unit mass object is proportional to the total force resultant on an object, while the force required to accelerate an object by a specified amount is proportional to the inertial mass of said object" is considerably streamlined to F=ma.

I can't remember for sure but Maxwell wrote out his equations using component by component form (as was common in the days of other people like Gauss) and then using quaternions. As Guest says, Heaviside didn't change their structure, only the way they were written to make it easier to work with them. Since his day we've had further advancements in things like differential forms and gauge theory and the entirety of Maxwell's work is covered by \(F=dA\), with Maxwell's equations becoming \(dF = d^{\dag}F = 0\). The generalisation to Yang Mills is simple, \(d \to D = d + A \wedge\) to get \(F = dA + A \wedge A\) where the second term is gauge valued. Extension to tensor valued 'vector' fields, ie \(A_{\mu} \to B_{\mu\nu}\) is straightforward in this formulation and string theory makes use of it in huge quantities.

Farsight, you're not only talking about something which is old news in theoretical physics, you're not even talking about it correctly.

 

The big impact is that the vector form describes "what it does" rather than "what it is". It removes Maxwell's attempts to describe the underlying reality.

I'll assume you meant to write "the observable phenomena produced by an electromagnetic field can be accurately described with the use of vector fields". This is reasonable, but we still see a lot of references to electric and magnetic fields as if they were two different things.

No. Sorry. You haven't tackled the actual science such as the right hand rule, pair production, electron magnetic dipole moment, the Einstein-de Haas effect, and so on.

Out of sequence:

It's a hubristic elitist reaction. The scientific evidence and the references are robust, there are no flaws that anybody can elucidate, and instead of sincere discussion we see outrage and dishonesty. It's perceived as a threat and is kicked into pseudoscience by a "moderator". Forums like this thus become moribund, with facile juvenile threads permitted, but sincere thoughtful threads censored.