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Getting to grips with electromagnetism

Getting to grips with electromagnetism

Postby Farsight » Tue Oct 26, 2010 6:12 pm

Introduction

I think it's important to get a conceptual grasp of electromagnetism before moving on to say the quantum of quantum mechanics, particles, and gravity. I'd say there's rather more synergy here than is commonly appreciated. Here's a little history to get this 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 1905 paper 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 energy and mass. This is 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:

Einstein wrote:Of course it would be a great advance if we could succeed in comprehending the gravitational field and the electromagnetic field together as one unified conformation. Then for the first time the epoch of theoretical physics founded by Faraday and Maxwell would reach a satisfactory conclusion.

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:

Image

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. I was a little surprised when I learned about this, and would say it's an example of how reading material yourself can put a different slant on things. You start noticing things, like a little something in Minkowski’s Space and Time paper from 1908. Most people are aware 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:

Minkowski wrote:"Then in the description of the field produced by the electron we see that the separation of the field into electric and magnetic force is a relative one with regard to the underlying time axis; the most perspicious way of describing the two forces together is on a certain analogy with the wrench in mechanics, though the analogy is not complete".

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. You scratch your chin and wonder about this wrench, then you read some original Maxwell. It's rather different to what is described as Maxwell's Equations. I presume that's because "Maxwell's Equations" aren't really 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:

Maxwell wrote: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.

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 look at the page heading. It's 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:

Image

If you're anything like me you're saying Huh? What? Why is this so different to what I was taught? 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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Re: Getting to grips with electromagnetism

Postby Farsight » Tue Oct 26, 2010 6:22 pm

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”.

Image

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.

Jefimenko wrote:"...neither Maxwell's equations nor their solutions indicate an existence of causal links between electric and magnetic fields. Therefore, we must conclude that an electromagnetic field is a dual entity always having an electric and a magnetic component simultaneously created by their common sources: time-variable electric charges and currents."

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:

Image

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/ :

Image

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. Pushing upwards is emulating the current flow, and I can feel rotation as a result. In practice the force is rather weak because there's no net charge in the wire on account of the metal ions, but the the result really is rotation, as demonstrated by Faraday way back in 1844:

Image

See this NASA electromagnetism page for a little more history. Minkowski referred to a wrench and Maxwell referred to a screw because the electric field really is like this. It’s essentially a “twist” field. Move through and you start seeing it as a "turn" field. A magnetic field, where we talk about curl and rot, which is short for rotor. And it works both ways. 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 braided galactic jets and electron beams following a curved path in a uniform magnetic field:

Image Image

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 cocentric on the same line, 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 would be something like this:

Image

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 like a spiral because it's the only way to combine the radial electric field lines with the concentric magnetic field lines.
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Re: Getting to grips with electromagnetism

Postby Farsight » Tue Oct 26, 2010 6:42 pm

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 a magnetic field line. If you make the first rotor and a whole load more travel in a helical path like in a solenoid, then if you throw 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:

Image

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 ends into a plasticine sphere to get the general idea. Some say that this would be like a head of hair with a "crown", and to avoid this anisotropy, you need to stick them into a plasticine torus. The torus represents spatial stress-energy travelling in a rotational path, with the rotation in two orientations, frame-dragging the surrounding space. Something like this:

Image
(see http://www.cybsoc.org/cybcon2008prog.htm#jw)

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 as demonstrated by the Einstein de-Haas effect. 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). They were at CERN for 7 years. 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. There's more, such as Confined Propagation as a Particle Model by Don Jennings at the NASA Goddard Space Flight Center. See google for other instances, such as this undated Electron Ring Vortex Model by William Hamilton.
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Re: Getting to grips with electromagnetism

Postby Farsight » Tue Oct 26, 2010 6:42 pm

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 used to say:

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, went 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 that 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:

Image

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 kick them through the inhomogeneous magnetic field. You'd see a line on the screen as per the classical prediction:

Image

Now collect all your still-spinning particles together again, and set them down on the table like a bunch of spinning Earths. 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 kick 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.

Of course the Stern-Gerlach experiment was done with silver atoms where a single outer-shell electron is spinning around the nucleus. It was repeated by Phipps and Taylor in 1927 using ground-state hydrogen, so it's actually more like two globes spinning round one another. But I hope you get the picture anyway.
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Re: Getting to grips with electromagnetism

Postby Farsight » Tue Oct 26, 2010 7:17 pm

In summary

In summary, the electromagnetic field is curved space. You can say it's twisted or curled to account for curvature in more than one plane, but the curvature is the main thing. Note that this is curved space, not curved spacetime.

The picture hopefully gets even clearer when you start thinking about what an electromagnetic wave actually is. There's an electromagnetic field variation, the electric field is a "twist" field, so the positive sinusoidal peak is where space is twisted one way, and the negative sinusoidal peak is where it's twisted the other. The in-phase magnetic waveform is showing you the turn that occurs as space twists. That means the electromagnetic wave is a pulse of displacement current moving laterally at c. So the electromagnetic wave is just a wave of space in space. And if you've ever heard of pair production, you'll know that we can make matter out of it. But's that's one for another day.

Discuss!
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Getting to grips with electromagnetism discussion

Postby MartinBraun » Thu Nov 11, 2010 8:26 am

Farsight wrote:Note that this is curved space, not curved spacetime.
Discuss!

Well, I would rather say it is a curved grid.

But I do have another question: The moment matter gets created out of "free" waves, I wonder if the EM field is a compensation for that what was taken away. Imagine a universe without matter: When the first "slower than c" particle is formed, it takes free propagating waves (photons) out. So in a sense it leaves a hole in the "speed=c structure". To fill the hole, the grid has to be curved.

Is it possible, that an EM field as well as gravity, are just a compensation after the conversion of free waves (photons at c) into looped-waves (matter at slower than c)?
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Re: Getting to grips with electromagnetism

Postby Farsight » Fri Nov 12, 2010 1:10 am

MartinBraun wrote:But I do have another question: The moment matter gets created out of "free" waves, I wonder if the EM field is a compensation for that what was taken away. Imagine a universe without matter: When the first "slower than c" particle is formed, it takes free propagating waves (photons) out. So in a sense it leaves a hole in the "speed=c structure". To fill the hole, the grid has to be curved.
I suppose it is in a way. The photon is an EM field variation. Perform pair production, and that variation is now tied down as negative and positive charge, namely the electron and positron, each of which can be modelled as a chiral self-trapped 511keV photon going round and round. But light always travels in straight lines, so light going round in circles means the space is curved. Around what? A point? Or maybe a hole? If light can't get out, or light can't get in, space is "closed". The bottom line is that If light can't go there, it's a hole in space. A hole in nothing? Now, that would be something!

martinBraun wrote:Is it possible, that an EM field as well as gravity, are just a compensation after the conversion of free waves (photons at c) into looped-waves (matter at slower than c)?
Yes for the EM field, but no for gravity. We see positive and negative charge, but we don't see the same for gravity. Energy causes gravity, the disposition doesn't count.
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Re: Getting to grips with electromagnetism

Postby MartinBraun » Sun Nov 21, 2010 4:21 am

Farsight wrote: The bottom line is that If light can't go there, it's a hole in space. A hole in nothing? Now, that would be something!


Not so fast. If a wave runs in a closed loop complex, it does not leave because it is locked (stable standing wave, which can stay that way on its own).
I do not like pair production because it involves matter. It is far more interesting to think about creating matter without matter.

To do that, the structure has to be very turbulent. If the turbulences are the right size reltive to the wavelengths and amplitudes, a photon might be forced into a closed loop. How many times that happens is statistics. It basically depends on how big the big bang was and what the surrounding looks like (low temperature pattern of the environment around the big bang).

A wave that is locked in a closed loop can takes away energy from the "straight" waves, which are not in a closed loop.
And taking away the energy (energy = necessary to make a wave flying sharp curves), requires compensation of course. So the structural density around the particle has to weaken. But due to the dynamic principal (any universe has to be dynamic, because only nothingness can have no dynamic), it must be a non-linear implementation of the weakness. This is why gravity (like everything else) does not decrease linear with distance.

In a grid, where every point is connected to the neighboring points, there cannot be any holes or other wonders. There must be smooth transitions, because a perfect jump would require infinite energy. A hole in the grid is not a logical conclusion, because a hole would not generate gravity. Which is precisely why a black hole is anything else but a hole. Oh, and by the way, it is not black either. To the naked eye, it actually is bright white.

To get gravity, the grid must compensate and fill any (theoretical) holes. Only if the grid closes a hole, it can weaken on that location, making the area less dense. Everything will tend to head towards the area of lesser density, because it generates lower resistance for both, light and matter.

A hole would not compensate and gravity around a hole would be non-existent.

Do you see my point?
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Re: Getting to grips with electromagnetism

Postby Farsight » Fri Dec 10, 2010 7:26 am

Sorry Martin, your post went under my radar:

MartinBraun wrote:Not so fast. If a wave runs in a closed loop complex, it does not leave because it is locked (stable standing wave, which can stay that way on its own). I do not like pair production because it involves matter. It is far more interesting to think about creating matter without matter.
No problem, see photon-photon pair production and the Stanford experiment as per Little Bang's link to Scientists Using Light to Create Particles.

MartinBraun wrote:To do that, the structure has to be very turbulent. If the turbulences are the right size reltive to the wavelengths and amplitudes, a photon might be forced into a closed loop. How many times that happens is statistics. It basically depends on how big the big bang was and what the surrounding looks like (low temperature pattern of the environment around the big bang).
IMHO it's displacement current rather than turbulence. An electromagnetic wave is a "pulse" of alternating displacement current, propagating linearly at c. This is why vacuum impedance Z0 = √(μ00) applies wherein c = √(1/ε0μ0), impedance being resistance to alternating current. If it is further displaced such that it travels through itself, it displaces its own path, which ends up as a closed path.

MartinBraun wrote:A wave that is locked in a closed loop can takes away energy from the "straight" waves, which are not in a closed loop.
Again no problem, this is Compton scattering.

Image
http://hyperphysics.phy-astr.gsu.edu/hb ... ompeq.html

MartinBraun wrote:And taking away the energy (energy = necessary to make a wave flying sharp curves), requires compensation of course. So the structural density around the particle has to weaken. But due to the dynamic principal (any universe has to be dynamic, because only nothingness can have no dynamic), it must be a non-linear implementation of the weakness. This is why gravity (like everything else) does not decrease linear with distance...
The compensation is that the electron moves. I don't think there's any impact on density or gravity. A concentration of energy causes gravity, regardless of how its configured. Let's talk about gravity and black holes on the appropriate threads.
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Try Lorentz

Postby yngveha » Mon Nov 07, 2011 11:20 pm

Most of the time when i read attempts to explain electromagnetism it ends up in either the right hand rule, Maxwell, or some kind of visualization of the magnetic field - which really doesn't explain much at all, they only describe how stuff work.

The key to understand the link between electricity and magnetism, which in reality is more like electricity and relativity is quite simple, it is the Lorentz contraction. Now the Lorentz contraction in it self is considered tough learning by many, but for this point, you need only to accept the concept, not fully understand it:

1: When you observe an object moving by you at a certain speed it appears to be shorter than if it were standing still.

So, how does this relate to explaining magnetism? Instead of thinking of coils and magnets (which can be deduced later), think of two parallel electrical wires (conductors) leading current in the same direction.

2: Imagine taking the place of a proton in one of the wires and observe the other conductor; there you see a group of pesky protons standing still, while all the beautiful electrons are passing by. Due to the Lorentz contraction, the distance between the electrons seems smaller than the distance between the protons in the opposite wire. Thus you see more electrons than protons (on a given length of the wire) which makes that other wire quite attractive.

3: Now do the same thought experiment from an electrons point of view in the same pair of wires. As the electrons in both wires are moving in the same direction, you will see more protons (as they move relative to you) than electrons in the other wire- thus also electrons is being attracted by the other wire.

In both cases the charges in one wire are electrically attracted to the charges in the other wire, which gives a net pull. This explains the basic concept of magnetism without touching the right hand rule. (Personally i use it to deduce the right hand rule if i need it). Mathematics proving this was given by WGV Rosser in the sixties. Following the chain of thought a little bit further, it is easy to understand concepts like induction, self induction, electrical generators etc. It is perhaps a bit tricky at first when it comes to permanent magnets (But hey- it can actually be used to indicate that the charges moving around in permanent magnets actually does require space / they are not spinning in an infinitely small point--).

Normally, when teaching physics, you touch electricity and magnetism separately before going into relativity, thus you are stuck with confusing visualizations of magnetic fields, right hand rule etc before you bump into Maxwell (ouch) and then the confusion is complete. Personally, my findings (having worked as a teacher) is that interested students or pupils in the age of 15+ is perfectly able to follow the three points given above, even though they may not be familiar with special relativity or the Lorentz transformation. In my world of thinking, giving this explanation, not only opens up for a deeper understanding of electromagnetism, it may also give some incentive for learning the concept of the Lorentz transformation at a later stage.
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