Most people have heard of Minkowski’s Space and Time
paper from 1908. They’re aware that it constituted an important development for special relativity. However very few people notice a little paragraph two pages from the back:"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 perspicuous way of describing the two forces together is on a certain analogy with the wrench in mechanics, though the analogy is not complete".
A wrench turns a bolt which has a screw thread. You turn a screw and it moves forward. Or you can use a pump-action screwdriver to convert linear motion into rotational motion. This is why alternators and generators and electric motors work, and you can find a reference to a screw mechanism in Maxwell’s On Physical Lines of Force
. See http://en.wikipedia.org/wiki/File:On_Ph ... _Force.pdf
and note this line on the wikipedia page 53:"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 "
Look at the page heading and see where it says The Theory of Molecular Vortices
. Maxwell didn’t get this right, but it turns out he wasn’t far off. Once you understand the dualism of the electromagnetic field, it’s horribly simple: it's a "twist/turn" field with an underlying curved spatial geometry.
Think about a vertical column of electrons and try to envisage the surrounding electromagnetic field. If you are motionless with respect to this, you’ll see the electric aspect of the field, with radial “electric field” lines and linear motion along them. If however you move downwards past the column of electrons, you’ll see the magnetic aspect of the field, with orbital “magnetic field” lines and rotational motion around them. Your downward motion is relative, so the magnetic aspect is visible if you
are motionless and the electrons
are moving upwards, as per a current in a wire and the right-hand-rule:
Note that it’s one field, it’s the electromagnetic
field, not separate electric fields and magnetic fields. 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 electromagnetic
field, and it exerts force in two ways. It doesn’t actually look like anything, but iron filings on a piece of paper tells you that you can visualize a field. Note though that the iron filings only show you a slice through a “magnetic” field, and you need to see the electromagnetic twist/turn field in three dimensions. You can use a drill bit for this, but a reamer is better. This kind of thing:
Grasp a reamer in your right fist, place your left thumb on the bottom of it, and push upwards. It turns. The disposition of the electromagnetic field around a column of electrons is like a reamer. It has an innate twist, and motion through it causes turn. If you imagine a nested family of reamers all centred on the same vertical line, you can get an idea of how the field strength diminishes with distance. Then when you imagine a horizontal slice through the field, it would have a spatial twist like this:
This twist is however in three dimensions, which is why Minkowski said the analogy is not complete
. Take a piece of wire and bend it to form a Fibonacci spiral. It is now curved, and resembles one of the lines in the picture above. Now lie the wire flat on your desk and bend in another Fibonacci spiral orthogonal to the first. Your wire is now “curled”. Hence magnetic curl
. In Europe this is called rot, which is short for “rotor”. It’s caused by a frame-dragging effect by a central soliton or more properly "vorton" rotating in two dimensions, like this:
This is a depiction of the electron. It''s a self-trapped photon. See http://www.cybsoc.org/electron.pdf
. Note the black line in the depiction, indicating a double-rotation, hence spin ½ . Again we see twist and turn. The electron is often called an elementary or fundamental particle, but it isn't. You can create an electron via pair production:
It's like throwing a wave at an obstruction and seeing two opposite eddies coming out. These affect the surrounding space - something like a rotating electric floor polisher on a thin rubber sheet, but in three dimensions. The result is an electromagnetic field. Conservation of charge is rather like conservation of angular momentum - if you were up in space in a spacesuit and you manhandled a satellite to give it a rotation, you’d find yourself counter-rotating.
The reason why the photon self-traps at 511keV is straighforward. An electromagnetic field is a twist/turn field, and it is a spatial geometry. A light wave is an electromagnetic field variation, which is actually a pulse of "twist/turn". It's best to think in terms of a pulse of spacewarp
in a cubic lattice. Imagine a lemon-shaped extensional distortion of the lattice in the centre - a bulge like a swell wave on the ocean surface, but symmetrical top and bottom because this is in a bulk. The archetypal sinusoidal electromagnetic wave is telling you the slope of the horizontal lattice lines. Around a lemon-like shape, the slope rises to a maximum a quarter-way along the lemon, goes back to zero at the top of the lemon, then falls to a negative maximum three-quarters along, then goes to zero again. If this pulse of spacewarp encounters another pulse of spacewarp, it's moving through warped space, and so its path changes. If this causes it to encounter more spacewarp, its path will change further. That black line in the depiction above is telling you that here we have spacewarp that is travelling entirely through itself. At 511keV, where the degree of spacewarp is just right. The path keeps changing, and as a result the photon energy/momentum is now travelling in a circular path. Hence angular momentum and magnetic dipole moment with a g-factor of 2.0023.
But we don't call it a photon any more. We call it an electron.