Take a look at Minkowski’s Space and Time dating from 1908. Towards the back is this:
"In the description of the field caused by the electron itself, then it will appear that the division of the field into electric and magnetic forces is a relative one with respect to the time-axis assumed; the two forces considered together can most vividly be described by a certain analogy to the force-screw in mechanics; the analogy is, however, imperfect".
Note how he said the field, and referred to electric and magnetic forces. The electron doesn't have an electric field or a magnetic field, it has an electromagnetic field. See Wikipedia and note this:
"Over time, it was realized that the electric and magnetic fields are better thought of as two parts of a greater whole - the electromagnetic field".
Also note the word screw. If you have a pump-action screwdriver you’ll appreciate that linear force is converted into rotational force. That’s like an electric motor: current flows along the wire, and the motor turns. When you use an ordinary screwdriver, rotational force is converted into linear force, and the screw is driven into the wood. That’s like a dynamo: turn the rotor, and current flows along the wire. We even have the right-hand rule which applies not just to electromagnetism, but to screw threads.
But you don’t usually hear about this "screw nature of electromagnetism". Instead you tend to read about the electric field E and the magnetic field B as if they’re separate fields rather than “two parts of a greater whole”. In John Jackson’s authoritative textbook Classical Electrodynamics you have to wait until section 11.10 before he says "one should properly speak of the electromagnetic field Fμv rather than E or B separately". By and large, physicists who are taught about electromagnetism think of E and B as fields rather than forces, and have no real concept of the Fμv electromagnetic field. They don't know how to visualize it. They can visualize the E and B easily enough. There's plenty of depictions out there. E is usually drawn with radial lines of force, and B is usually drawn with concentric lines. There's no problem visualizing them. But there's nothing that lets you visualize the "greater whole". However I think there is a way. A simple way. You just combine the radial and concentric lines. Like this:
Once you do this, you immediately appreciate the screw nature of electromagnetism in a visceral way. Other things start falling into place too. You read about the frame-dragging of gravitomagnetism and spot things like "there is a space-time vortex around Earth" and "if space is twisted". You appreciate why gravitomagnetism is an analogy of electromagnetism. You follow the lead back to Maxwell and you spot 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". And you spot Maxwell’s page title too, which is "The Theory of Molecular Vortices". You appreciate Faraday all the more, and you realise why spinors are called spinors. You read about Dirac’s belt and you start to see things that were never in your textbooks. You can create an electron along with a positron in pair production. Out of light. And you can diffract the electron, because it has a wave nature. Like it’s light trapped by its own displacement current such that what was an electromagnetic field-variation now looks like a standing field. Like it's an optical vortex.
It fits. Especially since counter-rotating vortices attract, and co-rotating vortices repel. A cyclone is a vortex. If you could set down two cyclones next to one another they’d move linearly apart. If you could set down a cyclone near to an anticyclone, they’d move together. And if you could hurl the cyclone past the anticyclone, they’d swirl around one another too, like electrons and positrons do in positronium. They're dynamical spinors in frame-dragged space, and E and B denote the linear and rotational forces between them. The forces that result from electromagnetic field interactions, where it takes two to tango. Hence when you look at Wikipedia again, now you notice this:
"The electric field is a vector field. The field vector at a given point is defined as the force vector per unit charge that would be exerted on a stationary test charge at that point".
Yes, it makes sense, but you don’t hear much about the screw nature of electromagnetism. Or the geometry of electromagnetic systems. It ties in with topological quantum field theory, but not the Standard Model. People say the electron is a fundamental particle, and some even say it's a point particle, even though the electron is supposed to be a field excitation. Even though it's quantum field theory, not quantum point particle theory. For myself I think this needs to go into the Standard Model, and work is required "within the Standard Model", not "beyond the Standard Model". But it isn't easy persuading the sort of people who say the electron is surrounded by a cloud of photons popping in and out of existence. Spontaneously. Like worms from mud. As if hydrogen atoms twinkle, and magnets shine. So whilst we'll get there one day, it will be a while yet. And meanwhile, just like Max Planck said, science advances one funeral at a time.
"In the description of the field caused by the electron itself, then it will appear that the division of the field into electric and magnetic forces is a relative one with respect to the time-axis assumed; the two forces considered together can most vividly be described by a certain analogy to the force-screw in mechanics; the analogy is, however, imperfect".
Note how he said the field, and referred to electric and magnetic forces. The electron doesn't have an electric field or a magnetic field, it has an electromagnetic field. See Wikipedia and note this:
"Over time, it was realized that the electric and magnetic fields are better thought of as two parts of a greater whole - the electromagnetic field".
Also note the word screw. If you have a pump-action screwdriver you’ll appreciate that linear force is converted into rotational force. That’s like an electric motor: current flows along the wire, and the motor turns. When you use an ordinary screwdriver, rotational force is converted into linear force, and the screw is driven into the wood. That’s like a dynamo: turn the rotor, and current flows along the wire. We even have the right-hand rule which applies not just to electromagnetism, but to screw threads.
But you don’t usually hear about this "screw nature of electromagnetism". Instead you tend to read about the electric field E and the magnetic field B as if they’re separate fields rather than “two parts of a greater whole”. In John Jackson’s authoritative textbook Classical Electrodynamics you have to wait until section 11.10 before he says "one should properly speak of the electromagnetic field Fμv rather than E or B separately". By and large, physicists who are taught about electromagnetism think of E and B as fields rather than forces, and have no real concept of the Fμv electromagnetic field. They don't know how to visualize it. They can visualize the E and B easily enough. There's plenty of depictions out there. E is usually drawn with radial lines of force, and B is usually drawn with concentric lines. There's no problem visualizing them. But there's nothing that lets you visualize the "greater whole". However I think there is a way. A simple way. You just combine the radial and concentric lines. Like this:
Once you do this, you immediately appreciate the screw nature of electromagnetism in a visceral way. Other things start falling into place too. You read about the frame-dragging of gravitomagnetism and spot things like "there is a space-time vortex around Earth" and "if space is twisted". You appreciate why gravitomagnetism is an analogy of electromagnetism. You follow the lead back to Maxwell and you spot 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". And you spot Maxwell’s page title too, which is "The Theory of Molecular Vortices". You appreciate Faraday all the more, and you realise why spinors are called spinors. You read about Dirac’s belt and you start to see things that were never in your textbooks. You can create an electron along with a positron in pair production. Out of light. And you can diffract the electron, because it has a wave nature. Like it’s light trapped by its own displacement current such that what was an electromagnetic field-variation now looks like a standing field. Like it's an optical vortex.
It fits. Especially since counter-rotating vortices attract, and co-rotating vortices repel. A cyclone is a vortex. If you could set down two cyclones next to one another they’d move linearly apart. If you could set down a cyclone near to an anticyclone, they’d move together. And if you could hurl the cyclone past the anticyclone, they’d swirl around one another too, like electrons and positrons do in positronium. They're dynamical spinors in frame-dragged space, and E and B denote the linear and rotational forces between them. The forces that result from electromagnetic field interactions, where it takes two to tango. Hence when you look at Wikipedia again, now you notice this:
"The electric field is a vector field. The field vector at a given point is defined as the force vector per unit charge that would be exerted on a stationary test charge at that point".
Yes, it makes sense, but you don’t hear much about the screw nature of electromagnetism. Or the geometry of electromagnetic systems. It ties in with topological quantum field theory, but not the Standard Model. People say the electron is a fundamental particle, and some even say it's a point particle, even though the electron is supposed to be a field excitation. Even though it's quantum field theory, not quantum point particle theory. For myself I think this needs to go into the Standard Model, and work is required "within the Standard Model", not "beyond the Standard Model". But it isn't easy persuading the sort of people who say the electron is surrounded by a cloud of photons popping in and out of existence. Spontaneously. Like worms from mud. As if hydrogen atoms twinkle, and magnets shine. So whilst we'll get there one day, it will be a while yet. And meanwhile, just like Max Planck said, science advances one funeral at a time.
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