crackpot derivation of a crackpot cartoon
Any progress on this? You've had 7+ years to refine your model and work out some of its experimentally verifiable consequences. I'm keen to hear your results.
I want to make my own plot of your greyscale spiral. I have Maxwell's Equations and a differential-equation solver. What boundary conditions should I plug in, to exactly which equations, to obtain this spiral? Your plot seems to show an unidentified scalar quantity (represented by the greyscale). What quantity, precisely, maps to the greyscale?
Those are the relevant questions. In my own response to
Farsight below, I will explain why his previous answers have been insufficient (or worse).
That is not a mathematical equation. That is a crackpot equation.
It's a depiction relating to
one should properly speak of the electromagnetic field Fuv rather than E or B separately.
It's a crackpot depiction of the electromagnetic field F
μν.
You have never been able to provide any scientific explanation of what
that cartoon has to do with the F
μν tensor or its components.
Your references to F
μν are just like your references to Einstein's g
μν. After years of quoting a passage in which Einstein refers to those g
μν,
you had to admit you had no idea of what those gμν actually are.
You don't understand the F
μν any better. Had you actually read the book you've been citing as your proof-text (Jackson's
Classical Electrodynamics, Third Edition), you'd realize that (in inertial reference frames) the 12 nonzero components of that tensor consist of the three components of
the electric field E and the three components of
the magnetic field B, together with their additive inverses (because the electromagnetic tensor is antisymmetric).
By the way, that's Jackson's equation (11.138). Note well how the equation uses Einstein's g
μν to lower the indices of the contravariant F
μν. (You can't possibly understand what's that's about without understanding Einstein's g
μν, and
we know you don't know what those gμν mean.)
Jackson's equation (11.138) is basically the same as Einstein's equation (62) (in the paper where
you got lost at equation (3)), except Einstein uses the g
μν to raise the indices instead of using the g
μν to lower them. Einstein's equations (60b) and (63a) are Maxwell's equations in vector form. Jackson's equation (11.146) is just Einstein's equation (9) applied to the contravariant electromagnetic tensor F
μν. (You, of course, have a long history of denying the coordinate transformations stated by Einstein's equation (9).)
Your cartoon can't depict a magnetic field because
you've said the field is isotropic, which implies your picture violates
Gauss's Law for Magnetism, which is one of Maxwell's equations.
Your cartoon can't depict the electric field of a static electromagnetic field because
Faraday's Law of Induction says the curl of an electric field is zero unless the magnetic field is changing over time. That too is one of Maxwell's equations. (It might be possible to generate a dynamic electromagnetic field whose electric field looks like your cartoon, but we needn't consider that further because you've always denied that your cartoon depicts an electric field.)
You have always claimed
your cartoon depicts an electromagnetic field. As we have seen, however, it depicts neither an electric nor a magnetic field, and every component of the full electromagnetic field is a component of either the electric field or the magnetic field. That's why people who actually understand electromagnetism have greeted your claim with extreme skepticism.
This morning, you finally told us
your cartoon depiction of the electromagnetic field was obtained via a crackpot equation:
See that screw? You depict E with radial lines of force, you depict B with concentric lines of force. To visualise that greater whole, the field caused by the electron itself, you combine the radial and concentric lines like this:
A sufficiently ignorant person might indeed think he could add two radially symmetric pictures, both without twist, to obtain a third picture that incorporates twist.
Here, however, you seem to be saying you can add an electric field to a magnetic field. That doesn't work because the units are fundamentally different:
This difference in the units arises because forces produced by the magnetic field are proportional to speed (and orthogonal to both velocity and the field lines), while forces produced by the electric field are not. (That's related to the fundamental difference between time and space, whose dimensions are related by the speed of light.)
Adding fields of fundamentally incompatible units is
crackpottery of Shakespearean misdimensions. I was therefore not surprised to learn
your crackpot depiction of the electromagnetic field was obtained by making that mistake.
So far as I can figure out, the only possible connection between
your cartoon and the electromagnetic field is that your cartoon does show one (atypical) set of possible trajectories for charged particles moving within an electromagnetic field. Although the trajectories of charged particles are determined by the electromagnetic field interacting with their charge, mass, and velocity, those trajectories are quite different from the six-dimensional electromagnetic field itself. As a depiction of electromagnetic fields, therefore,
your cartoon is (and will always remain) a complete failure.
I'm adding this paragraph to address ben m's objection immediately below this post. Trajectories that bear some resemblance to the lines shown in Farsight's cartoon can be obtained by tossing a charged particle slightly to the side of an oppositely charged central body, even if the magnetic field is zero or negligible. I am in complete agreement with the rest of ben m's post.
As I have said elsewhere, the decomposition of an electromagnetic field into electric and magnetic fields is directly analogous to the decomposition of spacetime into space and time.
Minkowski did talk about spacetime. But he referred to a screw too. As did Maxwell. Obviously you've never read the original material.
Your estimates of what others have read or know continue to be less accurate than could be explained by random guessing.
More to the point,
you failed to read your own sources.
.
!
stuff that you think is significant for some unknown reason, Farsight: 
!
