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Originally posted by -PLB-
Yes.
Originally posted by Mary Rose
Originally posted by -PLB-
Yes.
That's the extent of your response?
Is this your way of saying that you see nothing in Maxwell's original equations that is lost to electrical engineers today?
Originally posted by buddhasystem
Mary, of course, would rather rely on intuition rather than on info and/or experience.
Originally posted by -PLB-
. . . I could also not find the original paper by Heaviside. . . . Too bad I can not verify what Heaviside actually published. If anyone knows where I can find this publication I would be happy to hear it.
Originally posted by Mary Rose
Bearden references the Proceedings of the Royal Society of London for Heaviside's discovery and publication, but I haven't figured out yet how to locate a 19th century document.
Originally posted by -PLB-
I would try a library
Originally posted by Mary Rose
Originally posted by buddhasystem
Mary, of course, would rather rely on intuition rather than on info and/or experience.
No, Mary considers more than one source for interpretation and information.
Originally posted by Mary Rose
Do you intend to try a library?
A scalar is a magnitude.
Originally posted by Mary Rose
Heaviside simply chopped off the scalar component of the quaternion and discarded it, then formulated this new "truncated to a vector" version as a much simpler mathematics, albeit of decreased topology.
If you add directional components to a scalar, you have something very much like a vector, you have a magnitude and direction, but instead of saying the direction is northeast as the vector in the previous example, you have an easterly component and a northerly component (and a vertical component which really doesn't apply in your car on a flat road). That's a bit of a simplification of quaternions but that's the idea.
Vector quantities have two characteristics, a magnitude and a direction. Scalar quantities have only a magnitude. When comparing two vector quantities of the same type, you have to compare both the magnitude and the direction. For scalars, you only have to compare the magnitude. When doing any mathematical operation on a vector quantity (like adding, subtracting, multiplying ..) you have to consider both the magnitude and the direction. This makes dealing with vector quantities a little more complicated than scalars.
Game developers apparently have the same math issues in rotating things as NASA. I found some interesting discussions between game developers regarding which math is easier for which applications, but I didn't find a single argument that they thought they were dealing with anything other than relative complexity between using the two mathematical approaches.
From the mid-1880s, quaternions began to be displaced by vector analysis, which had been developed by Josiah Willard Gibbs, Oliver Heaviside, and Hermann von Helmholtz. Vector analysis described the same phenomena as quaternions, so it borrowed some ideas and terminology liberally from the literature of quaternions. However, vector analysis was conceptually simpler and notationally cleaner, and eventually quaternions were relegated to a minor role in mathematics and physics. A side-effect of this transition is that Hamilton's work is difficult to comprehend for many modern readers. Hamilton's original definitions are unfamiliar and his writing style was prolix and opaque.
However, quaternions have had a revival since the late 20th Century, primarily due to their utility in describing spatial rotations. The representations of rotations by quaternions are more compact and quicker to compute than the representations by matrices. In addition, unlike Euler angles they are not susceptible to gimbal lock. For this reason, quaternions are used in computer graphics,[8] computer vision, robotics, control theory, signal processing, attitude control, physics, bioinformatics, molecular dynamics, computer simulations, and orbital mechanics. For example, it is common for the attitude-control systems of spacecraft to be commanded in terms of quaternions.
Originally posted by -PLB-
No, although I find the subject interesting, I have absolutely no doubt that the current maxwell equations are correct. So I am not as excited as you are.
Originally posted by -PLB-
Where is the experimental data that shows this "giant curled EM energy flow component" really exists? How did Bearden came to the conclusion it exists other than "Heaviside said so"? Too bad I can not verify what Heaviside actually published. If anyone knows where I can find this publication I would be happy to hear it.
Originally posted by Mary Rose
Quaternions: higher topology than vector or tensor algebra
PLB, you were looking for what Heaviside published? He never published it according to this unreliable source which I don't condone, but only provide to answer your curiosity about why you won't find it published by Heaviside (see third paragraph):
Originally posted by Mary Rose
What happened to your curiosity about:
Originally posted by -PLB-
Where is the experimental data that shows this "giant curled EM energy flow component" really exists? How did Bearden came to the conclusion it exists other than "Heaviside said so"? Too bad I can not verify what Heaviside actually published. If anyone knows where I can find this publication I would be happy to hear it.
Originally posted by -PLB-
It isn't clear what publication Bearden is talking about as he doesn't seem to add references to his claims.
Originally posted by -PLB-
He nowhere shows what aspect of the original equations exactly got "truncated".
Originally posted by -PLB-
The reason he does not do that is because it didn't happen.
Originally posted by -PLB-
I have already clearly laid out why the Lorentz gauge was correct; it is correct because it is in agreement with all known observations.