Ciro Santilli @cirosantilli 37

Static case of Maxwell's law for electricity only.

Is implied by Gauss' law if Maxwell's equations: physics.stackexchange.com/questions/44418/are-the-maxwells-equations-enough-to-derive-the-law-of-coulomb

The "static" part is important: if this law were true for moving charges, we would be able to transmit information instantly at infinite distances. This is basically where the idea of field comes in.

It appears that Maxwell's equations can be derived directly from Coulomb's law + special relativity:This idea is suggested by the charged particle moving at the same speed of electrons thought experiment, which indicates that magnetism is just a consenquence of special relativity.

In the context of Maxwell's equations, it is vector field that is one of the inputs of the equation.

Section "Maxwell's equations with pointlike particles" asks if the theory would work for pointlike particles in order to predict the evolution of this field as part of the equations themselves rather than as an external element.

Measured in amperes in the International System of Units.

A different and more elegant way to express Maxwell's equations by using the:instead of the:

As of the 20th century, this can be described well as "the phenomena described by Maxwell's equations".

Back through its history however, that was not at all clear. This highlights how big of an achievement Maxwell's equations are.

The majority likely comes from physics:

The following aspects of Maxwell's equations make no sense without special relativity:

When charged particle though experiment are seen from the point of view of special relativity, it becomes clear that magnetism is just a direct side effect of charges being viewed in special relativity. One is philosophically reminded of how spin is the consequence of quantum mechanics + special relativity.

Bibliography:

In the standard formulation of Maxwell's equations, the electric current is a convient but magic input.

Would it be possible to use Maxwell's equations to solve a system of pointlike particles such as electrons instead?

The following suggest no, or only for certain subcases less general than Maxwell's equations:This is the type of thing where the probability aspect of quantum mechanics seems it could "help".

Currently an informal name for the Standard Model

Chronological outline of the key theories:

This section discusses the pre-photon understanding of the polarization of light. For the photon one see: photon polarization.

polarization.com/history/history.html is a good page.

People were a bit confused when experiments started to show that light might be polarized. How could a wave that propages through a 3D homgenous material like luminiferous aether have polarization?? Light would presumably be understood to be analogous to a sound wave in 3D medium, which cannot have polarization. This was before Maxwell's equations, in the early 19th century, so there was no way to know.

Atoms exist and last for a long time, while in classical electromagnetic theory punctual orbiting electrons should emit radiation quickly and fall into the nucleus: physics.stackexchange.com/questions/20003/why-dont-electrons-crash-into-the-nuclei-they-orbit

In other sections:

Bibliography:

In many important applications, what you have to solve is not just a single partial differential equation, but multiple partial differential equations coupled to each other. This is the case for many key PDEs including:

The history of light if funny.

First people thought it was a particle, as per corpuscular theory of light, notably Newton supported the corpuscular theory of light.

But then evidence of the diffraction of light start to become unbearably strong, culminating in the Arago spot.

And finally it was understood from Maxwell's equations that light is a form of electromagnetic radiation, as its speed was perfectly predicted by the theory.

But then evidence of particle nature started to surface once again with the photoelectric effect. Physicists must have been driven mad by all these changes.