Unified all previous electro-magnetism theories into one equation.
Explains the propagation of light as a wave, and matches the previously known relationship between the speed of light and electromagnetic constants.
The equations are a limit case of the more complete quantum electrodynamics, and unlike that more general theory account for the quantization of photon.
The equations are a system of partial differential equation.
The system consists of 6 unknown functions that map 4 variables: time t and the x, y and z positions in space, to a real number:and two known input functions:
- , , : directions of the electric field
- , , : directions of the magnetic field
- : density of charges in space
- : current vector in space. This represents the strength of moving charges in space.
Due to the conservation of charge however, those input functions have the following restriction:
Equation 1.
Charge conservation
. Also consider the following cases:
- if a spherical charge is moving, then this of course means that is changing with time, and at the same time that a current exists
- in an ideal infinite cylindrical wire however, we can have constant in the wire, but there can still be a current because those charges are movingSuch infinite cylindrical wire is of course an ideal case, but one which is a good approximation to the huge number of electrons that travel in a actual wire.
The goal of finding and is that those fields allow us to determine the force that gets applied to a charge via the Equation "Lorentz force", and then to find the force we just need to integrate over the entire body.
Finally, now that we have defined all terms involved in the Maxwell equations, let's see the equations:
Equation 2.
Gauss' law
. Equation 3.
Gauss's law for magnetism
. Equation 4.
Faraday's law
. Equation 5.
Ampere's circuital law
. You should also review the intuitive interpretation of divergence and curl.
These often come pre-soldered on devboards, e.g. and allow for easy access to GPIO pins. E.g. they're present on the Raspberry Pi 2.
Why would someone ever sell a devboard without them pre-soldered!
Underside of a Raspberry Pi 2
. Source. At the top of this image we can clearly see how the usually pre-soldered pin header connectors go through the PCB and are soldered on both sides.
- youtu.be/HQ1lrEQsj4c?t=51 shows Fluke 731B Voltage Standard which contains 1.018 values due to Weston cell voltage standard
Covariance and contravariance of vectors by 
Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01As mentioned at: cirosantilli.com/china-dictatorship/falun-gong#christine-marie Ciro Santilli considers this a synonym for "Prophet".
Sometimes it feels like this could be how we finally make experiments to see what the theory of everything looks like, a bit like the first high energy experiments were from less exotic cosmic rays.
Local symmetries appear to be a synonym to internal symmetry, see description at: Section "Internal and spacetime symmetries".
As mentioned at Quote , local symmetries map to forces in the Standard Model.
Appears to be a synonym for: gauge symmetry.
A local symmetry is a transformation that you apply a different transformation for each point, instead of a single transformation for every point.
TODO what's the point of a local symmetry?
Bibliography:
- lecture 3
- physics.stackexchange.com/questions/48188/local-and-global-symmetries
- www.physics.rutgers.edu/grad/618/lects/localsym.pdf by Joel Shapiro gives one nice high level intuitive idea:
In relativistic physics, global objects are awkward because the finite velocity with which effects can propagate is expressed naturally in terms of local objects. For this reason high energy physics is expressed in terms of a field theory.
- Quora:
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