3 ms·
Maxwell's equations are not the simplest formulation for electromagnetic theory, and they're not a foundation, but merely a formulation of the physics. The mor
by jiggawatts 3y ago
Maxwell's equations are not the simplest formulation for electromagnetic theory, and they're not a foundation, but merely a formulation of the physics.
The more elegant mathematical foundation for understand electromagnetism is Noether's theorem.
The more elegant formulation of the physics is just:
∇F = J
Which uses natural units and the geometric algebra of spacetime to encode everything contained in Maxwell's equations, but in a way that is coordinate-free and relativistic.
See: https://en.wikipedia.org/wiki/Mathematical_descriptions_of_the_electromagnetic_field#Spacetime_algebra https://en.wikipedia.org/wiki/Mathematical_descriptions_of_t...
- computerfriend 3y agoBut ∇F = J is Maxwell's equations (written very concisely).
- jiggawatts 3y agoThat's like saying C++ is just machine code written very concisely.
- Koshkin 3y agoIn all fairness, it should be noted that, for better or worse, GA is not part of the mainstream; modern treatments use differential forms instead. For an accessible account, see, for example, https://www.jpier.org/ac_api/download.php?id=14063009 https://www.jpier.org/ac_api/download.php?id=14063009.
- jiggawatts 3y agoIMHO: Differential forms are just half-arsed GA. Physics is littered with incomplete implementations of GA using a mish-mash of random bits of mathematics because of a perverse insistence on refusing to use the appropriate algebra.