Ab-Initio

[william]

Starting from fundamental mathematics, where some axioms are taken to be true, all of mathematics that exists today can be reproduced (albeit by introducing extra axioms). With this the language is developed to use in physics. Classical mechanics is an excellent example as this theory has been developed to try an imitate the real world as closely as possible, the fundamentals behind this theory starts in the same way mathematics did, by describing the positions of objects through coordinates and expanding upon this by defining derivatives, integrals and so on. It is not just a theory that works because it assumes it does. It works because it build upon itself through first principles.

Then came quantum mechanics which is done by expanding upon classical mechanics by doing a first and then second quantization together with some axioms (like the axioms for operators on a Hilbert space). So working all the way back, one also finds that this theory is first principle based.

Electromagnetism on the other hand, is (at least I think so for now), not first principles. It is not a theory that you can develop by itself, you need other theories to create the maxwell-laws, you need a coulomb potential to describe electrostatics. In the most fundamental way this is just a potential energy parameter. However, in electromagnetism the coulomb potential is ~qQ/r, which we get through empirical means, and not through fundamental physics.
There is also the case that many, many theories can reproduce maxwell’s equations. Classical mechanics can (field theory), special relativity, QED, etc.

[Author]

Posts