The ab initio way — Liam Pattinson’s response

[LiamPattinson]

“Why do we call quantum physics an ab initio model? Why do we call classical mechanics an ab initio model? Is classical electromagnetism an an ab initio model (and if it is one, what are its first principles)?”

Quantum physics is called an ‘ab initio’ (first principles) model as, starting from a mathematical model and some basic postulates, it is possible — at least in principle — to exactly capture all relevant physics. It is not necessary to introduce additional assumptions or postulates for specific applications of quantum theory. In this sense, it is a universal theory.

Classical mechanics is called ‘ab initio’ for similar reasons. Though it cannot describe any quantum behaviour whatsoever, within the bounds of classical physics it is possible to describe every possible outcome of an experiment using Newton’s laws. (Or the laws of general relativity, depending on how one defines ‘classical’).

Classical electromagnetism may also be considered ab initio — its fundamental laws are described by Maxwell’s equations (though one may equally use the language of electromagnetic potentials), and the Lorentz force. The inclusion of the Lorentz force allows one to solve for cases such as a charged particle moving in an electromagnetic field, which cannot be described using Maxwell’s equations alone.

[LiamPattinson]

Since watching the interesting videos in the ‘dig deeper’ section for this topic, I believe I hadn’t quite understood the meaning of ‘ab initio’.

Quantum physics can be considered ‘ab initio’ because of the way it is formally structured: the 5 postulates of quantum mechanics serve as axioms to the theory, calculus as a derivation rule, and a number of statements and symbols can also be defined. Classical mechanics is similar, with axioms of Newton’s laws (or some equivalent).
Classical electromagnetism is similar again, with Maxwell’s laws serving as axioms. Contrary to my initial answer, I’m no longer sure if the Lorentz force is required to form a complete theory — I suspect that it isn’t, as the addition of the Lorentz force widens the possible applications of the theory but does not affect whether or not it is formally sound.

Even if classical electromagnetism can be considered ‘ab initio’ as a theory, not all electromagnetic problems may be solved from first principles. Properties such as electric permittivities, magnetic permeabilities, and conductivities cannot be predicted using classical electromagnetism, and must be inserted into the equations as experimentally determined parameters. Alternatively, they could be determined using methods from quantum physics.

[Author]

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