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rationalnoodles comments on Yet More "Stupid" Questions - Less Wrong Discussion
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Is it a good idea to learn physics not from classical mechanics to quantum mechanics but the other way around i.e. from lesser scale to larger, to decrease the amount of things one needs to memorise and increase actual understanding?
No. You should follow an established curriculum because the textbooks are written that way, such as where mathematical techniques are introduced.
Memorizing enables fast recall. If you have to know it, you'll have to memorize it even if you can derive it. And there is very little to memorize in physics. You have to know that metals are ductile, but that's not a lot of information; you're not going to check it by going back to quantum mechanics. In principle, you could use QM to derive a quantitative version, but it's computationally intractable.
In the direct relation between quantum and classical mechanics, QM is simply more complicated: you generally start with the classical laws and modify them, so they are a prerequisite. I think that there is a recent QM textbook by quantum computing researchers that get to quantum weirdness with very few prerequisites. This sounds like a good place to start, but if you want to cover the whole thing, you'll need classical mechanics.
Thanks, I think I'm gonna follow this.
You don't get to memorize less this way. You learn from simpler to harder, not from smaller to larger. If you already know all the relevant math (linear algebra, complex analysis, partial differential equations), it might be interesting to start from, say, QM and then derive CM from it. But wait, shouldn't you start even smaller, with QFT, or at least with the Standard Model of Particle Physics, then proceed to peel off QCD and QED, then extract a Hilbert space from the Fock space and do QM, then construct CM and E&M... But that's not enough, what about gravity? Better learn GR, then derive SR from it, and Newtonian gravity as well.
I suppose it's not impossible, but the amount of math you would have to learn before you finally derive that F=ma is rather significant. In some parallel world, where every physicist learns a lot of math first, it might even make sense. But if you want to get some useful results early, and not spend 4 years learning math before you even think about physics, then you should probably start with classical mechanics and classical electrodynamics.
Thanks. Looks like that, although learning physics from "basics" is possible and immensely cool, it's also really difficult, so, I think I'm gonna follow ordinary approach.
That said, I had an instructor who started the first course in electricity in magnetism by writing out the Maxwell equations, then working through them down to the Coulomb's law and other special cases, which is the opposite of the standard approach. But he knew what he was doing and was careful to only inflict the minimum necessary amount of math and rigor on the poor unsuspecting suckers in his class. I do not know of anyone deriving F=ma from the least action principle at an introductory physics course, though it seems doable.