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If you gave them the equivalent of a modern university education in physics, you most probably could.
There is very little that's actually difficult about relativity or
quantum mechanics at the purely conceptual level. Anybody can pick up
the basics from countless books written for the public if they
like. The true difficulty is technical. You cannot join the scientific
conversation without a mastery of Riemannian geometry or operator
theory, and these take many years to approach.
Yet the technical aspects are only used to actually solve problems,
and in principle one is free to solve a problem any way one likes.
I would claim that with nothing but the purely conceptual foundation of
the modern theories, such as could be explained in an evening,
the likes of Huygens and Newton would have had no difficulty
in solving real problems. They did so with the problems of their day after all, which were
just as vaguely expressed.
Their solutions would have looked nothing like what we expect to see today of course,
but would have been solutions nevertheless.
$E(X_t|F_s) = X_s,\quad t > s$
Heck, in Newton's case, you'd have to explain electrostatics before you could even get started on QM, and electrodynamics and electromagnetism before you could get very far. And I would claim that electromagnetism in particular is impossible to understand until and unless you're familiar with PDEs, because you have to be able to quantify the positive and negative feedbacks in order to even give a qualitative description of the system's behaviour.
Friends come and go. Enemies accumulate.
I would disagree. There is an entire conceptual apparatus that developed with
17th-19th century mathematical physics - generator functions, matrix algebra,
vector calculus - etc. I don't see how you can make meaningful predictions in
QM outside that framework.
Electrostatics is actually a bad example to use, precisely because the theory is mathematically identical to
Newtonian gravity. Even relativity would have been no problem to these guys. Einstein's contribution, while crucial,
is technically really very small, as it amounts to doing hyperbolic geometry instead of the Euclidean one. Newton
knew more about conics than most mathematicians probably do today.
As to making useful predictions in QM without these methods, remember that matrix mechanics is only Heisenberg's
picture. The Schroedinger picture is about wave equations, which had already been worked out in the middle of the
17th century by Euler and the Bernoulli gang.
$E(X_t|F_s) = X_s,\quad t > s$
Netwon would have been a pig to persuade, but I doubt he would have had problems with the theory. Every year hundreds of ordinarily talented undergrads work their way through the basics without falling off anything tall and hurting themselves, so a genius really wouldn't find it difficult.
Ed Witten of string theory fame apparently worked through an entire three year undergrad physics curriculum over a summer holiday - competently enough to enrol as an applied maths postgrad, even though his original major was history, and he was planning to be a political journalist.
He may have had help from his father, who was another theorist. But even so.
He also lasted one term as an economics wannabe, which may or may not say something relevant and interesting about economics.
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