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If you gave them the equivalent of a modern university education in physics, you most probably could.
I don't see this as the issue at all. Newton, Descartes, Huygens, Leibniz were first rate minds who were quite capable of bridging the conceptual and philosophical with the practical. This is in fact what they did and what we celebate them for.

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.



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$E(X_t|F_s) = X_s,\quad t > s$

by martingale on Mon Jun 1st, 2009 at 03:15:23 AM EST
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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.

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.

- Jake

Friends come and go. Enemies accumulate.

by JakeS (JangoSierra 'at' gmail 'dot' com) on Mon Jun 1st, 2009 at 04:14:43 AM EST
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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.
There's nothing specifically QM about any of your examples (generating functions, matrices or vector calculus). Historically, these ideas were developed for entirely different areas of mathematics in the 19th century or earlier, but even that late arrival had no limiting effect at all on scientists' ability to solve complex real world problems much earlier. For example, Euler (as for that matter Newton) was perfectly capable of treating full 3d motion in the middle of the 18th century without requiring the crutch of matrices or vectors. Monge was a master of PDE theory - in 1795!

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.

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$E(X_t|F_s) = X_s,\quad t > s$

by martingale on Mon Jun 1st, 2009 at 05:47:47 AM EST
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Also, they were terrifyingly smart.

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.

by ThatBritGuy (thatbritguy (at) googlemail.com) on Mon Jun 1st, 2009 at 02:53:52 PM EST
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Give Newton the Feynman Lectures on Physics and a summer and he'd be up to speed.

The brainless should not be in banking. — Willem Buitler
by Migeru (migeru at eurotrib dot com) on Wed Jun 3rd, 2009 at 04:33:02 AM EST
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