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RolfAndreassen comments on Local truth - Less Wrong Discussion
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You don't even have to leave fundamental physics. Firstly the existing equations are (presumably) approximations to the underlying unified theory; secondly, we can't solve them exactly anyway, and even in the relatively tractable electroweak case we use the approximation of a truncated sum. As for the strong force, where that technique doesn't converge, don't even ask.
I meant actual fundamental physics, not the standard model, which is already known to be a (very good) approximation. There are some statements we can make which at least have the possibility of being exactly correct - the general form of the Schrodinger equation, General Relativity, conservation of momentum... that sort of thing.
As for truncated series etc, that fits exactly into the sort of approximation I was talking about.