There's even an argument that separability is sufficient for most of mathematics let alone physics (http://arxiv.org/pdf/math/0509245.pdf http://arxiv.org/pdf/m

There's even an argument that separability is sufficient for most of mathematics let alone physics (http://arxiv.org/pdf/math/0509245.pdf http://arxiv.org/pdf/math/0509245.pdf) but you're going to have to work very hard to persuade me that if we're going to describe any sets as physical then uncountable ones are less physical than countable ones.