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There is of course a catch, since physics can be simulated (with an exponential slowdown) by a Turing machine.

The catch is that "macroscopic behavior" in this context includes things that are not really macroscopically observable, or require conditions that cannot easily be specified. For the spectral gap, I think the way this manifests is that you can't ever be certain that you're in the ground state, but I'm not sure this is correct.

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> since physics can be simulated

I must object. Our current models of physics can be simulated. But we cannot model what we do not understand, such as quantum gravity. And even then, we don't even have that many decimal places for certain bits of our models.

By definition the universe can “simulate” itself. Although it’s true we have no proof that this doesn’t go beyond Turing machine in power (yet it’s a reasonable assumption).

Of course the goal of physics is to compress the universe into simpler laws. But there’s no inherent reason that it should be possible.

> By definition the universe can “simulate” itself.

A 1:1 scale map is still just a map. Simulation isn't an identity operation.

> yet it’s a reasonable assumption

What are the reasons for this claim?

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