[1502.04573v2] Undecidability of the Spectral Gap (full version)

emperorpenguin:

argumate:

emperorpenguin:

argumate:

argumate:

I’d ask someone to explain this to me as one would to a child of five, but perhaps you’d just tell such a child to work harder at school and then study physics at university, so yeah.

emperorpenguin said: If you have a tiny chessboard with one atom per square, sometimes you can’t use maths to tell if the atoms talk to each other or not

what is it they’re saying

They’re saying “Hello! Let’s change our energy levels to a smooth spectrum since there are lots of us close to one another!”

But sometimes they don’t say that, even when there are infinity of them. And we can’t always use maths to find out.

where does an atom store its energy levels?

That’s actually a very deep question! Possible answers include:

-Inside the atom (energy levels as an emergent property from its other fundamental properties)

-Outside the atom (if quantum systems are nonlocal and everything in the universe talks to each other at once)

-An atom *is* the storage of its properties (quantum systems are just condensed information, if looked at in a certain way)

-Nowhere (the notion of “storage” is inapplicable for fundamental properties)

-Everywhere (energy levels are products of the boundary conditions of the universe)

But the truth is that we don’t know for sure. We don’t even know if that’s a valid question.

energy levels as an emergent property from its other fundamental properties

^^I like this one. I’m not convinced energy “exists” in any real sense.

[1502.04573v2] Undecidability of the Spectral Gap (full version)

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