The notion of “a single particle” turns out to be problematic. The thing that requires arbitrarily much information is the amplitude for a particle to be in some particular state.
I should emphasize that amplitudes aren’t just a creature of our models—they are the thing that interfere to give you an diffraction pattern, or the shapes of an electron orbital cloud, or that get manipulated in a quantum computation.
So even in quantum mechanics, it takes an infinite amount of information to represent a single particle? That’s a problem.
It’s a problem for us. But the universe doesn’t have to care.
The notion of “a single particle” turns out to be problematic. The thing that requires arbitrarily much information is the amplitude for a particle to be in some particular state.
I should emphasize that amplitudes aren’t just a creature of our models—they are the thing that interfere to give you an diffraction pattern, or the shapes of an electron orbital cloud, or that get manipulated in a quantum computation.