If Hilbert space is just a mathematical tool like a column for an accountant and doesn't have factual existence. How about the quantum vacuum. Isn't it quantum vacuum is just another tool? Is it like Hilbert space or does the quantum vacuum have more factual existence? If the quantum vacuum is just a math tool but has more factual existence. And since quantum vacuum uses Hilbert space.. can't we say the Hilbert space also has factual existence?