Based on the double slit experiment we know that in the case of a single particle system the wave function or state vector of position is in a superposition of possibilities before measurement.
But does this rule apply in the case of the vacuum state?
Is it in a superposition of (non degenerate energy) possibilities before measurement?
A physicist has replied to this question, in a personal correspondence, by noting that:
It is thought that in quantum field theory, different vacuum states are essentially classical, and don't get superposed quantum mechanically. The reason is their effectively infinite spatial extent, so the distinct vacuum configurations are mathematically very distant.
Yet I am not well convinced by his answer.
Isn't a quantum state, either a single particle or a vacumm, a nonlocal object in the Hilbert space and independent of physical space?
So why the vacuum state is an exception from the general rule of quantum theory that applies to position or momentum quantum state?
Why being "mathematically distant" rules out being "superposed" in the case of vacuum.
This is not trivial to me. Is there a theorem about this?
Should we suppose that there are multiple Hilbert spaces and therefore in a single Hilbert space there is only one quantum state for vacuum? and "by mathematically very distant" we need to consider another Hilbert space with its own vacuum state?
