Undergrad "Different" energy eigenstates - clarification of meaning?

[asimov42]

Apologies for an additional thread (could not delete the previous one which was not coherent). After reading this paper:

https://link.springer.com/article/10.1007/s10701-021-00464-7
"Fast Vacuum Fluctuations and the Emergence of Quantum Mechanics" Gerard ’t Hooft

I was struck by a general question - the paper states (in relation to interference in the double slit experiment that): "It does something else however: if we select one slit, and repeat this experiment many times, then we are making a selection among the initial states chosen for the fast variables. This selection will not be an even one! Therefore, the initial state of the fast variables must now be described as a superposition of different energy eigenstates."

't Hooft's formulation requires all so called "fast variables" to be in their ground state always (as far as I can tell). So my question is: what does it mean to have "different" energy eigenstates when all variables must be in their lowest-energy eigenstates? This is a more general question that is not specific to this paper. That is, what's different?

Are two energy eigenstates considered "different" if they differ by phase only? Or can variables with different energy eigenstates have the same energy but be distinguished by other aspects of the state that may be different? I am confused in general about how two variables can be in their lowest energy states and yet be "different."

 

[asimov42]

I should have been more careful, I meant the Hamiltonian - from the paper: "Therefore, the initial state of the fast variables must now be described as a superposition of different energy eigenstates."

My understanding was that only one energy eigenstate was allowed in this case, in which all the fast variables have their lowest energy. Hence the superposition mentioned above confuses me.

Also, in a related paper 't Hooft mentions that "the excited modes [of the fast variables] are only virtually present."

Since the excited modes of the fast variables are forbidden by energy conservation, what does a 'virtual state' mean in the context above?