Response to "Are Hilbert Spaces Unphysical? Hardly, My Dear!''

Abstract: A recent criticism of our paper ``The unphysicality of Hilbert spaces'' by Nivaldo Lemos refutes our central argument that a state with finite expectation value can be mapped to a state with infinite expectation value by a coordinate transformation. By conflating coordinate transformation with change of basis in quantum mechanics, Lemos argues that expectation values are invariant under change of variables. In the present work, we clarify the distinction between coordinate transformation and change of basis, and rebut Lemos' main argument.