  Without a complete theory of quantum gravity, the question of how quantum
fields and quantum particles behave in a superposition of spacetimes seems
beyond the reach of theoretical and experimental investigations. Here we use an
extension of the quantum reference frame formalism to address this question for
the Klein-Gordon field residing on a superposition of conformally equivalent
metrics. Based on the group structure of ``quantum conformal transformations'',
we construct an explicit quantum operator that can map states describing a
quantum field on a superposition of spacetimes to states representing a quantum
field with a superposition of masses on a Minkowski background. This
constitutes an extended symmetry principle, namely invariance under quantum
conformal transformations. The latter allows to build an understanding of
superpositions of diffeomorphically non-equivalent spacetimes by relating them
to a more intuitive superposition of quantum fields on curved spacetime.
Furthermore, it can be used to import the phenomenon of particle production in
curved spacetime to its conformally equivalent counterpart, thus revealing new
features in modified Minkowski spacetime.
