The possibility of quantum interference of a composite object with many internal degrees of freedom
is studied, such that the internal degrees play a role of an internal environment. In particular, if
the internal degrees have a capacity for an irreversible record of which-path information, then the
internal-environment induced decoherence prevents external experimentalists from observing
interference. Interference can be observed only if the interfering object is sufficiently isolated
from the external environment, so that the object cannot record which-path information.
Extrapolation to a hypothetical interference experiment with a conscious object implies that being a
Schrödinger cat would be like being an ordinary cat living in a box without any information about
the world external to the box.