  Tomographic locality is a principle commonly used in the program of finding
axioms that pick out quantum theory within the landscape of possible theories.
The principle asserts the sufficiency of local measurements for achieving a
tomographic characterization of any bipartite state. In this work, we explore
the meaning of the principle of tomographic locality by developing a simple
scheme for generating a wide variety of theories that violate the principle. In
this scheme, one starts with a tomographically local theory -- which can be
classical, quantum or post-quantum -- and a physical symmetry, and one
restricts the processes in the theory to all and only those that are covariant
with respect to that symmetry. We refer to the resulting theories as twirled
worlds. We show that failures of tomographic locality are ubiquitous in twirled
worlds. From the possibility of such failures in classical twirled worlds, we
argue that the failure of tomographic locality (i.e., tomographic nonlocality)
does not imply ontological holism. Our results also demonstrate the need for
researchers seeking to axiomatize quantum theory to take a stand on the
question of whether there are superselection rules that have a fundamental
status.
