What after CERN? Opportunities from co-responding systems

We offer some arguments in favor of the construction of an experimental facility, where to test fundamental theories of Nature by using co-responding systems. Co-responding systems are physical systems such that certain behaviors of one system are clearly related to certain behaviors of the other system. Physical systems available at our energy scales, co-responding to the unreachable high-energy systems, are what we need, to attack from an experimental perspective the open questions beyond the reach of CERN. The focus here is on two scenarios with which we have some familiarity: hadron production in high energy scattering processes as a Unruh phenomenon, and graphene as a quantum field theory in a curved spacetime, the latter being our prime bet.