Tachyonic media in analogue models of special relativity

Abstract: In sonic models of special relativity, the fact that the sonic medium violates (ordinary) Lorentz symmetry is apparent to observers external to the sonic medium but not to a class of observers existing within the medium itself. We show that the situation is symmetric: internal observers will judge physics in the external laboratory to violate their own sonic Lorentz symmetries. We therefore treat all observers on an equal footing such that each is able to retain a commitment to their own Lorentz symmetries. We then generalize beyond the case of subsystem-environment decompositions to situations in which there exist multiple phonon fields, all obeying Lorentz symmetries but with different invariant speeds. In such cases, we argue that all observers have freedom to choose which field is symmetry preserving, and so -- in a certain precise sense -- which other fields are perceived as having an 'ether.' This choice is influenced -- but not determined -- by a desire for simplicity in the description of physical laws. Sending information faster than sound serves as a model of tachyonic signalling to a distant receiver. Immutable causality of the laboratory setup when perceived externally to a sonic medium manifests internally through the confinement of the tachyons to an apparent ether (with a rest frame), which we call a 'tachyonic medium,' thereby preventing tachyonic exchange from emulating the scenario of a round-trip signal travelling into an observer's past causal cone. The assignment of sonic-Lorentz-violating effects to fields that obey 'photonic' Lorentz symmetries thus ensures that causality associated with the 'sonic' Lorentz symmetries is preserved.