  Many condensed matter systems are such that their collective excitations at
low energies can be described by fields satisfying equations of motion formally
indistinguishable from those of relativistic field theory. The finite speed of
propagation of the disturbances in the effective fields (in the simplest
models, the speed of sound) plays here the role of the speed of light in
fundamental physics. However, these apparently relativistic fields are immersed
in an external Newtonian world (the condensed matter system itself and the
laboratory can be considered Newtonian, since all the velocities involved are
much smaller than the velocity of light) which provides a privileged coordinate
system and therefore seems to destroy the possibility of having a perfectly
defined relativistic emergent world. In this essay we ask ourselves the
following question: In a homogeneous condensed matter medium, is there a way
for internal observers, dealing exclusively with the low-energy collective
phenomena, to detect their state of uniform motion with respect to the medium?
By proposing a thought experiment based on the construction of a
Michelson-Morley interferometer made of quasi-particles, we show that a real
Lorentz-FitzGerald contraction takes place, so that internal observers are
unable to find out anything about their `absolute ' state of motion. Therefore,
we also show that an effective but perfectly defined relativistic world can
emerge in a fishbowl world situated inside a Newtonian (laboratory) system.
This leads us to reflect on the various levels of description in physics, in
particular regarding the quest towards a theory of quantum gravity.
