  An unstable field theory is what we obtain when we linearise the equations of
an interacting field theory near an unstable state. Theories of this kind are
adopted to model the onset of spontaneous symmetry breakings, when the fields
are sitting on the top of the Mexican hat, and they start to ''roll down'' to
the bottom. At present, there exists no rigorous proof that unstable quantum
field theories are Lorentz-invariant (in the sense of Wigner's theorem). Here,
we show that they shouldn't be. In fact, unstable theories always have a
limited regime of applicability, and they are valid only for a very short time.
As consequence, there is a preferred simultaneity hyperplane, along which the
unstable theory is everywhere applicable, while a generic observer (whose
four-velocity is not orthogonal to such hyperplane) must use the full
non-linear theory. In summary: the current quantization schemes are ''ok'',
independently from whether they lead to a Lorentz-invariant theory.
