Lorentz invariance is the cornerstone of modern physics. However, many ‘real-world’ systems from condensed matter to cosmology have a preferred background which spontaneously breaks Lorentz invariance, consequently yielding Goldstone bosons. In this talk, we will show that the notion of microcausality survives the symmetry breaking, implying analyticity of the retarded two-point function. Using that, we show that dispersion relations of non-dissipative Goldstone modes can be written in terms of ‘typically-real functions’, yielding two-sided bounds on Wilson coefficients of higher-derivative operators as explicit functions of the sound speed. We check these bounds against multiple systems such as the U(1) superfluid and QED. Finally, we will comment on the implications for cosmology through the EFT of Inflation.