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Nonlinear modifications of quantum mechanics have a troubled history. Theywere initially studied for many promising reasons: resolving the measurementproblem, testing the limits of standard quantum mechanics, and reconciling itwith gravity. Two results substantially undermined the credibility ofnon-linear theories. Some have been experimentally refuted, and moreimportantly, all deterministic non-linear theories can be used for superluminalcommunication. However, these results are unconvincing because they overlookthe fact that the distribution of measurement results predicted by non-linearquantum mechanics depends on the interpretation of quantum mechanics that oneuses. For instance, although the Everett and Copenhagen interpretations agreeon the expression of Born's rule for the outcomes of multiple measurements inlinear quantum mechanics, they disagree in non-linear quantum mechanics. Wepresent the range of expressions of Born's rule that can be obtained byapplying different formulations of quantum mechanics to a class of non-linearquantum theories. We then determine that many do not allow for superluminalcommunication but only two seem to have a reasonable justification. The firstis the Everett interpretation, and the second, which we namecausal-conditional, states that a measurement broadcasts its outcome to degreesof freedom in its future light-cone, who update the wavefunction that theirnon-linear Hamiltonian depends on according to this new information.

Different interpretations of quantum mechanics make different  predictions in non-linear quantum mechanics, and some do not violate the  no-signaling condition