# Different interpretations of quantum mechanics make different predictions in non-linear quantum mechanics, and some do not violate the no-signaling condition. (arXiv:1709.06639v1 [quant-ph])

Nonlinear modifications of quantum mechanics have a troubled history. They

were initially studied for many promising reasons: resolving the measurement

problem, testing the limits of standard quantum mechanics, and reconciling it

with gravity. Two results substantially undermined the credibility of

non-linear theories. Some have been experimentally refuted, and more

importantly, all deterministic non-linear theories can be used for superluminal

communication. However, these results are unconvincing because they overlook

the fact that the distribution of measurement results predicted by non-linear

quantum mechanics depends on the interpretation of quantum mechanics that one

uses. For instance, although the Everett and Copenhagen interpretations agree

on the expression of Born's rule for the outcomes of multiple measurements in

linear quantum mechanics, they disagree in non-linear quantum mechanics. We

present the range of expressions of Born's rule that can be obtained by

applying different formulations of quantum mechanics to a class of non-linear

quantum theories. We then determine that many do not allow for superluminal

communication but only two seem to have a reasonable justification. The first

is the Everett interpretation, and the second, which we name

causal-conditional, states that a measurement broadcasts its outcome to degrees

of freedom in its future light-cone, who update the wavefunction that their

non-linear Hamiltonian depends on according to this new information.