Group velocity of electromagnetic waves in plasmas derived by standard relativistic resistive magnetohydrodynamics equations is superluminal. If we assume that the group velocity represents the propagation velocity of a signal, we have to worry about the causality problem. That is, some acausal phenomena may be induced, such as information transportation to the absolute past and a spontaneous decrease in the entropy. Here, we tried to find the acausal phenomena using standard relativistic resistive magnetohydrodynamics numerical simulations in the suggested situation of the acausal phenomena. The calculation results showed that even in such situations no acausal effect happens. The numerical result with respect to the velocity limit of the information transportation is consistent with a linear theory of wave train propagation. Our results assure that we can use these equations without the problems of acausal phenomena. © 2011 American Physical Society.