The interplay between spectator and participant matter in heavy-ion collisions is investigated in the context of a microscopic transport model. Transport simulations show that flow patterns for the participant matter are strongly influenced by the presence of the nearby spectator matter. However, the influence is mutual. During the explosion of the participant zone, the spectator matter acquires a transverse momentum P x /A that shows sensitivity to the nuclear incompressibility and to the momentum dependence of the nuclear mean field (MF). An observed change in the net average momentum per nucleon, ∆| P/A |, can be associated with the momentum dependence of the MF. For a momentum-dependent MF and a low impact parameter in a heavy system, the spectators may emerge faster than in the initial state, accelerated by the violent participant explosion. The average excitation energy and the mass of the spectators, in contrast to the momentum, show little sensitivity to the nuclear equation of state. 25.70.z, 25.75.Ld, 21.65.+f Typeset using REVT E X