We study how the notion of time can affect the motion of particles within the No Integrability Aesthetic Field Theory. We show that the Minkowski hypothesis of treatingx4as pure imaginary as well as the fourth component of vectors as pure imaginary, does not lead to different solutions provided we alter the sign ofdx4and certain origin point field components. We next show that it is possible to introduce time in the situation where all fields are real so that: (1) The field equations treat all

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... oordinates the same way; (2) The "flow" concept is associated with time but not with space; (3) Data is prescribed at a single point rather than on a hypersurface as in hyperbolic theories. We study the lattice solution in the approximation that ignores zig-zag paths. This enables us to investigate the effect of a non-trivial superposition principle in the simplest way. We find that such a system, combined with our new approach to time, gives rise to an apparent infinite particle system in which particles can be looked at as not having well defined trajectories. This result is similar to what we obtained when we treated time in the same manner as the space variables in our previous work.