> flows in one direction
_Everything_ flows in one direction, all particles goes in a straight line from their self reference, fields "modifying direction" is just an observer point of view. The separation of time and space is purely a perception matter.
A gross comparison would be to compare with objects perception, it only exists because our mind can leverage it for a strong evolutional advantage (I'm not only speaking of humans here).
No, a particle can flow left OR right, up AND THEN down, forward THEN reverse THEN forward again.
But in time, it can only go forwards, at very slow rates like far from gravity wells, or fast like in relativistic situations. Never backwards. Never stop.