There is no 'negative' field as such . Field is a vector quantity , a negative field would mean , a field having an opposite direction to the positive field.Its more like how we take the signs to be rather than fields having a sign of their own.But the field wouldn't be negative, so you wouldn't be able to travel backward.
Referring to the title of your post. Its not about what do scientists believe what time is , but more peculiar is how time wants itself to be.We define time as 'order of events' , slowing up of time implies 'slowing up of order of events' and vice versa in case of time-travel forwards.Does field repect 'order of events'? , Time has no strength as such but it has a linearity which changes with the view of the observer.A field would imply that you experience time, but that it may be of different strengths for different objects and observers