Both Newton's and Einstein's mechanics treat time as just another dimension. According to the math, movement forward and backward through time should both be normal. This cannot be the reality. Not only would such temporal freedom contradict our direct experience, there is a philosophical argument also.
Diffusion would occur.
Consider a box of gas. Every molecule of the gas is free to move in 3D. Molecules that try to occupy the same space at the same time collide and rebound. These collisions rapidly distribute the molecules evenly throughout the available space.
Now imagine the molecules are free to move in 4D. When they try to occupy the same space at the same time, they are now as likely to rebound in the temporal dimension as the spatial ones: this is what the math implies. So the molecules would become evenly spread throughout the available time as well.
But what would "available time" mean here? Presumably the construction and destruction of the box are involved. But these are temporal concepts. In our 3D universe, it is the unidirectional nature of Time that imposes order. All the molecules of the gas, and of the box that contains that gas, share a common Time value. In a 4D world, each molecule has a unique T value, similar to its unique X Y and Z values. Unless there is a unidirectional fifth dimension, such a world could not work: there could be no specific construction and destruction events separated by an invariant value.
There seems to be a general principle that every physical thing must be unique. In a1D world, atoms on a line could never pass each other. Their X values are unique, but their Y value is common; the X must remain unique. In a 2D world, where Z is common, it is the combination of X and Y that must reamin unique. In our 3D world, T is fixed and the combination of X, Y, and Z must be unique.
Time travel will only be possible if we can "break through" to the universe where F is fixed, enabling our T value to become just a component of the necessary uniqueness rather than the enabler of it.
Regardless, our mechanics will not be accurate until the unidirectional nature of Time is represented within the equations.