To go forward in time you need to approach the speed of light. Due to the effect of time dilation, you experience time flow at a slower rate than someone in a stationary inertial frame compared to you. In theory, to go back in time you must actually exceed the speed of light which is not thought possible.
I suppose time travel is possible within the physical laws of the reality that we have constructed / observed ( as a result of our construction). But what if we step outside the confines on that reality to the underpinnings of our reality? If one was to do this one could do this with consciousness only as far as I know, because our bodies exist in the framework of the the reality we have constructed and the laws of that structure. But if we were to step outside the confines of reality we could see that time is a constant only to the point of view inside the reality and not necessarily true outside. So my point here is that by letting go of ordinary reality we can "travel" through time because it ceases to exist.
In that scenario, when we create the physical construct and insert our physical selves into it, we are then subject to the laws or parameters of that construct. If the laws permit time travel, then we can find out how to accomplish it. However, if a construct is created for a purpose, then it seems that to time travel out of it would negate that purpose.