Time and the ability to travel in many directions in it is only limited in the human ability to understand how time is measure or how it "moves." Humans have been bound by the notion that time is linear. Einstein's theory of General Relativity provided that space and time are intertwined. We live, then, in a four dimensional world, which is all good and dandy if that's all we ever have grasp of with quantum mechanics. There is a slight problem here. When referring to a thing's "time" in a particular space using quantum measurements, we are in effect locating its quadrants relative to its specific time and physical measurements. This is human measurement and nothing more; our way of locating a particular event, such as John Kennedy's death or the eruption of Mt. St. Helen. We can travel back and forth between two physical space points, but we are bound by time moving "forward." Despite our ability to move back to our point of origin, we still arive at that point in a new "time." This leaves room for a theory that time and space are not intertwined; they exist freely of each other.
Quantum physics states that space may have 10 or 11 dimensions. All but three are unperceivable to humans and we can only have knowledge of the fourth, time. This reminds me of a presentation in the series "Cosmos" where Dr. Sagan demonstrates how a two dimensional world, invaded by a three dimensional object, only "see" the two dimensional part of the three dimensional object. They are limited in perception by their two dimensional reality. Dr. Roger Penrose states that although there are many dimensions, those outside of our own perception are "unstable" and therefore it is "natural" for these alternate universes to exist in only our one. The universe is only as we perceive it and this is again confining and it can be assumed that Dr. Sagan's demonstration may be more likely to exist in reality than the comfort of Dr. Penrose and his only one universe theory. Comfort, however, does not always make good science.
Time, as our fourth dimension, is something we can see but not move in any direction but one. To find that travel can be made throughout our other three dimensions yet time only marches in one direction is limiting. Science itself is continually being rethought; paradigm shifts in a new direction are constantly being made, yet the paradoxes created with the ability to travel time are so uncomfortable that the human mind is incapable of "wrapping itself" around such notions. If time indeed is relevant, then this fact allows for some form of time travel. Einstein showed this in a most simplistic form by stating that something or someone able to travel at a velocity close to the speed of light will find their "time" slows down and they move much slower through the dimension of time. Indeed, if one were to stand at the edge of a black hole, time would "stand still" for them. Unfortunately it still moves in a "forward" motion of sorts. But our very notions of science have consistently stated that for every action there is an equal and opposite reaction, creating yet another point for the idea that if time and velocity are related, and someone who travels at the speed of light can in effect move forward by their time relative to those moving at a slower velocity, then it can only be theorized that there must be an opposite; the ability to move "back" through the very time relative to the time traveler. Although velocity may be our current catalyst in relativity, it need not be the only one.
There has been observation in an accelerator which finds that there are some atomic particles which appear at the "end" of the accelerator faster than the light wave being pushed through. Scientists working on this experiment theorize that there may be some "things" or "thing" which can travel faster than the speed of light, since these particles arrived prior to the light waves. I suggest that perhaps these particles actually moved through time, arriving at the end of the accelerator ahead of the light wave, and not due merely to its velocity alone. Confining ourselves to the constraint of the impossibility of time travel will limit our ability to understand our universe and should be explored.
There is one more small observation which somehow keeps badgering. Listening to a CD which is damaged it was observed how the laser bounces back and forth through the "time" of the song, then finds its way back to the very point on the CD's space where it began skipping. In listening to the song, it appears that there are "bleeds" through from later parts of the song to earlier parts. Perhaps there is such "bleeding" in our world. This could account for "ghostly apparitions" which some credible people swear they have seen. Just a thought.