It is mathematically possible to create some instances in which an object goes back in time relative to some observer. For example, simply going faster than light causes such an effect, but of course, speed of light is the limit for any massive object.
While it is mathematically possible, there are many paradoxes caused by time travel to past, unless you accept existence of some sorts of multiverses, which doesn't really qualify as a time travel to past anyway, rather travel between said multiverses. Mainly, and most importantly, time travel to past violates "casuality", one of the main principles the universe is thought to have, in which the cause precedes the result, i.e. your father is born before you are born. Through time travel to past, it is possible for the "result" to eliminate its "cause" before it causes the result, that is, you killing your father before you were conceived. This is not the only paradox caused by time travel to past, however this is one of the main ones.
Also, I think it was Hawking that suggested this, we see no time-travelers around us, pointing out to the fact that humanity will not achieve the technology to go back in time as far as it wants. HOWEVER, it is possible that time travel to past may be discovered, only limited to taking travelers back to the creation of the machine, as some time travel machines work on this principle, namely wormholes.
Needless to say, wormholes require extremely exotic conditions to form and maintain, and therefore are very far from being created deliberately, if they even exist.