Let's all "assume" that it is indeed possible to travel back in time, ok?
Then, for every smallest unit of time that exists, there would be a copy of your self, wouldn't it? (something like a frame from an animation)
Using out assumption that time travel is possible, then it would be possible for every single "frame" of yourself in the entire existance of yourself to appear at specific time. Now consider every "copy" of yourself to have considerable mass. Wouldn't you have introduced new "mass" and upset the whole rule that an equilbrium in mass, matter and energy? Not only have you upset the equilibrium in your that "specific" time frame, other time frames would be affected too since they have loss the "mass" that was formerly you at that particular "time frame".
Even if the above-mentioned problem didn't occur, what if I decided to kill let's say myself? Would it affect my existance? It really depends on how we view time. If we see time as continuous loop, then killing myself would destroy the loop. A paradox would occur if I were to go back in time to kill myself since if I'm dead how would I kill myself? If we consider that every single "existance" of me in every time frame to be independant, then it "would" be possible to kill myself. That would mean that I'm assuming that time is an indefinite figure and it never goes through a loop. This would also mean that when I kill myself at let's say 10.00am (correct down to the smallest unit of time), i would create 2 possible futures for myself, one with me dead and one with me alive. That would make it possible for me to make an infinite number of futures for myself at that time. Should that be so, even if I could travel through time, how would I decide which future I would end up in?
If you ask me, travelling back to the past is not a likely thing to happen since you will upset most of Einstein's theory of Relativity and a whole lot of idea's in Physics. It is already a known fact that travelling in an object at a faster speed makes time progress at a slower rate, thus time appears to slow down for people within the object. Time passes as usual for people outside the object. Should we accelerate as near as possible to the speed of light, we would reach a stage where time passes at an extremely low rate. What we have to remember is that the speed of light is the speed limit of the universe so nothing "theoratically" can be faster than it. Let's assume we do somehow manage to break that rule and travel at the speed of light. That way, time completely stops within the object that is travelling. Your object would then be completely useless since no one within it can control it since time has stopped anyway. should you then decide that you would control the object externally so you can stop it, we still have a problem; we have not gone back in time, we have only made time not pass for us. What if we go faster than the speed of light then? It is assumed by many that if we go faster than the speed of light, we will move back in time. Note that this travelling back in time would only occur within the moving object and thus would be completely useless within the object. Should time travel backwards, wouldn't we be in trouble? Every object within the object was formally something else before that and should going into the past make them "really" go back to the past, then the objects would not exist in the first place would they? Looks like the only kind of thing that we're gonna get from this method of travelling through time would be "disaging" old objects into new ones?
Honestly, with the currect laws of physics time travel is nowhere near possible. I would elaborate longer with formulas and examples(though Qhimm's formula is a good one) but my exam is tomorrow