No. At least, as far as physics can discern.
The problem is incredibly complex to explain, and in fact if one were interested Stephen Hawking does a far better job of it that I can, but I'll do my best. The field of physics, if one were interested in studying the problem in depth is of course relativity, which is a fairly modern field of physics (launched by Einstein in the early 1900's).
Before relativity, the study of physics was concerned primarily with electromagnetism and mechanics - the studies of electric field and engergy and the study of the motion of matter respectively. Through the study of mechanics in particular, one will find that that matter and it's motions are actually little more than the mathematical relationship of a handful of things. Mass (quantity of matter), distance or space, and time. Force for example is not a unique quantity - it is instead the relation ship of mass and acceleration. According to newton, the simplest way to express this relationship is force = mass*acceleration, or more correctly force = mass*momentum. (In more detail: force = mass * (change in velocity/change in time)). Some people may decry such a statement as overly simple or outright false because the force equation given results in the average force over a length of time (mathematically a secant line if graphed) when in reality we are usually more concerned with instantaneous force (mathematically a tangential line), but I hope you'll find this isn't important. The key is to recognize that physics is based upon the understanding of the relationship between these quantities.
During the course of physics investigation, one may come to realize that mechanics are often just a bit off, especially when things start moving very quickly (say greater than 1/10 the speed of light) or become very small (single smaller than a handful of atoms). Investigation in this regard lead to interesting discoveries, not the least of which is relativity.
I can assume that we all know that speed is itself nothing more than the relationship of displacement (space) and time (literally, displacement/time). Einstien's essential theory, if you dig deep enough is a statement that is as simple as it is profound - space itself is not a constant, it is relative to time. Now, I'm sure we are all thinking "so what" at this point but bear with me. If Space is directly related to time, it stands to reason that speed itself (which is also a relationship between space and time) ought to modify the percieved passage of time. There have been a number of famous tests done over the years, from the first experiments that provided the first proof of Einstein's theory (measuring the difraction of a star during a complete solar eclipse) to experiments using sets of super accurate clocks moving at different velocities. The tests prove time and again that this theory seems to hold true - the faster you move the slower time passes.
If we accept the previous part as being true, then we can come to a conclusion - if time slows in a linear fashion (as it appears to) with speed, there must be a speed at which time would reverse itself, and this would follow the general assumption that science has come to. The speed required is, coincidentally enough, the speed of light. The problem is, as near as physics can tell there isn't a way to directly propel an object with mass to the speed of light. The energy required, if graphed actually resembles an exponential curve. As one approaches the speed of light with an object of any mass you find that the energy required to accellerate increases. Mathematically, this is what is known as an asymptote - a line that a graph approaches but never actually meets no matter how far one feels like going. The short version is of course that to exceed the speed of light and thus go backwards in time, one would need an infinite supply of energy. Here, a classical field of physics comes back to bite us - thermodynamics. It turns out that there doesn't seem to be any way to collect an infinite amount of energy thanks to the second law of thermodynamics that states no mechanic process that does work is fully reversible (the law that says useful perpetual motion is impossible).
Of course, there are kinks in this plan, and it comes to us from the absolute leading edge of physics. It appears that certain objects are moving faster than the speed of light, apparently the result of the expansion of space itself. Interesting experiments in quantum mechanics have given results that suggest things as strange as tests done in the future affect the past, or that in some circumstances one can get a result before a test has been completed. There are a number of working theories related to the idea of FTL travel, the most plausible of which revolve around the premise of modifying space itself. The assumption goes that if space can indeed be bent and broken (modern theories regarding gravity for example) then it may be possible to bend or warp space in such a way as to allow for faster than light travel.
Of course, this brings up an interesting question. If the assumption that matter cannot travel faster than light holds true, then will warping space actually resolve this problem? Afterall, relative to space itself this super fast object might only be traveling at a small fraction of light speed, but from the perspective of an observer it might be travelling at many times the speed of light. My own theory (and keep in mind this would be coming from the furthest edges of physics knowledge and is being postulated by someone who has a mere 2 years of college physics under his belt so I'm hardly qualified to make such a statement) is that even in this case you would not travel in time (or at least not backwards). The reason is fairly simple - at the point at which the object is traveling while warping space it is still not exceeding the speed of light. Such a statement is fortutious in some ways - it's utterly impossible to test and one could certainly generate the math required to make it seem true.
I'll end basically where I began - based on our current understanding of physics, travel in time may vary in terms of rate but never in direction. There are things coming out of the theoritical physics departments the world over that suggest our understanding of both space and time is still hilariously limited, but thus far nothing has surfaced that has made me believe that time is reversible.
lol ... I can imagine the pr though IF he got back "We rocked out like it was 2000 all over again!!! WOOOO........ 30000000 light years from Earth ... but still ..... well worth the 20 trillion dollars" XD
