Is time travel impossible because it implies total energy in the universe is non-constant over time? I have always argued with my friends regarding Time Travel that it is impossible. My argument has been that it will destroy the theory that all the energy in the universe is constant since when one travels to a different time, the universe at that time requires extra energy for accommodating the extra person. Similarly the total energy of the universe of that person's current time will be lesser.
I would like to know whether I'm thinking correctly? Has anybody ever experimented or proved anything in similar veins?
 A: It is true that general time-travelling violates conservation of energy. If you transport yourself into yesterday, you appear twice in the universe for that day, which means twice your rest energy, which is a lot of energy.
It may mean that time-travelling is inconsistent and therefore impossible. But not necessarily. In general relativity, it is very hard to formulate the law of energy conservation and it might even be violated. In fact, in physics, there is implication that says the following. 


*

*If laws of physics do not change with time, energy is conserved.

*If laws of physics do not change by translation in space, momentum is conserved.

*If laws of physics do not change with rotation of your system, angular momentum is conserved.


They part of the so-called Noether's theorem. They are valid locally (there is no particular place, where the energy conservation is violated, for example). This is because locally, space-time always has the aforementioned properties. It is still possible, that you can go around some topologically-special trajectory, the conservation of energy would be violated. Such trajectory might be the time machine, for example if it is some strange fold in spacetime like a wormhole.
This can be illustrated by an analogy. You may know the Möbius strip - a loop of paper that has only one surface. If you have arrow pointing up and you send it around the Möbius strip and still hold it pointing in the same direction, it returns pointing down, even if you didn't perform any rotation and there is no particular place, where it was rotated around. It might be the same with the conservation of energy and time machines - there is no particular place, where it is broken, but globally, it is. 
In fact, if you can imagine 3D Möbius strip, it is be even more mind-blowing. If you have a screw and a nut that fit together and you send one of them around the strip, when it returns, they will not fit together anymore, because travelling around changes handedness. Topology of space can really do a lot of unexpected stuff and breaking conservation laws might easily be one of them.
Another possible answer to your question is, that the time machine pays the energy debt. Personally, this seems more likely to me and makes creation of such machine even more complicated.
A: No, conservation of energy is for the entire system. If you can travel from time A to time B then both time A and B are parts of the same system as far as conservation of energy is concerned. Even if you assumed that despite travel being possible the times were separated, time travel would simply require the transfer of equal energy from in the reverse direction or be unstable and require the return of the traveller.
Basically, if time travel is possible then different times are part of the same system and conservation of energy is conserved. Conversely, if they are not parts of the same system, time travel will be impossible. So I am not saying different times are part of the same system, merely that you can't deduce whether time travel is possible from conservation of energy, because both the way conservation of energy works and possibility of time travel depend on the exact same unknown variable.
A: Consider that most elevators have a counterweight to store energy. The counterweight isn't perfect, but it reduces the overall energy needed to move the carriage. As the elevator moves up, the counterweight moves equally down.
Likewise, a time machine would have to overcome the energy deficit/surplus caused when moving from one point to another, but it could even the exchange somewhat by moving energy in the reverse direction of travel. If you can move a person backwards, you can move energy forwards.
This may make such a time machine more complicated, but there's no reason to assume it's impossible because it has to perform an exchange rather than a simple transfer.
A: I won't answer on the energy part of the question, but here a few remarks which in my opinion are worth adding:


*

*The laws of physics are not frozen, the evolve (more precisely, they get more and more accurate ; e.g. Newton, replaced with the general relativity, etc.). Maybe one day someone will come up with an even more general theory, a part of which is the general relativity, with some new assumptions.

*Although the contribution of physics is strikingly impressive, nothing guarantees that it covers everything (e.g. why would cats be able to model nothing, and humans everything?)

*Proving that something does not exist, or will never happen(*), might be impossible. You may be able to prove that in the paradigm of modern physics time-travelling is not possible, but it will not prove that time-travelling is, in general, impossible. For example how could you prove that I'm wrong if I stated that I can travel in the past, but that when I do so another parallel world is created, which has its own evolution (and slightly less energy than ours :D)? (some people think these kind of questions are not worth spending too much time, cf positivism).


(*) Would the great scientists of the XVth century have believed that we would be able to communicate, travel, etc. as we do today? Would humans a few thousand years ago have believed we would be able to date their bones? etc.
A: Hmmm, a very interesting question. 
Your logic seems sound, but I'm not a physicist, so I can't really say. 
What I can say as a non-physicist is that time flows in the direction of increasing entropy, so moving back in time would mean that the Universe should go back to a state of lesser entropy, which is supposed to be prohibited. Interestingly, this in itself does not preclude travelling to the future.
I would be very interested to hear what the real physicists on here think about all of this.
A: Here is how time travel is understood by today’s established science, namely general relativity. To simplify matters, I’ll only talk about single particles time travelling, not sentinent beings: this doesn’t mean there is any fundamental difference, but it makes the whole thing sound much more plausible.
Consider a simplistic model of time travel, described in chapter eight of Science of Discworld III by Terry Pratchett et al. if nowhere else. First, picture the history of an ordinary world on a sheet of paper, with (one dimension of) space running horizontally and time unfolding vertically, from bottom to top. Points of such a picture correspond to events happening in different places at different times. The life of a point particle is represented by a line. Energy conservation means that one can draw how energy flows on that picture, from one point now to another a second later, without any sources or sinks.
I will pause here to remark that this picture has no notion of the present turning into the future: the state of the world “now” is just the points on a correspoinding horizontal section of its history. If you can understand that your idea of a horizontal section can be different from that of someone moving relative to you, you understand the crucial point of special relativity. Basically, all that remains is to find out how exactly it is different.
All you need for time travel is to roll up your sheet of paper into a horizontal cylinder. If the top and the bottom of the original sheet match up, there is no discontinuity anywhere, and the result is as consistent with the laws of physics as the original was. In fact, locally everything looks exactly the same: you can’t tell if you are on a cylinder or on a plane by exploring a small region of spacetime. Globally, however, we see that time has become periodic1. The line representing the life of a particle will necessarily return to the same point again after making some number of turns. Move a horizontal section (a “now”) along the cylinder and you’ll see that the particle turns into a past instance of itself after you make several turns. (This is what’s less realistic for a complex system than for a single particle.) This is not Groundhog Day where everything stays the same except you: in a very real sense, the previous morning is the same thing as the next one, and you can’t help repeating yourself. There is much less hope in a real physical time loop than in a fictional one.
On a cylinder as on a circle, energy can flow without being created or destroyed. Energy conservation need not be violated. Moreover, energy always flows from the past to the future. It’s just that after flowing into the future for some amount of time, it finds itself back in the past, and so does everything else.
Feynman’s idea of antimatter as matter going back in time is an intuitive description of a completely unrelated and rather technical point in quantum field theory. Consider drawing a circle on a plane (not a cylinder) and moving a horizontal section from bottom to top to watch the story unfold. You’ll see two particles appear out of nowhere, move away from one another, then turn around, meet each other again and disappear. If you complain about energy conservation here, you’ll be right: in fact this process, called pair creation and annihilation, needs energy at the beginning and releases energy at the end—usually, but not necessarily, in the form of gamma radiation (a fancy word for really, really blue light).
In the periodic universe, everybody who lives long enough is a time traveller, and must relive the same thing time and time again (although they probably wouldn’t experience it that way2). However, if you let the shape of your sheet of paper become a bit more complex—a plane with a mug handle attached, for example,—you can imagine a line—a life–that goes around two times around the handle and then continues into the future. But whatever the universe, a time traveller can’t change the past, because time is just another direction on a sheet of paper! The only thing he can do is experience the same moment two times from different points in space.
Finally, just for fun, consider curling up not time but space—a vertical cylinder. Now if you go far enough to the left, you find yourself arriving from the right. The world is finite, but there are no boundaries anywhere. This is what people mean when they talk about a finite universe.

1 The cognoscenti should note that this periodic Minkowski time is not the same as periodic Euclidean time used to turn quantum mechanical evolution into partition functions of statistical mechanics.
2 I don’t think there can be a thermodynamic arrow of time in this world, so it wouldn’t bear any resemblance to the real one, but I’m not aware of any descriptions in the literature. Edits welcome.

A: I am not a physicist but all you experts seem to have not understood some basics. Your molecules are not unique - they have always existed as something else. When you go back in time your molecules are already existing as a tree or a bird or grass or Napoleon bleeding Bonaparte, etc. So if you appear in the past what are you made of? Every molecule in the universe has already been assigned in that time period therefore you must be made of brand new molecules that didnt exist before. It's like having a 100 piece set of lego: You can use the 100 pieces to make a motorbike or to make a rocket ship but if you send the rocket ship back in time to when the lego was a motorbike, all of a sudden you have 200 pieces of lego. Or am I missing something?
A: Time travel is not impossible because of conservation of energy, time travel is not impossible at all. Entropy does not allow you to go backwards in time, but forwards does not present any problems. 
