Time travel is one of many concepts I love to ponder on. So I'd like to share my view on time travel.
Explanation of dimensions and time travel.
The present as we know it and perceive is 3 dimensional. Width, length and height. It is the now we live in. The simple representation fo 3d is the x, y and z axis existing in one point of time as we know it.
The fourth dimension adds a line from past to present to future along with the first 3 dimensions travel. As shown in this picture I just drew!
In the picture you see the x, y and z axis and the horizontal line represents the 4th dimension of time.
A common misconception is that the xyz is moving along the time axis, I do not believe that is the case. Time is a relative constant to any given place in space. However, comparing two seperate places in time, can show differences. Speed has proven this aspect of the 4th dimension. If an object travels fast for a long duration of time, time for the traveler as well as time for the non travelers have always remained constant. But comparing the two afterwards would show that in the traveler has experienced more time then the non travelers. The traveler has thus, relative to others, traveled forth in time.
A real life time traveler is the current record holder of a Russian that spend years on MIR, the space station. I can't recall the exact amount, but I believe he has traveled a full second into the future.
Peanuts, ofcourse. But how does one explain this?
Relativity theory mentions that the speed of light is a constant to the eye of the beholder. The speed of light is 299,792,458 metres per second. But suppose someone would travel half that speed, and someone behind the traveler switches on a beam of light. As the light passes the traveler, the traveler would still see the light moving 299,792,458 metres per second. As if he himself was still in space. So, how does that make sense?
Time, for a traveler, slows down. Not for the objects and himself traveling, but compared to everything that is not moving. Light should move half its speed, but as time is moving half the speed for the traveler, he still sees light moving at its full speed. As light is not affected by time as normal matter. Not until you reach the speed of light itself that is.
Traveling into the future.
So, this is already done, and is relatively easy to assume. When you are driving your car with the movement of the earth, you are very slowly moving into the future compared to someone standing still. Driving the other way, and everyone else is moving into the future, compared to you. It's all relative ofcourse, the person standing still or the person moving, both do not notice this difference in time. A clock on board a space station for a very long time compared to a clock on earth however will show slight differences, and that is where we can actually see it.
Traveling back in time.
This is where it starts getting interesting. We all know the grandfather paradox, saying that it is impossible. And logic would agree. However, a fifth dimension does make it possible. However impractical.
In theory it is possible, though it would require immense amounts of energy. But theoretically, moving faster then the speed of light itself however impractical, would allow as to flip our relative time to a negative time around us. And thus end up in a time before that of which we knew. We would dissappear from our time line, and after slowing down, re-appear on an earlier time. I read somewhere this is already possible with nano particles. That scientists have already been capable to move particles back in time, or rather said out of our time. Out of our time you say? Here's an explanation.
Suppose you lose someone close to you, you build a time machine and go back in time to save that person. The fifth dimension would be influenced and this would happen:
You would leave your timeline and go back to a different timeline. You will be able to save the person close to you, but there will also be a younger version of you. The timeline you came from will still exist on but without you, and the new timeline will have a different future with two of you!
So, how about sending a message to yourself? All good and possible, but as you are sending the message back in time, you would not cease to exist, nothing will change around you. To that you, nothing will happen. The message will travel along the fifth dimension to another version of you, it will create a new you as it were, a new universe, and he might very well live a much better life because of your message, or worse even, but you'll never know. Because if he sends a message along the fifth dimension, it will just go to the other seperate line again. Each time you send something back in time, it dissappears from your universe and enters a newly created one. It'd theoretically impossible to go back to the same timeline twice.
Suppose you send a message to 4am back in time, then you send a message to 3am back in time. The message you send to 3am back in time would be in a third timeline and will not receive the message you send back to 4am. There will be three seperate universes along the 5th dimension.
Why doesn't traveling forth in time affect the fifth dimension then? That is because traveling forth in time does not severe us from our time line. It merely shifts for a duration before it joins up again. The person inside the mir station was traveling in his timeline, along our timeline, until he stopped moving again and relativity got fused again. Traveling back in time, severes you completely, into a whole new timeline.
You are totally capable of killing your grandfather in theory. But it would only serve you not existing twice in the time line you travelled towards.
Is it possible for a living being to move faster then the speed of light? In theory, yes. In a closed compartment outside of external inteference or friction, it should be possible. Will traveling faster then the speed of light in fact move you to a time earlier to your known present time? It is possible. But it it also possible you experience time while the universe around you is entirely still. Ie. traveling along the null You experience time, the rest does not. You may travel for years, while the world experiences a blink of an eye. Ouch, wouldn't that suck. But theoritically, it is also possible to travel into the negative of the 4th dimension.
My conclusion as it stands now, on time travel. Is that I think it is theoretically possible. Without any paradoxial effects. (Paradox's are mere products of mis-understanding anyhow. The paradox itself is the greatest paradox of all.)
But time travel back in time has in no way practical uses. It has no methods of testing, there will be no way for us to know what effect it has on the fifth dimension. We can test the fourth dimension because of relativity but the fifth dimension is something we have no tools for measuring.