I personally believe that time travel is possible but only into the future. Time only travels in one direction which is obviously forward. Traveling back in time would b be quite dangerous anyway. One reason why time travel would be dangerous is due to what is known as the Grandmother Paradox (someone goes back in time to kill their grandmother for revenge but ends up nonexistent when trying to travel back to the present).
Traveling back in time trying to alter a situation or prevent a death could drastically change the world the smallest altercation could have big affects upon return to the present. Traveling through the past could have great benefits though but it is to risky.
Since time only travels forward and is not infinite and does not flow in a circulatory direction then time travel could only be possible to travel in the future unless somehow time could be bent into a circle, to travel into the future tin=me would only have to be stretched.
Even if time could be bent into a circular form the universe can only hold so much matter so traveling in the past, which the people in the past see as the present you are adding to that matter and if there is to much matter then a black hole could form or the universe could explode and this is not a risk I think anyone who is sane and cherishes life would want to take.
If time could go forward and backwards I believe that the future and past would clash causing the present to malfunction in some type of way. I have a few examples and hypothesis of my own: Light travels in a straight very quickly and can travel very far. Some might say light can travel into the future but light cannot travel backwards.
The same law that permits time travel permits light to travel in a straight line in one direction so this would mean the same for time travel you could only travel into the future. If i bent light with a mirror making it go backwards it still moves forward just in a different direction changing its place of position.
I do believe that time travel s possible people have invented such amazing things capable of what would be thought of as impossible just fifty years ago. So I do believe in the next few centuries we will have figured a way to travel through time successfully and that eventually it would become a norm for a all. These are all just my personal ideas nothing has been proven or tested to my knowledge.