Time travel sounds feasible. However it would still be hazardous because even at a fraction of the speed of light, if one were to collide with a speck of dust, you would be torn to shreds. So much for the warp drive of the USS Enterprise. One would need indestructable ship for this to be possible.

Einstein also said that nothing could exceed the speed of light which -if true- poses another problem. Some scientists have theorised of a sub-atomic particle named a 'tachyon' which supposedly can but to date there is no evidence that they exist. 

This is why modern science-fiction writers, instead of lightspeed travel, now use the 'wormhole' theory which are basically black holes which act as a shortcut, through a 'white-hole'. (Strictly speaking, white-holes are purely hypothetical and black-holes haven't been empirically proven to exist yet, not to mention the problems arising with anything that would have the misfortune of being sucked into it)

Also, the ethical repercussions of time-travel could be horrendous. If some immoral person got hands on the technology, then history as we know it would cease to be. Each decision we make has an impact on everything and everyone else in the world eventually, even though due to our limited locality and time cannot see it.

Truely, free will is a powerful & grave responsibility which is why God has entrusted it solely to His creation made in His own image.

This is related to the 'chaos theory'. The movie 'The Butterfly Effect', while fiction, shows at least the ethical problems with time-travel.

Humans with their limited intellect and experience cannot comprehend nor foresee what the outcome of their actions will be which is why I believe God has disallowed time-travel to fallable mortal beings and even immortal beings such as angels; for if Satan knew that Jesus' crucifixion would lead to his defeat, then he would go back in time to kill Jesus, or even Adam with the foreknowledge he has in the present.

The devil has made several attempts to thwart God's plan, but only based on what God has revealed. eg, God told Adam and Eve that even though they brought sin into the world, He, Himself would provide a Saviour through the 'seed of the woman'- the virgin birth. This is why the devil and his fallen ones attempted to pollute the human gene pool in Genesis 6 by raping women, and thusly producing the 'Nephillim' , powerful half man, half angelic beings where the pagan religions and myths get their heroes and 'gods'. (A sobering thought is Jesus' words the days before his return would be like the days of Noah)- This was one of the reasons for the flood incidentally,- there were few true humans left. That should be taken into consideration by those who use the flood as an (self-defeating) excuse not to believe in God.

Another example is when God stated that the Saviour would be born a Jew. Satan then proceeded to attack them throughout history to this today. There is no other logical and rational reason why this minority is so hated, maligned and misrepresented by the world, aside from the Biblical rationale that Satan is the 'god' of this world. (See this article by Terry James for more information:)

The point is that each time, Satan failed and will continue to do so because he lacks to omniscience to see where history is going and he lacks to omnipotence to go back in time to rectify his mistakes which leads me to my next point.

At least, the ability to go backwards is impossible, given the that time/space is a 4 ^th dimension of creation and as such has its own limitations (eg time is linear and can only  travel forward.) 

This is not to say that theoretically for the sake of argument, that being able to catch glimpses of past or present events is impossible.

However, given the law of cause and effect (the cause is always greater than the effect) this necessarily entails that the source of this ability would be omnipotent. This is why God considers psychics etc to be an abomination. For eternity belongs to YHWH alone. He is the Alpha and the Omega..He alone, being outside of time and space (finite, created contructs) sees past, present and future all at once.

Though demons, being of greater intelligence and power than us can be convincing, consider that even the 'genuine' occultists cannot get it right all the time. This is because demons, like humans, lack the ability to know the future. Reflect on that the times that psychics do get it 'right' almost invariably are in regards to a tragedy (eg a murder) which is quite telling, given their 'spirit guides' were the ones that caused the evil event to occur in the first place. When was the last time Madame Cleo won the lottery?

(For some examples of real prophecy with a historically proven and exclusive 100% accuracy rate read this:)

Indeed this is truly a fascinating and thought-provoking subject, but ultimately I am convinced that time-travel isn't possible....... At least, this side of eternity