We know that time travel into the future is possible. Stephen Hawking says, "We do not have the technology today to do this, but it is just a matter of engineering; we know it can be done."
In Einstein's Book: Time Travel in Einstein's Universe: The Physical Possibilities of Travel Through Time , physicist J. Richard Gott says "if we can accelerate protons to greater than 99.995 percent of the speed of light, we could also send off an astronaut at the same speed. It's just a matter of cost."
The idea of time travel into the past is a far more exciting prospect though. Who hasn't wanted to travel back into the past? Some would like to return to the past permanently to live in a simpler time and escape forever the stress, crime, pollution, and other unpleasant aspects of 21st century living. Some would like to be time tourists and actually be present in the crowd to hear the Gettysburg Address delivered by President Lincoln himself, to watch the pyramids being built, or to witness firsthand any number of historical events. Some would like to go back to do or undo things that affected their own lives.
There was a young lady called Bright
Who could travel far faster than light;
She set off one day,
In a relative way,
And returned home the previous night.
---A.H. R. Buller
A cute limerick, but is it possible? Yes, says, Stephen Hawking, if one can travel faster than the speed of light, one can travel back in time in the same manner that one can travel into the future—by riding a really fast spaceship. The problem, he says, is that while we can accelerate particles to 99.99 percent of the speed of light, we have as yet been unable to exceed the speed of light. Nevertheless, Hawking says, travel to the past may be possible through the use of wormholes.
The idea of wormholes is not new. In 1935, Einstein and Rosen wrote a paper saying that the Theory of Relativity allowed for the existence of wormholes and much has been written about them since, but as yet we have no conclusive evidence that they actually exist.
Some scientists theorize that time travel into the past may be possible through the use of cosmic strings, which are thin strands of high-density material left over from the early universe. Like wormholes, we don't know if cosmic strings exist, but Gott says, "If cosmic strings exist, you could travel in a spaceship [at 99.9999999999 percent of the speed of light] and outrun a light beam by taking the shorter of two paths around a cosmic string. The door to time travel to the past begins to crack open."
Doubts that travel into the past might become possible in the future are rooted not so much in terms of physics and technology, but in terms of intuition and what are perceived to be the use of logic or common sense. For example, if a man were to travel back in time and kill his grandfather before his grandfather ever had any children, then he never would have existed himself and therefore could have never traveled back into time. Furthermore, if time travel to the past becomes a reality at some point in the future, why has there never been any record of people from the future showing up in all of recorded history?
There are many similar questions and many possible answers, some simple and some very complicated. Many people are convinced that time travelers from the future have made trips into the past. There are two popular pieces of evidence.
The first is artifacts left behind by time travelers. One example is a watch/ring found in December 2008 in a Chinese tomb that had been sealed for 400 years.
The second type of evidence is photographs in which there are people who appear to be from another era. An example is the unknown woman in the 1928 Charlie Chaplin movie, "The Circus." She is walking along in a background shot speaking into what appears to be a communications device. She is alone, and appears to be carrying on a conversation. These and similar examples can be found on the internet as well the opinions of people seeking to debunk the evidence. Who knows?
The only thing certain about time travel into the past is that people will always dream of it and always be fascinated by it.