To make time travel a reality using the speed of light theory then a time machine that can out run the speed of light would need to be created or the machine would have to be able to slow light down.
An Introduction to Bose-Einstein Condensates.
During the final part of the 20th century and into the 21st century scientists have been doing experiments concerning Bose-Einstein Condensates.
These condensates are created by cooling atoms and taking their temperature to absolute zero. Their existence was first theorised by Albert Einstein and Satyendra Bose in 1925, but their theories could not be tested at the time because there was no technology advanced enough to do so. It was not until 1995 seventy years later that their theory was actually proved in an experiment at the University of Colorado at Boulder NIST-JILA lab by Eric Cornell and Carl Wieman. They cooled rubidium atoms down to 170 nanokelvin creating a huge cloud of gas with an undefined size and shape and properties and behaviors that are currently not completely understood.
What does this have to do with Time travel?
When you cool things down to absolute zero all motion stops, so the particles making up an atom will have no velocity, meaning momentum will be zero.
In later experiments scientists shone light in to the cloud to see what would happen. In the first known experiment of this type the light's speed was slowed from its normal 186,000 miles per second down to a crawl of 38 miles per hour as it moved through the cloud of the condensate.
The slowing of light is the first step in defeating the time barrier and the Bose-Einstein condensate could be the first step to creating a working time machine.
If you take away time making the universe timeless then Time Travel could become a possibility. Well by slowing down light and stopping it in its tracks the Bose-Einstein Condensate light experiments have come close to removing time. So if light cannot flow then it cannot convey information to us and so we do not see the passage of time. Meaning if we stop the flow of light we can theoretically stop time in its tracks and create the timeless universe that could make time travel a reality.
How would a Bose-Einstein Time Machine work?
The Bose-Einstein Condensate will not be the creator of a machine that would take a human back in time, instead it would create a place where light could be stopped then started again when the viewer wanted to see what information that light beam was carrying. Using the condensate would be like using a video camera and player to record and playback images from the past.
A Time Travelers Story
In November 2000 a series of posts began appearing on the Internet calming to be from a John Titor from the year 2036. He claimed he had travel back through time by traveling faster than light. We don't have any proof that this is true but I would love to believe this story.
But if this story were true why did no one come back and warn us about events like 9/11?
This is where I bring in the paradox theory.
If a person went back in time to change events in their passed then those events would not have happened so the traveler would not have traveled back in time to change the events.
So if there are time travelers among us they will probably only be here to observe and learn about history first hand, not to interact and get involved in events.