Time travel and paradoxes
We already talked about time travel pointing out as in theory it is possible, but in fact at the moment it is impossible because of energy and technology it would require, currently unavailable.
Scientists like Tardis
Yet recently two scientists, Ben Tippett of the University of British Columbia and David Tsang of the University of Maryland, published un article entitled “Traversable acausal retrograde domains in spacetime” claiming that would be theoretically possible walking backward and forward in time.
Doctor Who tv show's fans have probably noticed that the acronym of such a research is Tardis, identical with the definition of time machine (disguised as a blue box) that “the doctor” uses to trivel in time and space, except in this case Tardis means “Time and relative dimension in space”.
Time travel and the grandfather paradox
“The doctor” himself, btw, often remembers as time travel exposes the traveller to many risks because of paradoxes that it may generate. The first and most popular is the “grandfather paradox”: if the traveller goes backward in tima an willingly (or not) kills his grandfather, how can he be born and therefore had a chance to make the fatal journey?
The bootstrap paradox
Another very popular paradox is the “causal loop paradox” or “bootstrap paradox”, explained once again by “the doctor”: a traveller goes backward in time to meet a famous people, but finds out that nobody has ever heard of him, literally he never existed. Btw, traveller has brought with him a work of this people, so decided to take the place of hinm and publish the work himself, using as his alias the name and surname of the famous figure (maybe William Shakespeare or Ludwig Van Beethoven). Thus the reason for the travel depends on the travel itself, making a casual loop.
Nevertheless it exists a paradox which could exceed all these limits and make it possible to develope, in the short or long term, time travel (whistle at the same time becoming a forbidden technology), the “predestination paradox” (also known as “causal curve”). Should there be a thing like the predestination, any action a time traveller had to perform it should be “predestined” and thus not able to modify the traveller's timeline.
Do you want an example of predestinatino paradox? In the movie Harry Potter and Azkaban prisoner, Harry carries out an enchantment of which indeed has not yet fullly mastery, the patronus, because in the first instance he recognizes himself in the act to successfully carry out the enchantment, then go back in time and do actually the patronus. But predestination paradox works remarkably well also in the story of Oedipus, taken away by his father Laio because of a profecy who at the end, not knowing his true identity, ends up making it happen killing his father and wedding his mother Jocasta.
Except both Harry Potter both Oedipus are fictional characters and our knowledge of the universe is exclusionary predestination. Thus time travel remains an undertaking at time just mathematically theorizable, unless you believe to Alfred Bielek and his story about the Philadelphia experiment.