There is a basis...

The common objection to time travel deals with resolving 'the paradox'. What happens to the time traveler if they journey back in time and kill their mother at birth?. Well, of course in theory, the traveler would never have been born so the journey couldn't have be made; but if the journey never occurred then the mother would be born - which means the traveler would have been born and could have made the journey - and on and on! This is the paradox.

The two most-discussed solutions to this paradox include the posit that the past is completely and irreversibly defined. This first solution, the past is totally defined, dictates everything that has happened (or as some say -needs to happen) cannot be changed. The paradox is avoided since nothing can change the timeline of history, including the attempt to kill the mother. Seems that the murderer will bungle the attempt each time. Time can't be altered, nothing changes.

The other solution is the quantum idea of parallel universes. Far more complex, it depends on an understanding (or awareness!) of the theories/laws of quantum physics. Again, the paradox is avoided, for when the traveler kills their mother, a new quantum universe is created - a parallel universe - where the mother and the traveler never existed. The original universe still remains unchanged. The prominent champion of the parallel universe theory is Stephen Hawking: http://www.hawking.org.uk/lectures/warps.html