We share the same molecules at different moments of time. We meet - it's absolutely realistic, nothing strange. The professor qualifies that statement when talking about the appearance of his older self from a supposed connection to another time in the future. Strange of course because if the older version of myself came from the future it means I can know something from the future. I can use this information, pass this information to the younger version of myself and so on.
All bets are off the day the time machine hits the street.
This scientific assertion that time travel is possible stands up because it can be proven mathematically. Professor Novikov shares credit for the discovery with Prof. Kip Thorne of Caltech, USA and other colleagues in this field. They were both nervous about publishing their findings not least because it's at odds with just about everybody else's personal theory on time-travel. He also admits they do not know many details of the time machine itself as it appears in the real world but they are making progress in producing more complicated and realistic situations to simulate. In principle though time travel works as strict mathematics.