Notes from 'Time Travel In Einstein's Universe: The Physical Possibilities Of Travel Through Time'. By J. Richard Gott
Locating an event in the universe requires four coordinates -
Russian physicist, George Gamow:
"If I want to invite you to a party, I must give you four coordinates. I may say the party will be at 43rd Street and 3rd Avenue on the 51st Floor next New Year's Eve. The first 3 coordinates locate its position in space. Then I must tell you the time. The first 2 coordinates tell you where to go on the surface of the Earth, the third tells you how high to go, and the firth tells you when to arrive. Four coordinates - four dimensions." WIDTH, BREADTH, HEIGHT & DURATION
Your world line starts with your birth, snakes through space and forward in time, threading through all events of your life, and ends at your death. A time traveller who visits the past is just someone whose world line somehow loops back in time, where it could even intersect itself. This would allow the time traveller to shake hands with himself. The older man could meet up with his younger self. The younger self would continue his life becoming old and eventually looping back to that same event. (Note: So does this mean that this event will loop forever with the younger self meeting the older self, growing up and looping back, the older self carrying on life and dying, whilst the younger self grows up, loops back, carries on life, dies, the younger self grows up, loops back...?)
The Grandmother Paradox:
What happens if you go back in time and kill yourself, or even your grandmother? If you kill your grandmother, then your mother would never have been born, and you would never have been born; if you were never born you could never go back in time, and so you could not kill your grandmother.
However, if you were never born, your entire world line, from the point of your birth to your adventures as time traveller, should vanish leaving the grandmother alive and well - so your birth would have happened after all.
Some people believe that an infinite number of parallel universes exist, playing out all possible world histories. TIME SCAPE AND THE MANY-WORLDS THEORY
THE PRINCIPLE OF SELF-CONSISTENCY: The time traveller may have tea with his grandmother whilst she is a young girl, but he can't kill her - or he would not be born, and we already know he has. If you witness a previous event, it must play out just as before.