Paradox of Time Travel

In a TV programme "Into The Universe With Stephen Hawking" on Discovery
Channel, Stephen Hawking described the following paradoxical condition:

"Suppose you have somehow built a time machine. Now you open up a kit
containing parts of a revolver. You assemble all the parts and then load
the revolver with bullets. Now you go into the past, 5 minutes back (the
time when you have actually not set up your revolver) via the time machine
and you shoot yourself (the man that belongs to your past who was kind of
going to assemble the revolver) using the same revolver."

Here comes the twist. First of all, if the revolver has actually not been
assembled, then with what have you killed yourself, and the second part is,
"is it really possible to kill yourself in the past, if a time machine
would have existed?"

This is in fact known as *grandfather's paradox*. By definition, it is
described as follows:

"Suppose a time traveller goes back in time and kills his grandfather
before his grandfather met his grandmother. As a result, the time traveller
is never born. But, if he was never born, then he is unable to travel
through time and kill his grandfather, which means the traveller would then
be born after all, and thus we arrive at a contradiction and are ‘stuck’ in
this ‘loop’.

It was first described by the science fiction writer Nathaniel Schachner in
his short story Ancestral Voices and by René Barjavel in his 1943 book Le
Voyageur Imprudent (Future Times Three).  K R IRS 1623

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