Assuming we still had our time machine. Do you reckon you could make one in the shape of a blue policebox?
It'd probably be stolen too, and have a knackered chameleon circuit to boot.
Time travel paradoxes are very familiar to such science fiction writers. The question is, what does physicis to make of them? Do they imply that time travel is a non starter, or that reality is more complex than we suppose? This is where, as per usual, opinions start to diverge. There are some theoretical physicists, most notably David Deutsch, that maintain the way out of this is to assume that there are multiple realities, so that when you travel back into the past, the world you change is not the same one that you left, but a parallel imitation - a bit like Everett's Many Worlds in reverse.. This perhaps answers Hawking's main objection as to why reverse time travel is impossible by virtue of the fact that we haven't yet been overrun by people from the future.
Hawking also proffered Chronology Protection Conjecture which says Time Machines contravene the laws of physics. Basically, such scientists argue that nature will conspire to prevent the building of a time machine - one possibility is that runaway surges in quantum energy would generate massive gravitational fields and turn any time machine into pulp.
Arguably, the best hope for erstwhile time travellers still comes from the General Theory of Relativity. Kurt Gödel used this to produce equations indicating the possibility of time travel to the past. He demonstrated that a rotating universe, consistent with Einstein’s theory, would allow you travel back in time. Given that his model was unlike the real universe we inhabit and also that even if we
did live in such a universe, time travel would be practically unachievable because you would need a unfeasibly powerful energy source which to cover astronomical distances, Gödel’s work was nonetheless firm evidence that time travel to the past is, at least in
theory, possible - where the beginning is actually just a continuation of the end. In Godel’s universe there is not time and any physical event if possible including going back in time and killing your ancestor and still living.
Since then, innumerable other scientists have suggested other solutions of general relativity that permit time travel to the past. Most rely on the prediction of the hypothetical existence of 'closed time-like curves'. There are supposedly ways of distorting space-time to make it curved in such a way that shortcuts through space-time exist allowing you to effectively travel faster than light and journey back into the past.
Attempt to bring anything like that up in this space, and you're unlikely to 'woo' anyone to your cause.
Personally I find Penrose's notion of 'cosmic censorship' the most interesting.
Regarding the prospect of being overrun with Time Travel Tourists from the future, what was that film, I'm sure it stared Jeff Bridges, in which there was a bunch of people doing just that? - turning up at the scene of infamous events or to spectate on historical natural disasters? I think they arrived in the film to view a large meteorite strike.
