[EDIT}: I meant they will in 2023. Maybe. We can't possibly tell, of course.
Every time a startup tries to predict the stock market, they are investing in a time travel startup. And that's why they say the market is efficient - no one can predict when the next crash will come.
I think that would expand the scope of a question like this. Functional quantum computing comes to mind, but I can't think of too many examples...
http://www.livemint.com/Science/MxP4L2VV7teq4141X49u1I/Can-w...
And if the past you visit is read-only, then you've invented history, not time-travel.
It could be the case that time resembles a directed acyclic graph. Traveling "back in time" merely creates a new branch at a point on the graph in the past where that event (the presence of the time traveler) occurs, marking a divergence from the "original" past, in which where there was no time traveler. But you can't ever actually revisit your own timeline, forming a loop.
And, since every quantum interaction would create a new node in which all possible outcomes of that interaction are new branches (many worlds theory,) the concept of an "original" timeline wouldn't even make sense.
None, because there's an infinite number of branches. And every time someone travels back in time, it creates a new branch.
What'd be interesting is to do an experiment to disprove this: invent a time machine that allows traveling both backwards and forwards in time. Use it to send two people back in time. Person A goes first, and the person B warps back to a time an hour later in the same place, and tells person A a secret. Then person B comes back, then person A comes back an hour later. Have person A repeat the secret, and see if they met each other in the past. With a new universe created every time someone goes back in time, will person B go back to the same new universe that was created when person A went back in time, or will they go back to the original universe that person A tried to go back to, and which still exists without person A which would change the course of history there? Does person B create a new universe? Will person A have met person B, and will they have seen person B go back to the future before them?
However maybe forward time travel (faster than usual I mean) could be possible. But... how would it make any money? As soon as you've delivered the service, the deadbeat customer may not be back in town to pay his bill for decades or centuries! And 30-day jumps just seems silly.
How do you know we aren't? Are you assuming they would wear a sign saying "TIME TRAVELER FROM THE FUTURE HERE" or something? Or walk up to random people and say "Excuse me, I'm from 2077, and I just got here, and could you tell me how to get to the Smithsonian"?
I imagine if time travelers from the future were here, they'd be careful to be very discrete to avoid outing themselves. Or to avoid causing a paradox by accidentally changing something.