I love time travel movies. Seeing how the writers untangle, side-step or just ignore the inherent illogicality of the concept. How many paradoxes can you cram into one movie without ever drawing squiggly lines on a bit of paper labelled "now" and "past".
Now, clearly time travel is not easy, as otherwise it would be happening all the time. Flight is easy, and all sorts of animals do it. Nuclear weapons are fairly hard. Time travel is apparently at least as hard as building an atom bomb. But it might have happened. (Yes, the past tense - a time machine from the future landing in the past has happened. A time machine from the future landing in the future is of no interest to us until we get to the future at the boring old 60 seconds/minute rate.)
So how do we detect time travellers? Setting up our detectors for tachyon pulses or chronaton particles or whatever is no answer because, even if such things exist, we cannot detect them. (But - see Greg Benford's unsurpassed "Timescape"). We need a way of detecting time travellers that is independent of the way that their time machine works. And such a way now exists.
A second interest for many years has been the biology of aging, and what to do about it. Getting old sucks. Your brain slows down, your joints seize up, your ... well, other stuff stops working so well. I used to laugh at jet-lag. Now I moan at it, for 48 hours. Hangovers were things that lasted until lunchtime, now they last until the next day. And so on.
Are there people to whom this does not happen? There are novels about such an idea. Heinlein's "Time enough for love", or (much better in my view) Poul Anderson's "Boat of a million years". But writing a novel about a spontaneously immortal human does not mean that they exist. If they did exist, they have taken some considerable care to hide that fact. There is probably a good reason for this. Only the gods are immortal, and if you cannot prove you are a god by, e.g. throwing thunderbolts, turning into a bull or a shower of coins, or at very least flying, then you are demon or something and your unnatural life should be ended on the top of the next solstice bonfire. Same thing applies today, except substitute "Pharmaceutical research facility" for "solstice bonfire".
So, if such people exist, we must detect them despite them not wanting to be detected. And a way to do that exists now. Luckily, it is the same way as you use to detect time travellers.
Implausibly, it was suggested by an episode of Dr. Who. A minor plot point was that a WW-I bullet was being removed from the contemporary leg of (I think) Jack Harkness. How did it get there? Clearly someone had shot him with a WW-I vintage Brown Bess loaded, for no obvious reason, with authentic WW-I ammunition. But then someone finds a photograph of the trenches in WW-I where Captain Jack Harkness is clearly there, looking young and gorgeous, despite it being 90+ years ago. Clearly he has travelled in time. Or is immortal. Or (I think in this case) both.
Now, the implausibility of this is not that you have a time travelling immortal getting shot in the trenches. Well, OK, it might be, but that is not the plot improbability. The point is that you would have to spend several decades searching all the WW-I photography footage to find that photo, and in the show it happened in about 10 minutes. But this is where modern technology and the Google Time Traveller/Immortals project comes in.
What we are going to do is this. We are going to scan every photograph on the internet. Every one. Every historical archive, every uploaded family history picture, every newspaper report on historic events. We are going to scan every frame of every newsreel. We are going to look at every face captured on film, tape or disc since films, tapes or discs existed.
We are going to include every selfie on Facebook, all those trillions of them.
And then we are going to find all the faces in them, and compare them. This modest little computational task should be no more than a few thousand times what Google does now to index the entire internet.
There is a good chance that everyone alive today in the Western world can be found on dozens of online pictures if you look hard enough. So we look for their face appearing as it does today but 20, 30, 50, 100 years ago. How does Jack Harkness appear in 1916 and in 2005? The only explanation must be time travel or immortality.
Now, there will be a certain number of false positive hits. Say a few million. It will be implausible to track down a few million people and demand to see their birth certificate (they could have forged one, anyway, or assumed a false identity, or be Barak Obama.) But we do not have to say "this person is a time traveller". Not yet. All we have to say is that time travellers exist. Like the proof of the Higgs boson, our proof will be a blip on the curve of similarity of faces, a few comparisons more out of billions. This is why we need everything. The statistics mean that if we do enough comparisons even a very small difference will be significant.
Our control group will be comparing faces of people in the same photograph. Clearly it is unlikely that time travellers will pose for a photograph with themselves. It is quite possible ("Let's all meet up in the year 3000" etc), but that would be a tad obvious and we already know that time travellers are not obvious. People who do pose for photographs are families, and they do look alike, so a great control group will be how similar do people look like who are in the same picture at the same time. We compare this to people from different photos at the same time (higher chance of the same person being in two photos), and different photos from different times.
I think the output will look something like this
Robust and conclusive proof of the existence of natural immortals and/or time travellers will thereby be presented.
(Actually, there is a practical application of this. When our police say "we have identified this man from CCTV footage", the CCTV footage is usually so blurred and grainy that you cannot see if the 'person' is human, let alone their identity. This study would give robust statistical backing for saying whether a CCTV or other image is actually significantly like the suspect in the bank robbery/terrorist atrocity. But how dull is that?)
Google could then put up the 'hit' images on a site, and like the Galaxy Zoo project the general public could wade in and decide which were genuine hits and which were not. "Oh, look, there is Uncle Joe - no, but he can't be, that picture is from 1762. Uncle Joe, are you an immortal or a time traveller? Just where is your birth certificate?" This might cause a certain friction with a million or so Uncle Joes, but it will be worth it.
After all, knowing that something can have been done is half the way to being about to have done it.