Doyle, Castle and others in “Time Will Tell”

Look, after the bloody energy wars of 2031, funneling

Castle

Energy wars!

Yeah, you know fascists control the power, trying to control the world's energy supply for a select few - don't worry, we defeat them - turns out, that one of these new sources of power is a tachyon generator as it opens doors in time-stream continuum, allowing us to travel back in time! But of course because of the possibilty of abuse, it was technically regulated against, secret from the public...

Beckett

We have a witness that saw you leaving Shauna Taylor's apartment shortly after she was killed...

I'm getting to that - look, I'm a temporal anthropologist. What we do is travel back in time and we study culturally significant eras - ancient Egypt, middle ages, man I've been to Nazi Germany!

Castle

Aren't you worried about the Butterfly Effect, a slightly change in something in the past thus altering the future?

No, we're careful. The timestream is mostly self-correcting, you know? Any small changes like a little ripple [...] [snipping his fingers] doesn't matter, but if someone wants do do something big, if someonebody wants to do something massive, then yes, of course, you're damn right you can change the future! And by the way, that's exactly what just happened!