I more or less directly stole this idea from the last episode of Star Trek: The Next Generation, "All Good Things". It's arguably the greatest episode ever. Hell, I devoted a whole storyline to it.
Anyway, in the episode, Captain Picard finds himself bouncing between the past, the present, and the future. At one point, the Enterprise needs to scan the anti-time anomaly, but they can't figure out how. The Data of the "past" mentions that a certain device that should be able to do it, but the device is still only theoretical and Starfleet scientists are working on building one. When Picard returns to the "present", he asks the Data of that time period if they have one, and Data tells him they have one on board, and they are able to successfully scan the anomaly.
The two situations are similar: in the past there's talk of a device that doesn't exist yet, and rather than try to build it at that point in time, the protagonist simply waits until he'll be in the future where it's already been built. Quite ingenious.
Oh, and while I'm geeking out, Dr. Light's line is taken from a Star Trek: Deep Space Nine episode, where Miles is also jumping through time, and ends up meeting himself. The problem is that the past version is dying from poisoning, while the present version feels fine. When they stop to think about how that's possible, they give up and speak the line in unison. And, at the same time, it's a take on the recurring "I hate time travel" line.