Maybe I'm just crazy, but it seems strange to me how I never see the Novikov Self-Consistency Principle mentioned. If you're somebody who is trying to think up fantastical technology based on hypothetical physics, then nothing can ever hope to match what the Self-Consistency Principle provides.

Imagine you have a digital screen that generates random images when you push a button, and you have a second button that you can push in the next 20 seconds if the screen shows you what you "want". This machine is designed to create a time paradox if the second button isn't pushed within 20 seconds of the first, so when you push the first button, you "erase" all possible futures where the second button isn't pushed within 20 seconds. This means that the device is effectively an omniscient entity whose goal is to motivate you to push the second button by showing you something on the screen.

This can be used to find solutions to problems(as long as you are capable of checking that the solution is right within the 20 seconds), create art that is based purely off your ability to judge art rather than your own creativity, and also break all passwords. It is unfortunate that this technology could never be discovered in reality without completely uprooting modern society, due to that last part.