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At the beginning of Bill and Ted's Excellent Adventure, Rufus explains the Utopian life that Earth now enjoys and that it's all thanks to inspiration from the music of the band Wyld Stallyns, but that it all might never have come to pass had the band been forced apart as punishment for failing a history presentation. So apparently now he must go back in time to help them pass.

Since Rufus himself lives in the world where they formed the band and created low-mini-golf-score world, why does he feel the need to go back in time to help them pass the test?

The obvious answer is that history also records the pair passing only with his help and therefore he must go back in time to fulfill that destiny.

But if you think of it as that kind of loop, there must be a beginning-world where Wyld Stallyns were forgotten (akin to "Loser-George-McFly-World" at the beginning of Back To The Future), but for some reason Rufus decided to go back in time and help them pass, as if he knew that this pair of nobodies would turn out great music that would inspire major socio-economic reforms.

How could this happen?

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The way time travel appears to work in the Bill and Ted series is that there is just one unchanging timeline. Travelling back in time doesn’t overwrite existing history or create a branching timeline, anything a time traveller does in the past has already happened.

We get a demonstration of this near the end of the film. Early on Ted’s father accuses Ted of stealing his keys. Ted denies this, but later on when they need the keys this happens

Bill: If only we could go back to two days ago before your dad lost his keys, and steal them.

Ted: Well, why don't we?

Bill: Cuz we don't have time, dude.

Ted: We could do it after the report.

Bill: Oh, yeah! Where should we put 'em?

Ted: How 'bout behind this sign?

Bill: OK... Whoa! It worked!

Ted: Right, so when we're done with the report, we have to remember to do this or else it won't happen... but it did happen! Wow, it was me who stole my dad's keys!

The sequel takes this idea further in the final battle against the villain. Both the Stallions and De Nomolos keep revealing traps that they intend to set up in the future. Then, just as De Nomolos seems to have the upper hand, all his traps backfire on him. He wasn’t really able to travel back and set the traps, only Bill and Ted could, because they won.

As a final note, while Bill and Ted is far from being hard science fiction this concept does actually have some basis in real physics where it is known as the Novikov Self-Consistency Principle

The Novikov self-consistency principle, also known as the Novikov self-consistency conjecture and Larry Niven's law of conservation of history, is a principle developed by Russian physicist Igor Dmitriyevich Novikov in the mid-1980s. Novikov intended it to solve the problem of paradoxes in time travel, which is theoretically permitted in certain solutions of general relativity that contain what are known as closed timelike curves. The principle asserts that if an event exists that would cause a paradox or any "change" to the past whatsoever, then the probability of that event is zero. It would thus be impossible to create time paradoxes.

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    Interesting, but in that case they knew in advance they'd need the keys, so they were able to plan their trip back after the report - it's not like finding the keys gave them the idea to get the keys. But in Rufus (or all the people of the most excellent future)'s case, nobody could have known that what the world needed was a for these two guys to form a totally triumphant band in order to plan for a time-traveler to come back and make sure they don't break up.
    – komodosp
    Commented Dec 7, 2018 at 8:43
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    The point is that in a Novikov universe there was never a timeline where Rufus didn’t go back, or where Ted didn’t steal the keys, or they didn’t troll De Nomolos. Everything that happened in the past had already happened. Rufus always grew up in a world influenced by his own time travel, so there are plenty of ways he could figure out what was needed - maybe the early weirdness in their career was enough to piece it together, maybe they told the truth later on, maybe Rufus just told his younger self after finishing.
    – Princess Ada
    Commented Dec 8, 2018 at 22:36

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