Time Traveling was discovered/first used by Doctor Emmett Brown in Hill Valley on October 26th 1985.
He got the idea on November 5th 1955 when he slipped off the toilet and hit his head on the sink whilst he was hanging a clock. This gave him the idea for the flux capacitor which is the key to enabling Time Travel. He decided to build the time machine from a Delorean because "if you're going to build a time machine out of a car, why not do it with some style?"
It became a problem to the community when Doctor Brown and his young friend Mr.McFly started to significantly alter events for the worse. Doctor Brown decided to destroy the Time Machine when they got back to 1985 so that no more damage could be done with it.
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