There was an episode where something happens - the transporter malfunctions or something like that - [Tim's the Star Trek fan in the family, how's he supposed to know?] and a couple of the characters get stuck in this alternate universe where the Federation is evil, and they've suddenly got a bunch of psychopaths as coworkers who don't know why they're acting so differently from their usual, murderous selves.

Basically, imagine that exact same scenario except the Barge.