Science fiction is the only truly mind-expanding substance.
-- C.S. Lewis

'The Infinite Assassin' is a hard science fiction short story written by Greg Egan, first published in Interzone #48 in June 1991, then reprinted in the following places (list copied verbatim from author's website):

Like many of Egan's stories, it serves the primary purpose of taking an idea to its logical extent: in this case, the many-worlds theory of quantum mechanics, which states, in a nutshell, that every action that could go more than one way goes every way: the universe splits into many universes, one for each of the outcomes. If you flip a coin and it lands on its head, it landed on its tail in another universe (in many others, actually, thanks to unrelated splits that happened along the way; and in in others it landed on its side, and in others an errant gust of wind blew it into the sink, and in others it disappeared without a trace, etc. ad infinitum).

"The Infinite Assassin" adds a new twist -- some addicts to a bizarre hallucinogenic drug gain the ability (not really an ability, as it's involuntary, born of a desire to experience the real life they have been dreaming) to move between the universes; unfortunately, the universes are adjacent (they're "infinite like the real numbers, not the integers") and the druggies must move through all the universes between their own and the destination in order to get there -- but those universes are already occupied by other versions of themselves, which are then pushed "ahead" of them into other universes still. As Egan puts it, the junkies "must flow" through the 4-space. In doing so, they start to drag their surroundings along with them, like a hand moving through water. The ripples spread farther and farther, and as the areas closer to the dreamer are moving fastest, whole cities can be scattered into many universes, friends and family members seperated from one another forever.

The main character is an employee of The Company, which seems to be something of a constant between the worlds. It is his (infinitely many versions of him, of course, in all the different universes in which this is happening, though the story is told from the viewpoint of only one of the individuals) job to kill the junkie and stop the flow (or rather, for enough versions of him to kill enough versions of the junkie to interrupt the flow in enough places to disrupt its motion, which effectively stops it) before the ripples spread beyond the ghetto and start to wreak havock in the nice, clean suburbs.

It sounds like a lot to absorb, but Egan is a deft writer and along with the many-worlds science (which gets far cooler and more convoluted as the story progresses, causing plot twists a-plenty) comes fun and imaginative description -- at one point, for example, walking through the area of the flow, watching denisens flash into and out of existence around him (they're all moving through the unverses at different rates), the narraror sees a man who remains constant, but with radically shifting hairstyle.

In another Egan hallmark, the story is logically consistent: no plot holes, no convenient literary jumps, no unrealistic events. Even the most outrageous conclusions follow logically from the premises -- which is, of course, part of what makes his writing so much fun. This is science fiction, not fantasy; the world written about could be ours; the story could, in theory, actually occur.

The final ingredient: ideas, ideas, ideas. Egan's are complex and disconcerting, jumping off trains of staring-into-space contemplation, but his touch is light -- philosophical questions hinted at rather than proclaimed outright (e.g. who exactly is "I", if "I" exists, with variations gradually increasing from zero, in so many different universes? -- similar issues are touched upon again, and developed further, in Quarantine and Permutation City). Reading some of Egan's fiction is pure, joyous, socratic enlightenment in textual form. As one rhapsodic review of Axiomatic put it: "It will set your brain on fire."

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