I read this sometime in the 2000s, in another state, so I can't go back and check the shelves.
A scientist discovers time-travel, or something like it -- it's a time-sea. Swimming in it causes ripples or waves that change the timeline. More and more time-changed civilizations enter the sea to battle. The swimmers have tails, the length which represents their life-span or memories? Chop off the tail, and they remember less. The best warrior is one with a super-short tail and hardly any memories.
It was definitely a novel, and not a short story in a collection. Beyond that -- no idea of author, title, or even the cover. Except that I read it in hard-cover, so not a straight-to-mass-market pulp.