Maybe-functional time travel: The Time Walker (Class Prototype Design)

[Ranged Ranger]

The problem with Alter The Past not actually letting you change the past is that that's probably what a player who actually takes this class would want.-SNIP-

Actually experiencing going to the past w/o the ability to change anything is boring and pointless, but if the restriction is against visible changes to the timeline, that just becomes a challenge...

-SNIP-The inability to change the past is mostly taken from All Night Laundry, where at one point, the characters have to sneak around to avoid being seen by their past selves in order to save one person's life and swap their body with a dummy. ("Past is bad. Future is worse. Timelines lock.") Added memory alteration as a valid method of resolving this.

See this is good (as are multiple ways of resolving if you goof)

Stuff I'd like to add for the "complete time travel experience":
-A better definition of "distinguishably change" the past
-The ability to destroy paradoxes by saying that the person you summoned is from an alternate, doomed timeline.
-The ability to rewind your turn, for the Groundhog Day experience.

Another suggestion - ability for Time Walkers to interact with each other using their powers... such as the guy who closes his grandfather's paradox (NOT Grandfather Paradox, mind you - that's different) 150 years later, or the woman who was banished from the kingdom before she could send an item back, so she has her friend go send it back for her.

Also, a closed loop items aren't necessarily a bad thing for a story:

Spoiler: Babylon 5 Spoilers

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(i.e. Valen brought the Triluminary with him from the future; it becomes a sacred relic of Valen passed down through the Menbari generations; Delenn gives the Triluminary to Sinclair, who then took it into the past. it was only after he left that everyone else realized he was Valen... Sinclair found out that he was Valen earlier that day when he received a sealed note he had/would write to himself 1000 years earlier.

This example has both a closed loop person (Valen via Minbari reincarnation) and a closed loop item (the Triluminary)... Personally I wouldn't let a PC be a closed loop person (you're special, but not THAT special), but if the DM wants to have them interact with a closed loop relic, that could be a fun plot point - of course the DM would need to decide if/how such an item gets introduced, but for someone receiving such an item. closing the loop might actually be a matter of founding an organization or organizations that will ensure that the item is eventually sent back.