Saw people in the comments stating that Valve had experimented with this idea (or something similar to it). Would like to see the reasons valve scrapped the idea, as I think this could add much to the way we think portals.

I can think of many ways this could become a fine game, but I think if paired alongside portals then the game would lose its "complicated simplicity" and start asking too much of the player's short-term memory in order to solve hard puzzles.
Also, we can't overlook the fact that this Past Ordination Replicating Temporal All-in-one Laser brings about many new concepts... such as item duplication (An item coming from a "past" alternate timeline into this one), item disposal (the above, but then you move into the timeline that the object came from), as well as time traversal. I think these fundamental concepts of the device's use can bring about many great puzzles in a full game.
*Game Start
* Take screenshot
* Mess up
* Make portal
* Repeat
~Plystire
A rose is only a rose until it is held and cherished -- then it becomes a treasure.