Accepted Testing

From A Wheel of Time Wiki

In order to become an Accepted in the White Tower, one must first pass a special test using Ter'angreal in the basement of the white tower, which are described only as silver arches.

Candidates enter a ter'angreal where they must face their deepest fears — one each from the past, the present and the future. Some who take the test never return. While inside the arch, it is extremely dangerous to Channel. While trying to initially figure out what the Rings did Aes Sedai were Burned Out by Channeling within. However, walking through the Rings affects the memory, and most women don't remember that they can channel; thus, a warning isn't considered overly important.

They have the right to refuse to enter the ter'angreal, but three refusals result in being sent from the Tower; the chance to be Aes Sedai lost forever.

Also, as evidenced by the testing of Nynaeve al'Meara, these to an extent do show the future, as it referred to Sharina Sedai, who comes as a Novice later in the series after Egwene al'Vere, the Amyrlin Seat of Salidar.