Theory of Phaseshift
Since both playable Sirens have abilities that control time and space, the most likely explanation for Angel's Phaseshift is the ability to "extend" or "shift" her existence across multiple dimensions. When the player meets Angel in person, she appears to them in a "digital" dimension, and is subsequently dragged back to her containment field. Her ability seems most similar to Lilith's, but with a few key distinctions: whereas Lilith can actively walk and teleport herself and others between dimensions, Angel seems to exist in both dimensions, thus the "shift" of her existence. The easiest way to explain this would be to say that Angel can exist in both dimension A and B at the same time. Dimension A is Angel's entrapment in Jack's containment field. Dimension B would be the digital world that Angel percieves. So in Dimension A, Angel cannot leave her prison, but simultaneously existing in Dimension B, Angel has nearly full reign of her dimension. This leaves to question if Angel's ability allows her complete control over a dimension she perceives or if her abilities only extend to what she can comprehend, i.e. a digital world. Also, Angel's ability to bring the player into her digitally perceived world suggests that she can only do so at short distances from herself. Remember, this is only a working theory. - xmikeyxlikesitx
- Sounds plausible to me. Dimension B, as you call it, seems to be some sort of Electromagnetic energy. I beleive her Phaseshift allows her to manipulate this EM field. Because everything electronic emits EM waves, she can move between any that she can form a link with. Hyperion has access to the ECHO Net, so she can talk to you whenever she wants (and so can Handsome Jack). Because she is inside a Hyperion Control Core, she can also interface with other Hyperion technology, like the Uplink and Lunar Supply Beacon. She can even effect systems on the Moonbase. However, she also apparently must deal with firewalls, as she cannot directly control any Hyperion robot. That constaint only makes sense, as a means to prevent what is essentially an Organic AI from gaining an army of killer robots. Her ability to Phaseshift nearby people and objects (Vault Hunters, Vault Key, supplies) is proof that it is in-fact a Siren Phasing ability.