Originally Posted by
Petrikow
Well, we're not entirely sure. In fact, the whole phase-shifting thing in relation to Rayshifting is only mentioned in Melty Blood Back-Alley Nightmare (to my knowledge?), a work that contains many strange secrets.
As for phases themselves, it is the "plane" upon which different worlds lie upon. For example: INS has a different phase. Gudaguda is in a different phase generally speaking. SERAPHIX when it "flips" switches phases, etc, etc. In 4.5, Nemo briefly explains that the "shock" felt when going through the surface boundary (境界面) of phase space is similar to what goes on when they collide with things in INS. Sion also calls CHALDEAS a "sophisticated phase navigation system" in 3.5 (Ooku).
So why I tied "parallel worlds" with "phase" is thus that. Rayshifting apparently works through overcoming phase-differentials, meaning that (as MBBAN mentions) it operates through parallel worlds, not just time-travel.