Bilocation is the ability to be in two places at once. Both the original and projected version of a bilocater have the same thoughts; it is not 'dividing into two people' in that there is still one consciousness and one sentient being involved. The sensory information of both places is coming in just fine, although sensory overload is a very real risk. Both the projected self and the original have a physical presence and ability to interact with the world - touching things, moving objects, talking to people, walking, climbing, etc. Only the original needs to breathe, consume food and tend to other bodily functions, however, and anything that would kill or maim the projection destroys it due to sensory overload, leaving only the original.
Any sufficiently violent or jarring action can break the concentration needed to maintain the projection and cause it to dissolve. Tiredness, lack of nutrition or extreme emotion also make maintaining the projection harder. Involuntarily mixing up the sensory information of both locations is more likely to happen the longer that the projection is maintained. If the physical body isn't actively engaged in the world around it, the projection can last longer, with the caveat that lengthy projection will still drain the original body even if everything possible is done to keep it from being exhausting. Prolonged usage/pushing the time limit/interacting with things in both forms at great length are all things that can cause the bilocative abilities to short out entirely, resulting in an involuntary few days of no powers.
Since the projection does not need food or water and can exist in cold or heat that the regular would find unbearable for longer, in theory it could anywhere. In practice, the projection can't go anywhere the person themselves hasn't already been or that isn't within a ten mile radius. The strain of trying to force the issue can result in passing out. Power overusage results in a lot of hunger, bouts of chronic fatigue, oversleeping, and migraines. Involuntary bilocative episodes, by default, always adhere to the range limitations of the person.
As a bilocater gets older, their powers get increasingly impressive, which in Alex's case has manifested largely as being highly resistant to having her projection fade from physical damage. Anything short of what would be lethal damage for a normal person isn't going to be enough to make her projection poof out of existence (provided she isn't already injured or sufficiently exhausted to mess with her projective abilities), and training and time have made it much harder to successfully startle her out of projecting. She has also doubled her range of projection from when she was a child, but at the cost of experiencing worsening her own Depersonalization Disorder the more regularly she uses his powers. Worsening of whatever mental illnesses a person was susceptible to are common among bilocaters, unfortunately.
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