The problem for Threshold arises due to its status as a liminal space: it exists between, and thus outside of conventional spaces: it is a crossroads of both places and times. If one allows for the intersection of figures from multiple time frames in the city, the concept of linear time is confounded. If one adopts a "many worlds" approach, with Threshold serving as the nexus of a multi-verse, each plane of which has its own linear progression of time, then Threshold loses its distinctiveness as a place-between-places, as it simply becomes yet another of the many worlds, albeit one that is more closely intertwined with the others.
The solution was in formed by a liberal (and likely wholly inaccurate) reading of a few key concepts of Special Relativity in physics: the perception of time is relative to the observer, and so too can the order of a sequence of events be relative to observers at different points. Let us consider Threshold to be a self-contained space, where all possible permutations and combinations of events and states of being that can occur in this space occur simultaneously. Individuals navigate through this morass of possibility through a process of selective attention, constructing what may or may not be a perception of linear time from a timeless pool. One moves, for example, by selectively attending to the possibility of occupying a location apart from one's current location (or rather, from the location to which one is currently attending to as occupying). I would imagine that for most inhabitants of Threshold, this would also involve attending to the possibility of occupying all of the locations in between these points, as this process is likely to be subconscious. Most individuals are so attuned to constructing a linear perception of time based on causality that they would likely continue to do so, innately rejecting the notion of jumping between two points instantaneously (to continue the above example).
This has several interesting implications, not the least of which being that as one's awareness of how Threshold operates rises closer to consciousness, one's capabilities within Threshold become closer to omnipotent. This in turn increases the entrapping allure of the city, as individuals retain the power to perform "impossible" feats--to move instantly from one location to another, to slow down or reverse the perception of time, to re-live events ad infinitum--only within the bounds of the city.
Another implication concerns interactions between the city's denizens. If all actions, including interactions with others, are governed by selective attention, then one individual's interaction with another may be constructed wholly differently, or be entirely nonexistent, from the perspective of the other individual. For something to exist in Threshold, it need only be two things: possible, and attended two. If a possible conversation between two individuals is attended to by only one of them, then that conversation, that interactions, does not exist from the perspective of the second individual; it does not form part of his or her experience. It is in a sense the ultimate form of solipsism, as each individual's construction of a linear and causal perception of events is valid only to that individual.