Subjective spacetime derived from a causal histories approach

The internal description of spacetime can reveal ambiguity regarding an observer's perception of the present, where an observer can refer to the present as if he were outside spacetime while actually existing in the present. This ambiguity can be expressed as the compatibility between an element and a set, and is here called a/{a}-compatibility. We describe a causal set as a lattice and a causal history as a quotient lattice, and implement the a/{a}-compatibility in the framework of a causal histories approach. This leads to a perpetual change of a pair of causal set and causal history, and can be used to describe subjective spacetime including the déjà vu experience and/or schizophrenic time.