What self is?

The concept of self seems to be absolutely essential for the understanding of the macroscopic and macro-temporal aspects of consciousness and would be counterpart for observer in quantum measurement theory.

The original proposal was that self is conscious entity.

1. Self corresponds to a subsystem able to remain un-entangled under the sequential informational 'time evolutions' U. Exactly vanishing entanglement is practically impossible in ordinary quantum mechanics and it might be that 'vanishing entanglement' in the condition for self-property should be replaced with 'subcritical entanglement'. If space-time decomposes into p-adic and real regions, and if entanglement between regions representing physics in different number fields vanishes, space-time indeed decomposes into selves in a natural manner. Causal diamonds would form natural imbedding space correlates for selves and their hierarchy would correspond to self hierarchy.
2. The intuitive idea inspired by the formation of bound states of particles from particles was that self corresponds somehow to an integration of quantum jumps to single coherent whole. Later I gave up this idea since it was difficult to understand how the integration could take place.
3. The next suggestion was that quantum jumps as such correspond to selves. It was however difficult to assign to selves identified in this manner a definite geometric time duration. It is an empirical fact that this kind duration can be assigned to mental images (identified as subselves).
4. One could also introduce self as a subsystem which is only potentially consciousness and here the notion of negentropic entanglement suggests an obvious approach based on interaction free measurement. Negentropy Maximization Principle (NMP) implies that Universe is like a library with new books emerging continually at its shelves. This would explain evolution. One can however argue that negentropic entanglement - "Akashic records" - gives rise only to self model rather than self.
5. The approach which seems the most convincing relies on the observation that ZEO sequences of ordinary state function reductions leaving state unchanged are replaced with sequences for which the part of the zero energy state associated with a fixed boundary of CD state remains unchanged in state function reduction whereas the state at the other end of CD changes. This is something new and explains the arrow of time and its flow and self could be understood as a sequence of quantum jumps at fixed boundary of CD (with the average location of second boundary shifted towards geometric future like in dispersion). Amusingly, this is in accordance with the original proposal except that state function reductions take place on same boundary of CD.

   This view is extremely attractive since it implies that the act of free will interpreted as genuine state function reduction must mean reversal for the direction of geometric time at some level of hierarchy of selves. The proposal has indeed been that sensory perception and motor action are time reversals of each other and that motor action involves sending of negative energy signals to the geometric past.

For details and background see the chapter "Self and binding".