About the arrow of psychological time and notion of self: once again!
Quantum classical correspondence predicts that the arrow of subjective time is somehow mapped to that for the geometric time. The detailed mechanism for how the arrow of psychological time emerges has however remained open. Also the notion of self is problematic. I have proposed two alternative notions of self and have not been able to choose between them. A further question is what happens during sleep: do we lose consciousness or is it that we cannot remember anything about this period? The work with the model of topological quantum computation (see previous posting) has led to an overall view allowing to select the most plausible answer to these questions. But let us be cautious!
A. Two earlier views about how the arrow of psychological time emerges
The basic question how the arrow of subjective time is mapped to that of geometric time. The common assumption of all models is that quantum jump sequence corresponds to evolution and that by quantum classical correspondence this evolution must have a correlate at spacetime level so that each quantum jump replaces typical spacetime surface with a more evolved one.
 The earliest model assumes that the spacetime sheet assignable to observer ("self") drifts along a larger spacetime sheet towards geometric future quantum jump by quantum jump: this is like driving car in a landscape but in the direction of geometric time and seeing the changing landscape. There are several objections.
 Why this drifting?
 If one has a large number of spacetime sheets (the number is actually infinite) as one has in the hierarchy the drifting velocity of the smallest spacetime sheet with respect to the largest one can be arbitrarily large (infinite).
 It is alarming that the evolution of the background spacetime sheet by quantum jumps, which must be the quintessence of quantum classical correspondence, is not needed at all in the model.
 Second model relies on the idea that intentional action understood as padictoreal phase transition for spacetime sheets and generating zero energy states and corresponding real spacetime sheets  proceeds as a kind of wave front towards geometric future quantum jump by quantum jump. Also sensory input would be concentrated on this kind of wave front. The difficult problem is to understand why the contents of sensory input and intentional action are localized so strongly to this wave front and rather than coming from entire life cycle.
There are also other models but these two are the ones which come into my mind first.
B. The third option
The third explanation for the arrow of psychological time  which I have considered earlier but only halfseriously  began to look very elegant during last night. This option is actually favored by Occam's razor since it uses only the assumption that spacetime sheets are replaced by more evolved ones in each quantum jump. Also the model of tqc favors it.
 The simplest assumption is that evolution in a reasonable approximation means shifting of the field patterns backwards in geometric time by some amount per quantum jump. This makes sense since the shift with respect to M^{4} time coordinate is an exact symmetry of extremals of Kähler action. It is also an excellent approximate symmetry for the preferred extremals of Kähler action and thus for maxima of Kähler function spoiled only by the presence of lightcone boundaries. This shift occurs for both the perceiver spacetime sheet and perceived spacetime sheet representing external world: both perceiver and percept change.
 Both the landscape and observer spacetime sheet remain in the same position in imbedding space but both are modified by this shift in each quantum jump. The perceiver experiences this as a motion in 4D landscape. Perceiver (Mohammed) would not drift to the geometric future (the mountain) but geometric future (the mountain) would effectively come to the perceiver (Mohammed)!
 There is an obvious analogy with Turing machine: what is however new is that the tape effectively comes from the geometric future and Turing machine can modify the entire incoming tape by intentional action. This analogy might be more than accidental and could provide a model for quantum Turing machine operating in TGD Universe. This Turing machine would be able to change its own program as a whole by using the outcomes of the computation already performed.
 The concentration of the sensory input and the effects of conscious motor action to a narrow interval of time (.1 seconds typically, secondary padic time scale associated with the largest Mersenne M_{127} defining padic length scale which is not completely superatronomical) can be understood as a concentration of sensory/motor attention to an interval with this duration: the spacetime sheet representing sensory "me" would have this temporal length and "me" definitely corresponds to a zero energy state.
 The fractal view about topological quantum computation strongly suggests an ensemble of almost copies of sensory "me" scattered along my entire life cycle and each of them experiencing my life as a separate almost copy. My childhood is still sensorily lived but has moved about 57 years backwards in geometric time and would live the year 1897 but enjoy all techno conveniences of the year 1950!
 The model of geometric and subjective memories would not be modified in an essential manner: memories would result when "me" is connected with my almost copy in the geometric past by braid strands or massless extremals (MEs) or their combinations (ME parallel to magnetic flux tube is the analog of Alfwen wave in TGD).
C. Can one choose between the two variants for the notion of self?
I have considered two different notions of "self" and it is interesting to see whether this picture might allow to choose between them.
 In the original variant of the theory "self" corresponds to a sequence of quantum jumps. "Self" would result through a binding of quantum jumps to single "string" in close analogy and actually in a concrete correspondence with the formation of bound states. Each quantum jump has a fractal structure: unitary process is followed by a sequence of state function reductions and preparations proceeding from long to short scales. Selves can have subselves and one has self hierarchy. The questionable assumption is that self remains conscious only as long as it is able to avoid entanglement with environment.
 According to the newer variant of theory, quantum jump has a fractal structure so that there are quantum jumps within quantum jumps: this hierarchy of quantum jumps within quantum jumps would correspond to the hierarchy of dark matters labelled by the values of Planck constant. Each fractal structure of this kind would have highest level (largest Planck constant) and this level would corresponds to the self. What might be called irreducible self would corresponds to a quantum jump without any subquantum jumps (no mental images). The quantum jump sequence for lower levels of dark matter hierarchy would create the experience of flow of subjective time.
It would be nice to reduce the notion of self hierarchy to that of fractal quantum jump in the sense of dark matter hierarchy but there is an objection. Does this concept really make sense? Fractality is a geometric notion and subjective time does not reduce to the geometry. It is also not quite clear whether the reasonable looking idea about the role of entanglement can be kept.
The older variant of self looks more attractive if one accepts the new model for the arrow of psychological time.
 Entire Universe performs the quantum jump and there is an infinite fractal hierarchy of scales associated with quantum jump and state function reduction/state preparation part of quantum jump proceeds as a sequence from long to short scales. One cannot assign any finite geometric duration to a given step in this sequence since the geometric duration assignable to the entire quantum jump would in this case be automatically infinite. In this framework our life cycle would most naturally correspond to a sequence of quantum jumps.
 The simplest guess for the interval of geometric time assignable to single quantum jump is as CP_{2} time. pAdic time scales define alternative and perhaps more attractive identification. The larger the value of padic prime p, the faster the psychological time would flow and faster the experienced rate of evolution would be. Also the hierarchy of Planck constants suggests a hierarchy of these times and the concentration of attention to to dark matter levels would make the flow of psychological time much faster. The model of tqc suggests that each period of EEG rhythm corresponds to single quantum jump for corresponding "me" in unentangled selfstate.
 The ability to avoid entanglement with environment would be essential for the original notion of self. One can of however ask whether the assumption about the loss of consciousness in entanglement  that is during sleep  is really necessary. One could however argue that if consciousness is really lost during sleep, we could not have the deep conviction that we existed yesterday. Furthermore, during topological quantum computation entanglement is absent and thus this state should correspond to conscious experience. Night time is however the best time for tqc since sensory input and motor action do not take metabolic resources and we certainly do problem solving during sleep. Thus we should be conscious at some level during sleep and perform quite a long tqc. Perhaps we are!
Could it be that we do not remember anything about the period of sleep because our attention is directed elsewhere and memory recall uses only copies of "me" assignable to brain manufacturing standardized mental images? Perhaps the communication link to the mental images during sleep experienced at dark levels of existence is lacking or sensory input and motor activities of busy westeners do not allow to use metabolic energy to build up this kind of communications. Hence one can seriously ask, whether self is actually eternal with respect to the subjective time and whether entangling with some system means only diving into the ocean of consciousness as someone has expressed it. We would be Gods as also quantum classical correspondence in the reverse direction requires (padic cognitive spacetime sheets have literally infinite size in both temporal and spatial directions). This would be the most optimistic view that one can imagine.
This arguments look nice but more arguments are needed to exclude the model of self as single quantum jump.
D. What after biological death?
Could the new option allow to speculate about the course of events at the moment of death? Certainly this particular sensory "me" would effectively meet the geometrotemporal boundary of the biological body: sensory input would cease and there would be no biological body to use anymore. "Me" might lose its consciousness (if it can!). "Me" has also other mental images than sensory ones and these could begin to dominate the consciousness and "me" could direct its attention to spacetime sheets corresponding to much longer time scale, perhaps even to that of life cycle, giving a summary about the life.
What after that? The Tibetan Book of Dead gives some inspiration. A western "me" might hope (and even try use its intentional powers to guarantee) that quantum Turing tape brings in a living organism, be it human or cat or dog or at least some little bug. If this "me" is lucky, it could direct its attention to it and become one of the very many sensory "me's" populating this particular 4D biological body. There would be room for a newcomer unlike in the alternative models. A "me" with Eastern/NewAgeish traits could however direct its attention permanently to the dark spacetime sheets and achieve what might she might call enlightment.
For details see the chapter Quantum Model for Memory.
