Zero energy ontology, self hierarchy, and the notion of time

In the previous posting I discussed the most recent view about zero energy ontology and p-adicization program. One manner to test the internal consistency of this framework is by formulating the basic notions and problems of TGD inspired quantum theory of consciousness and quantum biology in terms of zero energy ontology. I have discussed these topics already earlier but the more detailed understanding of the role of causal diamonds (CDs) brings many new aspects to the discussion.

In consciousness theory the basic challenges are to understand the asymmetry between positive and negative energies and between two directions of geometric time at the level of conscious experience, the correspondence between experienced and geometric time, and the emergence of the arrow of time. One should also explain why human sensory experience is about a rather narrow time interval of about .1 seconds and why memories are about the interior of much larger CD with time scale of order life time. One should also have a vision about the evolution of consciousness takes place: how quantum leaps leading to an expansion of consciousness take place.

Negative energy signals to geometric past - about which phase conjugate laser light represents an example - provide an attractive tool to realize intentional action as a signal inducing neural activities in the geometric past (this would explain Libet's classical findings), a mechanism of remote metabolism, and the mechanism of declarative memory as communications with the geometric past. One should understand how these signals are realized in zero energy ontology and why their occurrence is so rare.

In the following my intention is to demonstrate that TGD inspired theory of consciousness and quantum TGD proper indeed seem to be in tune and that this process of comparison helps considerably in the attempt to develop the TGD based ontology at the level of details.

1  Causal diamonds as correlates for selves

Quantum jump as a moment of consciousness, self as a sequence of quantum jumps integrating to self, and self hierarchy with sub-selves experienced as mental images, are the basic notion of TGD inspired quantum theory of consciousness. In the most ambitious program self hierarchy reduces to a fractal hierarchy of quantum jumps within quantum jumps.

It is natural to interpret CD:s as correlates of selves. CDs can be interpreted in two manners: as subsets of the generalized imbedding space or as sectors of the world of classical worlds (WCW). Accordingly, selves correspond to CD:s of the generalized imbedding space or sectors of WCW, literally separate interacting quantum Universes. The spiritually oriented reader might speak of Gods. Sub-selves correspond to sub-CD:s geometrically. The contents of consciousness of self is about the interior of the corresponding CD at the level of imbedding space. For sub-selves the wave function for the position of tip of CD brings in the delocalization of sub-WCW.

The fractal hierarchy of CDs within CDs defines the counterpart for the hierarchy of selves: the quantization of the time scale of planned action and memory as T(k) = 2^kT₀ suggest an interpretation for the fact that we experience octaves as equivalent in music experience.

2. Why sensory experience is about so short time interval?

CD picture implies automatically the 4-D character of conscious experience and memories form part of conscious experience even at elementary particle level: in fact, the secondary p-adic time scale of electron is T=1 seconds defining a fundamental time scale in living matter. The problem is to understand why the sensory experience is about a short time interval of geometric time rather than about the entire personal CD with temporal size of order life-time. The obvious explanation would be that sensory input corresponds to sub-selves (mental images) which correspond to CD:s with T(127) @ .1 s (electrons or their Cooper pairs) at the upper light-like boundary of CD assignable to the self. This requires a strong asymmetry between upper and lower light-like boundaries of CD:s.

1. The only reasonable manner to explain the situation seems to be that the addition of CD:s within CD:s in the state construction must always glue them to the upper light-like boundary of CD along light-like radial ray from the tip of the past directed light-cone. This conforms with the classical picture according to which classical sensory data arrives from the geometric past with velocity which is at most light velocity.

2. One must also explain the rare but real occurrence of phase conjugate signals understandable as negative energy signals propagating towards geometric past. The conditions making possible negative energy signals are achieved when the sub-CD is glued to both the past and future directed light-cones at the space-like edge of CD along light-like rays emerging from the edge. This exceptional case gives negative energy signals traveling to the geometric past. The above mentioned basic control mechanism of biology would represent a particular instance of this situation. Negative energy signals as a basic mechanism of intentional action would explain why living matter seems to be so special.

3. Geometric memories would correspond to the lower boundaries of CD:s and would not be in general sharp because only the sub-CD:s glued to both upper and lower light-cone boundary would be present. A temporal sequence of mental images, say the sequence of digits of a phone number, could corresponds to a sequence of sub-CD:s glued to the upper light-cone boundary.

4. Sharing of mental images corresponds to a fusion of sub-selves/mental images to single sub-self by quantum entanglement: the space-time correlate for this could be flux tubes connecting space-time sheets associated with sub-selves represented also by space-time sheets inside their CD:s. It could be that these ëpisodal" memories correspond to CD:s at upper light-cone boundary of CD.

On basis of these arguments it seems that the basic conceptual framework of TGD inspired theory of consciousness can be realized in zero energy ontology. Interesting questions relate to how dynamical selves are.

1. Is self doomed to live inside the same sub-WCW eternally as a lonely god? This question has been already answered: there are interactions between sub-CD:s of given CD, and one can think of selves as quantum superposition of states in CD:s with wave function having as its argument the tips of CD, or rather only the second one since T is assumed to be quantized.

2. Is there a largest CD in the personal CD hierarchy of self in an absolute sense? Or is the largest CD present only in the sense that the contribution to the contents of consciousness coming from very large CD:s is negligible? Long time scales T correspond to low frequencies and thermal noise might indeed mask these contributions very effectively. Here however the hierarchy of Planck constants and generalization of the imbedding space would come in rescue by allowing dark EEG photons to have energies above thermal energy.

3. Can selves evolve in the sense that the size of CD increases in quantum leaps so that the corresponding time scale T=2^kT₀ of memory and planned action increases? Geometrically this kind of leap would mean that CD becomes a sub-CD of a larger CD either at the level of conscious experience or in absolute sense. This leap can occur in two senses: as an increase of the largest p-adic time scale in the personal hierarchy of space-time sheets or as increase of the largest value of Planck constants in the personal dark matter hierarchy. At the level of individual this would mean emergence of increasingly lower frequencies of generalization of EEG and of the levels of dark matter hierarchy with large value of Planck constant.

4. In 2-D illustration of the leap leading to a higher level of self hierarchy would mean simply the continuation of CD to right or left in the 2-D visualization of CD. Since the preferred M² is contained in the tangent space of space-time surfaces, and since preferred M² plays a key role in dark matter hierarchy too, one must ask whether the 2-D illustration might have some deeper truth in it.

3. New view about arrow of time

Perhaps the most fundamental problem related to the notion of time concerns the relationship between experienced time and geometric time. The two notions are definitely different: think only the irreversibility of experienced time and the reversibility of the geometric time and the absence of future of the experienced time. Also the deterministic character of the dynamics in geometric time is in conflict with the notion of free will supported by the direct experience.

In the standard materialistic ontology experienced time and geometric time are identified. In the naivest picture the flow of time is interpreted in terms of the motion of 3-D time=constant surface of space-time towards geometric future without any explanation for why this kind of motion would occur. This identification is plagued by several difficulties. In special relativity the difficulties relate to the impossibility define the notion of simultaneity in a unique manner and the only possible manner to save this notion seems to be the replacement of time=constant 3-surface with past directed light-cone assignable to the world-line of observer. In general relativity additional difficulties are caused by the general coordinate invariance unless one generalizes the picture of special relativity: problems are however caused by the fact that past light-cones make sense only locally. In quantum physics quantum measurement theory leads to a paradoxical situation since the observed localization of the state function reduction to a finite space-time volume is in conflict with the determinism of Schrödinger equation.

TGD forces a new view about the relationship between experienced and geometric time. Although the basic paradox of quantum measurement theory disappears the question about the arrow of geometric time remains.

1. Selves correspond to CD:s the own sub-WCW:s. These sub-WCW:s and their projections to the imbedding space do not move anywhere. Therefore standard explanation for the arrow of geometric time cannot work. Neither can the experience about flow of time correspond to quantum leaps increasing the size of the largest CD contributing to the conscious experience of self.

2. The only plausible interpretation is based on quantum classical correspondence and the fact that space-times are 4-surfaces of the imbedding space. If quantum jump corresponds to a shift of quantum superposition of space-time sheets towards geometric past in the first approximation (as quantum classical correspondence suggests), one can indeed understand the arrow of time. Space-time surfaces simply shift backwards with respect to the geometric time of the imbedding space and therefore to the 8-D perceptive field defined by the CD. This creates in the materialistic mind a kind of temporal variant of train illusion. Space-time as 4-surface and macroscopic and macro-temporal quantum coherence are absolutely essential for this interpretation to make sense.

Why this shifting should always take place to the direction of geometric past of the imbedding space? What seems clear is that the asymmetric construction of zero energy states should correlate with the preferred direction. If question is about probabilities, the basic question would be why the probabilities for shifts in the direction of geometric past are higher. Here some alternative attempts to answer this question are discussed.

1. Cognition and time relate to each other very closely and the required fusion of real physics with various p-adic physics of cognition and intentionality could also have something to do with the asymmetry. Indeed, in the p-adic sectors the transcendental values of p-adic light-cone proper time coordinate correspond to literally infinite values of the real valued light-cone proper time, and one can say that most points of p-adic space-time sheets serving as correlates of thoughts and intentions reside always in the infinite geometric future in the real sense. Therefore cognition and intentionality would break the symmetry between positive and negative energies and geometric past and future, and the breaking of arrow of geometric time could be seen as being induced by intentional action and also due to the basic aspects of cognitive experience.

2. Zero energy ontology suggests also a possible reason for the asymmetry. Standard quantum mechanics encourages the identification of the space of negative energy states as the dual for the space of positive energy states. There are two kinds of duals. Hilbert space dual is identified as the space of continuous linear functionals from Hilbert space to the coefficient field and is isometrically anti-isomorphic with the Hilbert space. This justifies the bra-ket notation. In the case of vector space the relevant notion is algebraic dual. Algebraic dual can be identified as an infinite direct product of the coefficient field identified as a 1-dimensional vector space. Direct product is defined as the set of functions from an infinite index set I to the disjoint union of infinite number of copies of the coefficient field indexed by I. Infinite-dimensional vector space corresponds to infinite direct sum consisting of functions which are non-vanishing for a finite number of indices only. Hence vector space dual in infinite-dimensional case contains much more states than the vector space and does not have enumerable basis.

   If negative energy states correspond to a subspace of vector space dual containing Hilbert space dual, the number of negative energy states is larger than the number of positive energy states. This asymmetry could correspond to better measurement resolution at the upper light-cone cone boundary so that the state space at lower light-cone boundary would be included via inclusion of HFFs to that associated with the upper light-cone boundary. Geometrically this would mean the possibility to glue to the upper light-cone boundary CD which can be smaller than those associated with the lower one.

3. The most convincing candidate for an answer comes from consciousness theory. One must understand also why the contents of sensory experience is concentrated around a narrow time interval whereas the time scale of memories and anticipation are much longer. The proposed mechanism is that the resolution of conscious experience is higher at the upper boundary of CD. Since zero energy states correspond to light-like 3-surfaces, this could be a result of self-organization rather than a fundamental physical law.
   1. The key assumption is that CDs have CDs inside CDs and that the vertices of generalized Feynman diagrams are contained within sub-CDs. It is not assumed that CDs are glued to the upper boundary of CD since the arrow of time results from self organization when the distribution of sub-CDs concentrates around the upper boundary of CD. In a category theoretical formulation for generalized Feynman diagrammatics based on this picture is developed.

   2. CDs define the perceptive field for self. Selves are curious about the space-time sheets outside their perceptive field in the geometric future (relative notion) of the imbedding space and perform quantum jumps tending to shift the superposition of the space-time sheets to the direction of geometric past (past defined as the direction of shift!). This creates the illusion that there is a time=snapshot front of consciousness moving to geometric future in fixed background space-time as an analog of train illusion.

   3. The fact that news come from the upper boundary of CD implies that self concentrates its attention to this region and improves the resolutions of sensory experience and quantum measurement here. The sub-CD:s generated in this manner correspond to mental images with contents about this region. As a consequence, the contents of conscious experience, in particular sensory experience, tend to be about the region near the upper boundary.

   4. This mechanism in principle allows the arrow of the geometric time to vary and depend on p-adic length scale and the level of dark matter hierarchy. The occurrence of phase transitions forcing the arrow of geometric time to be same everywhere are however plausible for the reason that the lower and upper boundaries of given CD must possess the same arrow of geometric time.

For details see chapters TGD as a Generalized Number Theory I: p-Adicization Program.