For both approaches state function reduction is central notion but what is meant with state function reductions is something
quite different. Also gravitation is important for both approaches but in totally different manner.
Penrose and Hameroff could give a better view about Penrose-Hameroff theory but I try.
- Orch OR is not postulated but there is no explicit proposal for what it really is since quantum theory of gravitation is not proposed. There seems to be an idea about reduction of state function reduction to deterministic time evolution and that the experience of free will somehow due to the loss of computability. There is a visualization for analog for quantum superposition of space-time geometries and selection of geometry from this virtual superposition, which I fail however to understand. It is not clear to me whether Orch OR is meant to correspond to ordinary state function reduction - maybe not.
Also a duration is assigned to Orch-OR, maybe it could correspond to the duration of conscious experience.
- Microtubule hypothesis represents the biological part of the conjecture. Somehow microtubules would be the seat of consciousness and gravitation would be important. There is also the idea that somehow Planck scale is important: here I however fail to understand.
In the attempt to understand state function reduction and consciousness one starts from two problems. The problem of quantum measurement theory is that state function reduction and time evolution for Schrödinger equation - unitary evolution or counterpart for that for Dirac equation - are not consistent with each. Second problem is that free will - which we experience directly - is not consistent with classical physics nor with determinism of unitary time evolution. Physicalism is the basic obstacle here.
- The solution of is zero energy ontology (ZEO): quantum states are deterministic time evolutions - preferred extremals of action analogous to Bohr orbits - connecting "initial" and "final" states. In standard ontology quantum states are 3-D snapshots of these time evolutions. In neuroscience/biology/computer science behavior/function/program as deterministic temporal pattern would be the counterpart of zero energy state. Mathematician could say that initial value problem is replaced with boundary value problem.
- "Small" state function functions (SSFRs) ("weak" measurement in standard quantum theory) occur between zero energy states with initial state fixed but final state changing. In statistical sense the temporal distance between initial and final states defining clock time increases. Sequence of SSFRs defines the flow of subjective time correlating with the clock time. The two basic problems are solved since there are two causalities: the causality of free will as state function reduction=moment of consciousness and causality of field equations.
- The roles of "initial" and "final" states can change. This "big" state function reduction (BSFR) corresponds to ordinary state function reduction. The arrow of time changes. One can say that self defined by the sequences of SSFRs dies and reincarnates with opposite arrow of time. The experiments of Minev et al last summer gave strong support for this. See this.
- Consciousness is universal - not only associated with microtubules or reducing to gravitation. Cognition is taken as a central and universal aspect of consciousness and p-adic number fields and their fusion to adele is identified as correlates of cognition -even at elementary particle level. One generalizes the notion of space-time surface to p-adic space-time surfaces and adelic space-time surfaces as representations of "thought bubbles". The fact that p-adic field equations are not completely deterministic, means that they only partially correspond to real space-time space-time surface - are "realistic". One can say that one has intention realizable only partially as real action. Imagined sensory percepts and motor actions are indeed partially realized percepts and motor actions.
- Each extension of rationals defined by roots of irreducible polynomial defines its own adele and one obtains evolutionary hierarchy since the dimension n of extension of rationals increases in the sequence of SSFRs and BSFRs in statistically sense and therefore the algebraic complexity - kind of IQ - increases. n has interpretation as effective Planck constant heff= n×h0 so that evolution corresponds to the increase of quantum coherence lengths. The interpretation for these phases of ordinary matter is as dark matter.
- Cognitive representation as a set of points consisting of points of H with H-coordinates belonging to an extension of rationals defines a unique discretization ofthe space-time surface, and provides a number theoretical representation of finite measurement resolution.
The higher the dimension of extension, the large the number of points in the discretization. At the never achievable limit one would obtain algebraic numbers and cognitive representation which is dense at space-time surface. Quantum TGD in finite measurement resolution can be formulated using quantum superpositions of cognitive representations as states and the Galois group of representation becomes symmetry group.
The first conjecture is that geometry and number theory provide complementary views about TGD so that all physical quantum states could have representations in terms of quantum states assignable to Galois groups of extensions. Spin and color represent two example of this. M8-H duality would be one aspect of this duality.
Second conjecture is that the sequence of SSFRs reduces to a sequence of purely number theoretical state function reductions for the wave functions in Galois group forming a group algebra. This state space has decomposition to a tensor product of subspaces associated with the normal subgroups of Galois extensions which is extension of extension of ... of rationals. SSFR would be a cascade of reductions leading to a product of states assignable to groups with prime order. The primes defining decomposition of the dimension n of extension to prime factors. Conscious experience would represent a sequence decompositions of integers n to their prime factors! See this.
The biological part of the story relies two key ideas. The notion of magnetic body (MB) and dark matter consisting of phases of ordinary matter labelled by the value of heff residing at it and controlling as intentional agent biological body (BB).
- Space-time as 4-D surfaces of H=M4xCP2 provides TGD view about quantum gravitation allowing geometrization of classical fields of standard model and leading also to a geometrization of entire quantum theory. One ends up with the notion of many-sheeted space-time.
In particular, the systems have space-time sheets carrying classical fields assignable to them and defining what one can call field identity/field body. This is new as compared to Maxwellian theory. Magnetic body (MB) is of special importance in TGD inspired quantum biology.
MB would be the wise guy controlling ordinary matter: one would have master slave hierarchy consisting of layers of MB and ordinary matter at bottom.
- TGD view about gravitation is very different from standard proposals for quantum gravitation. The dark matter hierarchy is crucial for explaining coherence of living systems. heff can be rather large and correlates with the scale in which interaction is important.
Since gravitation is mediated by massless quanta and is not screened, heff is expected to be very large for the flux tubes mediating gravitational interaction, and gravitation should be crucial for understanding higher evolution levels of consciousness.
heff= hgr= GMm/v0 for Mm => v0mPl2 was originally postulated by Nottale can be very large and central for quantum biology in TGD Universe. For water the condition can be satisfied in M=m case for water blocks with mass below Planck mass. Also h_em as its electromagnetic analog would be important in atomic and molecular physics. These values of heff would characterize dark matter at the flux tubes and sheets of MB mediating particular interaction.
- The quantum coherence of MB would force coherence of ordinary bio-matter and one would overcome the basic objections against quantum coherence against quantum biology. In particular, the change of arrow of time for dark matter at MB in BSFRs would induce apparent change of the arrow at BB.
Self-organization as generation of quantum coherence would require increase of heff requiring energy feed quite generally. In ZEO self-organization would reduce to dissipation in reversed arrow of time. The decay of structures in opposite arrow of time implied by generalized second law looks like their generation in the standard arrow of time. No separate theory of self-organization is needed. Metabolic energy feed would be just loss of energy by dissipation with opposite arrow of time. System extracts - or should one say steals - its energy from environment if it is available.
- Microtubules are predicted to be important level in the evolutionary and p-adic length scale hierarchies but not the fundamental seats of consciousness. There would be hierarchy of conscious entities and we would be only one level in it. Even astrophysical objects would be also conscious entities and the hypothesis that Mother Gaia controls biosphere must be taken seriously.
For a summary of earlier postings see Latest progress in TGD.