TGD inspired theory of conscious brain relies on assumption that the moments of consciousness correspond to quantum jumps realized as jumps between deterministic quantum HISTORIES. Free will and non-determinism are thus outside the realm of geometrical space-time and one avoids the wellknown difficulties resulting from the attempt to understand the non-determinism of quantum jump and the determinism of Schrodinger equation in standard conceptual framework of physical theories.
The hardware for conscious brain relies of various BE condensates made possible by the special structure of TGD space-time. Crucial role is played by the many-sheeted nature of TGD space-time. The following ideas represent TGD inspired theory of consciousness as it was for more than decade ago and some of them are therefore obsolete.
A. BE condensates of photons: quantum antenna hypothesis
One of the basic differences between induced gauge field concept and ordinary is that it is possible to get classical em and Z0 fields propagating with the velocity of light and with non-vanishing vacuum gauge current: these solutions are called 'massless extremals'. In Maxwell electrodynamics the solutions of free Maxwell equations have vanishing sources (currents).
The vacuum currents in turn serve as sources of BE condensates. To each Fourier mode there corresponds a coherent state of photons (eigenstate of photon annihilation operator). Mathematically situation is identical to that with harmonic oscillation in force F= A×x×cos(ωt) for each Fourier mode.
Quantum antenna hypothesis states that linear structures such as microtubules, DNA/etc. are associated with this kind of massless extremals creating BE condensates of photons when vacuum current is non-vanishing. Vacuum gauge current can be purely electromagnetic or Z0 type or combination of these two. Or all vacuum gauge currents vanish but there is electromagnetic wave propagating with velocity of light: in this case no BE condensate is created.
The massless extremal property is destroyed by the presence of charges creating Coulomb fields leading to Maxwell phase in which ordinary Maxwell equations are excellent approximate description of situation in sufficiently short length scales. Thus one should find a mechanism keeping the space-time sheet of massless extremal clean from charges.
The fact that microtubules and proteins are surrounded by ordered water suggests the mechanism. There are two space-time sheets essentially involved. 'Upper' (say) space-time sheet contains ordered water, which is identified as join along boundaries condensate of water molecules. The electric gauge flux flows totally at this sheet and enters to the 'lower' space-time sheet only at the boundaries of the upper space-time sheet through wormholes.
Fig. 23. Quantum antenna hypothesis
At the lower sheet massless extremals create BE condensate of photons. The frequencies are multiples of pi/L, where L is the length of the microtubule or any other linear structure. For microtubules the frequencies vary from IR to UV.
B. BE condensate of charged wormholes
The charged wormholes feeding the electromagnetic gauge flux from 'higher' to 'lower' space-time sheet behave as classical charges as far as classical em fields are considered and couple to photons extremely weakly. Their mass can be estimated from p-adic length scale hypothesis to be of order 1/Lp, where p is the p-adic prime associated with the 'lower' space-time sheet; mass is very small in biologically interesting length scales. For Lp about 10-8 meters the mass is about 102 eV: fraction 10-4 of electron mass.
Wormholes should behave like conduction electrons and thus concentrate on the boundaries of 3-surfaces. Charged wormholes are described by complex order parameter satisfying wave equation with very small mass. Thus one has energy gap: for a system with size L the energy of the first excited state is of order 1/L. Therefore BE condensation to ground state occurs.
One can obtain macroscopic BE condensates by glueing smaller 3-surfaces by join along boundaries bonds together. Good candidates are cells: now join along boundaries bonds are gap junctions.
Fig. 24. Gap junctions connect certain cells and can make them macroscopic quantum system.
Gap junction connecting two cells can be regarded as join along boundaries bond. Cells could be glial cells in brain, cells in skin, glands, gut, heart muscle fiber. For nerve cells gap junctions are rare. Nerve cells are connected with glial cells in Ranvier nodes.
The proteins connecting microtubules (MAPs) can also be regarded as gap junctions as well as proteins connecting different lipid layers of cell membrane.
Wormhole condensate behaves very much like super conductor. In particular Josephson junctions connecting two BE condensates are possible and Josephson current of wormholes flows between these condensates. The model of nerve pulse and EEG is based on assumption that the lipid layers of cell membrane are wormhole BE condensates and that Josephson current flows along proteins connecting the lipid layers. The situation is illustrated in the figure below.
Fig. 25. The lipid layers of cell membrane as wormholes 'superconductors' connected by 'Josephson junctions'. 2-dimensional visualization.
The model explains the difference between nerve cells and ordinary cells, explains nerve pulse as soliton and frequency coding, explains EEG and predicts new 'EG' type oscillation with frequency of order 1010 Hz possibly coordinating protein conformations as well as new ner pulse kind phenomenon with duration of order 10-10 seconds. The model is testable: for instance, the attribute exhibitory/ inhibitory should be associated with nerve pulse (solitonic/antisolitonic) rather with axon or synaptic connection.
C. Association sequences
In TGD inspired theory moments of consciousness correspond to quantum jumps. The contents of consciousness is determined somehow by the comparison of initial and final quantum histories. Essential point is that entire determistic quantum histories are involved and without further assumptions it seems that timelessness characterizes conscious experience. Thus the problem is how to understand the concept of subjective time and finite duration of subjective experience. Somehow the conscious experience is not localized to infinitely short time interval but has finite duration, multilocality in time.
Second problem is to understand cognitive aspects of conscious experience. Free will aspect is associated with any quantum jump, even that performed by electron whereas cognitive aspects and thinking probably only to very specialized quantum jumps. The concept of association sequence might provide a solution of these problems.
The idea of association sequence is simply the following. In TGD there is no reason to exclude 3-surfaces consisting of several disjoint 3-surfaces with time like separations.
Fig. 26. 'Association sequence': a geometric model for thought as a sequence of 3-surfaces with timelike separations.
It is tempting to identify this kind of 3-surfaces, with each 3-surface belonging to an orbit of classical space-time surface, as a simulation of the classical history by snapshot pictures and thus as a geometric model for thought. In introduced the name association sequence for these objects for long time ago: my recent belief is that associations are more probably related to quantum entanglement rather than 'association sequences' so that the choice for name is not the best possible.
There is however a problem: General coordinate invariance implies that all 3-surfaces for which the absolute minimum space-time surface is same, are physically equivalent. In particular, association sequences in general are expected to be physically equivalent with single space-time surface in t= constant plane of M4+.
There is a manner to overcome this difficulty based on CLASSICAL NONDETERMINISM. There are good reasons to assume that Kähler action is not completely deterministic. This means that in certain situations the absolute minimum space-time surface X4(X3) associated with 3-surface X3 is not unique but there are several of them. In this case on can fix a given branch only by selecting finite number of 3-surfaces on the 'orbit' of X3 besides X3 itself. In order to get rid of nonuniqueness of absolute minimum one can generalize the concept of 3-surface by allowing association sequences! Thus thoughts emerge naturally if classical theory is non-deterministic!
D. Association sequences as binary sequences
One can describe the situation also in following manner. Consider non-determistic dynamical evolution (also the space-time surface can be regarded as dynamical evolution of 3-surface X3 and thus orbit in the space of 3-surfaces). Assume that bifurcations occur for time values t1,t2,...,tn , which means that at these time values the orbits branches to two alternative branches. There are 2n possible orbits and one can specify these orbits uniquely by selecting besides x(t), n points x(τ1), x(τ2),...x(τn). where τk is suitably chosen moment of time between two successive bifurcations.
Fig. 27. Association sequence as sequence of bifurcations in presence of classical non-determinism.
This set of points defines association sequence. There is extremely tight correlation between points x(τk) to the extend that the association sequence can be equivalently described by specifying x(t) and n binary digits telling which alternative is realized in each bifurcation. Thus association sequences can be regarded as BINARY SEQUENCES! Ideal representation if one has quantum computer type operations in mind!
E. Criticality of Kähler action and non-determinism
The vacuum degeneracy of Kähler action suggests strongly non-determinism. Consider a 'vacuum' 3-surface, which has vanishing induced Kähler field. There is infinite number of vacuum extremals 'going through' this 3-surface. It is plausible that the absolute minimum of Kähler action is obtained by slightly deforming some of these vacuum extremals. Suppose this is the case.
There is enormous number of candidates for vacuum extremals: even their topology can wildly vary. It can well happen for two 3-surfaces not differing too much, the vacuum extremals giving rise to absolute minimum have different topology or differ in some other qualitative aspect. Then there must exist some 3-surface between them for which the vacuum extremals with both these topologies give absolute minimum with same value of action. Classical space-time surface is not unique in this case.
There is nice analogy with thermodynamical free energy and phase transitions. Kähler action is just like free energy: space-time surface corresponds to its absolute minimum. In phase transition one has the situation described by cusp catastrophe: see the figure below.
Fig. 28. Cusp catastrophe
At Maxwell line, where the phase transition occurs, both upper and lower sheet give same value of free energy and state is mixture of two phases. Elsewhere the phase is unique.
Biosystems, or systems with cognitive abilities would be thus critical systems, for which absolute minimum of effective actions (whose bosonic part is just Kähler action) have degenerate absolute minima.
F. Thoughts and vacuum extremals
Here is a receipe for constructing geometric model for thought. Take vacuum extremal with a definite duration of time: vacuum space-time surface begins at t1 and ends at t2. This surface behaves completely non-deterministically apart from the restriction coming from vacuum property. Thus it can be regarded as a model for completely free imagination. It need not be an absolute minimum of effective action.
Fig. 29. Non-determistic vacuum extremals as model for free imagination
To construct a model of thought, let this kind of vacuum space-time surface interact with matter. That is, join this surface to space-time surface containing matter with # throats (wormholes). Some energy flows to vacuum surface and deforms it: it ceases to be vacuum. For certain deformation(s) absolute minimum of Kähler action is achieved: typically Kähler electric fields are generated to minimize Kähler action.
What is essential that INTERACTION WITH EXTERNAL WORLD CODES SOME PROPERTIES OF THE EXTERNAL WORLD TO THE PROPERTIES OF THE DEFORMED VACUUM: some features of the external world is represented as properties of deformed vacuum. This is what cognitive systems do all the time: they construct representations.
Fig. 30. Interaction with matter forms a representation of external world in the properties of vacuum extremal. There are several deformed vacuum extremals with same absolute minimum of effective action.
This procedure can be repeated for any vacuum surface. It can however happen that absolute minimum value of effective action is same for several choices of vacuum extremal. Thus effective space-time surface is not unique but degenerate and one has classical non-determinism. This in turn implies that one must form quantum superpositions of effective space-times and quantum jump selecting one space-time from this superposition generates conscious thought. By putting vacuum extremal of finite duration above space-time sheet containing matter one obtains a representation for a small sample of time development as conscious experience.
More concretely. Put vacuum extremal of finite duration 'above' a group of neurons. The synchronous periodic firing of nerve pulses for this group of neurons could form a representation of sensory data in the properties of vacuum extremal. There is indeed some evidence that this kind of mechanism is at work: both the spatial configuration of nerve pulses and the organization of pulse sequences in time direction seem to be code sensory experience. Roughly: space-time is divided into 4-volumes: each 4-volume contains nerve cell and has nerve pulse duration. To each small volume one associates binary digit according to whether the neuron fired or not. Each nerve pulse could cause bifurcation and the time distance between surfaces of association sequence would correspond to the period between nerve pulses. EEG oscillations of glial neurons forming macroscopic quantum system would in turn coordinate the firing of neurons to occur synchronously.
A second argument for the degeneracy of absolute minimum. Suppose an absolute minimum of effective action has been found. Call it X4. Replace this surface with a new surface, which is disjoint union of X4 and of some vacuum space-time surface having vanishing Kähler action. Also this surface is absolute minimum! Does this mean that the each minimum of the effective action is infinitely degenerate? Is it possible to pose some conditions on the physical state eliminating this kind of degeneracy? Or should one just accept this degeneracy as a prediction of TGD. Is this free imagination aspect always present in quantum state?
Note: the vacuum surfaces are very much like vacuum bubbles of quantum field theory appearing in any Feynman diagrams and not actually contributing to scattering amplitude.