^{4}projections intersect. Summation of effects means at classical level summation of forces caused by them due to the fact that particles have topological sum contacts to both space-time sheets. The notion of hologram relies crucially on the superposition of fields and this this forces to reformulate the notion of hologram in TGD framework.

In TGD inspired theory of consciousness the idea about living system as a conscious hologram is central. It is of course far from clear what this notion means. Since the notions of interference and superposition of fields are crucial for the description of the ordinary hologram, the proposed general description for the TGD counterpart for the superposition of fields is a natural starting point for the more precise formulation of the notion of conscious hologram. In the following only the notion of conscious hologram is discussed. Also the formulation of the notion of ordinary hologram in TGD framework is an interesting challenge.

- Consider ordinary hologram first. Reference wave and reflected wave interfere and produce an interference pattern to which the substrate of the hologram reacts so that its absorption coefficient is affected. When the substrate is illuminated with the conjugate of the reference wave, the original reflected wave is generated. The modification of the absorption coefficient is assumed to be proportional to the modulus squared fro the sum of the reflected and reference waves. This implies that the wave reflected from the hologram is in good approximation identical with the original reflected wave.
- Conscious hologram would be dynamical rather than static. It would be also quantal: the quantum transitions of particles in the fields defined by the hologram would be responsible for the realization of the interference pattern as a conscious experience. The previous considerations actually leave only this option since the interference of classical fields does not happen. Reference wave and reflected wave correspond now to any field configurations. The charged particles having wormhole contacts to the space-time sheets representing the field configurations experience the sum of the fields involved, and this induces quantum jumps between the quantum states associated with the situation in which only the reference wave is present.
This would induce a conscious experience representing an interference pattern. The reference wave can also correspond to a flux tube of magnetic body carrying a static magnetic field and defining cyclotron states as stationary state. External time dependent magnetic field can replace reflected wave and induces cyclotron transitions. Also radiation fields represented by MEs can represent the reference wave and reflected wave.

If there is need for the "reading" of the hologram it would correspond to the addition of a space-time sheet carrying fields which in good approximation have opposite sign and same magnitude as those in the sheet representing reference wave so that the effect on the charged particles reduces to that of the "reflected wave". This step might be un-necessary since already the formation of hologram would give rise to a conscious experience. The conscious holograms created when the hologram is created and when the conjugate of the reference wave is added give rise to two different conscious representations. This might have something to do with holistic and reductionistic views about the same situation.

- One can imagine several realizations for the conscious hologram. It seems that the realization at the macroscopic level is essentially four-dimensional. By quantum holography it would reduce at microscopic level to a hologram realized at the 3-D light-like surfaces defining the surfaces at which the signature of induce metric changes (generalized Feynman diagrams having also macroscopic size - anyons or space-like 3-surfaces at the ends of space-time sheets at the two light-like boundaries of CD. Strong form of holography implied by the strong form of general coordinate invariance requires that holograms correspond to collections of partonic 2-surfaces in given measurement resolution. This could be understood in the sense that the charged particles defining the substrate can be described mathematically in terms of the ends of the corresponding light-like 3-surfaces at the ends of CDs. The cyclotron transitions could be thought of as occurring for particles represent as partonic 2-surfaces topologically condensed at several space-time sheets.

One can imagine several applications in TGD inspired quantum biology.

- One can develop a model for how certain aspects of sensory experience could be understood in terms of interference patterns for signals sent from the biological body to the magnetic body. The information about the relative position of the magnetic body and biological body would be coded by the interference patterns giving rise to conscious sensory percepts. This information would represent geometric qualia giving information about distances and angles basically. There would be a magnetic flux tube representing the analog of the reference wave and magnetic flux tube carrying the analog of reflected wavel which could represent the effect of neural activity. When the signal changes with time, cyclotron transitions are induced and conscious percept is generated. In principle it there is no need not compensate for the reference wave although also this is possible.
- The natural first guess is that EEG rhythms (and those for its fractal generalization) represent reference waves and that the frequencies in question are either harmonics of cyclotron frequencies or linear combinations of these and Josephson frequency assignable to cell membrane (and possibly its harmonics). The modulation of membrane potential (membrane is regarded as a super-conductor) would induce modulations of Josephson frequency and if large enough would generate nerve pulses. These modulations would define the counterpart of the reflected wave. The flux tubes representing unperturbed magnetic field would represent reference waves.
- For instance, the motion of the biological body changes the signal at the space-time sheets carrying the signal and this generates cyclotron transitions giving rise to a conscious experience. Perhaps the sensation of having a body is based in this mechanism. The signals could emerge from directly from cells: it could be that this sensation corresponds to lower level selves rather than us. Second option is that nerve pulses to brain induce the signals sent to the our magnetic body.
- The motion of biological body relative to biological body generates virtual sensory experience which could be responsible for the illusions like train illusion and the unpleasant sensory experience about falling down from cliff by just imagining it. OBEs could be also due to the virtual sensory experiences of the magnetic body. One interesting illusion results when one swims long time in windy sea. When one returns to the shore one has rather long lasting experience of being in sea. Magnetic body gradually learns to compensate the motion of sea so that the perception of the wavy motion is reduced. At the shore this compensation mechanism however continues to work. This mechanism represents an example of adaptation and could be a very general mechanism. Since also magnetic body uses metabolic energy, this mechanism could have justification in terms of metabolic economy.
Also thinking as internal, silent speech might be assigned with magnetic body and would represent those aspects of the sensory experience of ordinary speech which involve the quantum jumps at magnetic body- the associated geometric qualia- but not the primary sensory percept. This speech would be internal speech since there would be no real sound signal or virtual sound signal from brain to cochlea.

- Conscious hologram would make possible to represent phase information. This information is especially important for hearing. The mere power spectrum is not enough since it is same for speech and its time reversal. Cochlea performs an analysis of sounds to frequencies. It it is not easy to imagine how this process could preserve the phase information associated with the Fourier components. It is believed that both right and left cochlea are needed to abstact the phase difference between the signals arriving to right and left ear allowing to deduce the direction of the source neural mechanisms for this has been proposed but these mechanism are not enough in case of speech. Could there exists a separate holistic representation in which sound wave as a whole generates a single signal interfering with the reference wave at the magnetic body and in this manner represents as a conscious experience the phase?
- Also the control and reference signals from the magnetic body to biological body could create time dependent interference patterns giving rise to neural response initiating motor actions and other responses. Basically the quantum interference should reduce the magnitude of membrane resting potentials so that nerve pulses would be generated and give rise to motor action. Similar mechanism would be at work at the level of sensory receptors - at least retina. The generation of nerve pulses would mean kind of emergency situation at the neuronal level. Frequency modulation of Josephson radiation would be the normal situation.

## 6 comments:

Matti,

And we note that non-parallel lines in four space may not necessarily intersect (Riemann) or that a line can intersect a point in 3 space yet from outside that space.

I have had the good fortune to finally understand the complex analysis and rough pictures of the functions. (I think this sort of thing should have been taught much sooner- would save a lot of effort)

Now does your many sheeted idea relate that closely to Riemann? His space of infinite perpendiculars and no parallels?

I find it odd, having dared to post when a lot of viewers lately are more from the physics only side of things something as subjective as our landscape of dreams and consciousness... Is it not strange we have reached a similar topic and conclusion to post at the same time?

The PeSla (man, the more I do and if I slow down a little the more I can do- I got a lot of rest this holiday, hope you did too.)

I read your pdf about Martin Grusenick interferometer...

I think a similar explanation can be seen in the following article:

http://www.orgonelab.org/EtherDrift/CahillDeWitte2006.pdf)

And this can be linked to the OPERA experiment that measured a speed for the Neutrinos that seems more fast than light speed:

www.atomlig.com.br/poli/WitteEffect-IG.pdf

Best Regards

Policarpo

Dear Pesla,

Many-sheeted space-time does not refer to many-sheetedness in the sense of Riemann. If you want something familiar it would be analogous with the stack of branes. A visual picture would be in terms 2-dimensional slightly curved pieces of plane in E^3with various sizes and with very small distance between them so that they touch here and there (wormhole contact is created).

Many-sheetedness analogous to Riemannian many-sheetedness is associated with hierarchy of Planck constants giving (effective) Planck constant as integer multiple of its standard value.

At the 3-D ends and light-like 3-surface at which the signature of thee induced metric changes imbedding the sheets coincide. A simple analog is the sheets of sqrt(z) at origin but time derivatives of imbedding space coordinates are different although canonical momentum densities are same for each sheet.

The sheets in the interior do not co-incide. The structure is analogous to an N-stack of 3-branes which co-incide at these two kinds of 3-surfaces. As matter fact, N is product of two integers.

An interesting question is whether this many-sheetedness serves as a topological correlate for something? Brane inspired considerations suggest emergent gauge symmetry: SU(N)xU(1) in AdS/CFT correspondence could generalize and I have developed a little argument how the symmetry generators of this gauge group could emerges as fermion-antifermion composites.

This gauge group would be effective gauge group describing finite measurement resolution as gauge invariance. This would conform with the general idea that TGD Universe is like Turing machine able to emulate all possible gauge groups by utilizing finite measurement resolution.

Dear Policarpo,

thank for a very interesting article. After the hasty first reading my reactions are as follows.

a) The Witte effect looks very interesting. What was observed was a phase drift between between two clusters of atomic clocks linked by a coaxial cable. If I understood correctly, the time used to communicate the value of time between the ends of cable varied with time suggesting time variation of light velocity with period of one sidereal day ("cosmic time" defined by distant stars)

c) I am not sure whether the explanation in terms of General Relativity alone is possible although one can imagine that the effects of gravitational fields on the clocks sum up and use this to estimate the effect. By choosing special coordinate one can then deduce effective value of c from the resulting metric. This calculation is however highly questionable in GRT framework since everything depends on coordinate system used. What one can say in GRT framework in general coordinate invariant manner is that in geometric optics approximation photons travel along light-like geodesics.

In TGD framework Witte effect would have same general explanation as super-luminal neutrino-velocity.

a) The essential element of sub-manifold geometry. The maximal signal velocity depends on the space-time surface/sheet and is usually below its maximal value corresponding to light-like geodesics of empty Minkowski space. The light-like geodesics of the space-time surface have time-like projection to M^4 in general. The light velocity defined in terms of time to travel from point A to B depends on space-time sheet and on pair of points with fixed M^4 distance at the space-time sheet. Therefore also Witte effect might be understood.

b) Witte effect would result since the gravitational fields associated with various space-time sheets representing Earth, solar system, galaxy etc... would effectively sum up. For two weeks ago I could not have answered what this summation of gravitational fields really means in TGD where the usual perturbative treatment fails. Now I can!;-). Thanks to the progress in the understanding gained through the comparison of Maxwellian and TGD based gauge field concept.

*The massive and charged test particles have topological sum contacts to various space-time sheets representing topologically quantized fields assignable to various objects as their field bodies. Test particle experiences sum of the gravitational forces in excellent approximation. Only the effects of various fields (gauge and gravitational fields) sum in TGD Universe not the fields themselves. This means enormous relief since the dynamics of Kaehler action is extremely non-linear and linear superposition for field patterns cannot be expected to be a good approximation: in any case it is extremely ugly theoretically. Something more elegant is needed.

I want to emphasize that this is a dramatic difference as compared to the usual classical field theory paradigm. Summations of only effects of fields cannot be however distinguished operationally from summation of fields since classically the value of field at given point is defined by detecting the force that it causes. One can verify only the superposition of the effects of the field, not of fields. At quantum level one speaks of quantum transitions instead of force but the same summations of effects applies by the linearity of quantum theory.

*The effective summation of gravitational fields would mean also the change of light velocity as determined from the time taken to travel from point A to B which now varies periodically (variation of phase shift).

Dear Policarpo,

Witte effect would not be the only one of this kind.

a) The distance to Moon has been found to apparently increase: the time for a laser signal to travel back and forth increases slowly. The interpretation would be following. This time is measured using "cosmic" time which means that the light velocity in cosmic scales is taken as unit in terms of which local velocities are expressed. The light velocity in cosmic scales however increases as the density of matter decreases and hence approaches gradually to that for empty space. Therefore the standard for the light velocity increases. The light velocity for solar space-time sheet stays constant but apparently decreases using the cosmic standard so that the Moon apparently recedes.

b) There is also an effect observed by Masreliez having similar explanation.

About Grusenick effect. The situation with Grusenick is not completely settled. I have a blog posting about the effect. Some commenter told in comment section or later posting about Grusenick effect that he had performed the same experiment and found that the effect observed by Grusenick was not real and due to the problems with the apparatus which was not completely rigid. I felt this argument rather convincing.

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