p-Adic particle massivation and entanglement: are all physical states massless?!

p-Adic particle massivation and entanglement: are all physical states massless?!

Unlike Higgs mechanism, p-adic thermodynamics provides a universal description of massivation involving no other assumptions about dynamics except super-conformal symmetry which guarantees by the existence of p-adic Boltzmann weights.

The number theoretic picture leads to a deeper understanding of a long standing objection against p-adic thermodynamics (see this) as a thermodynamics for the scaling generator L₀ of Super Virasoro algebra.

If one requires super-Virasoro symmetry and identifies mass squared with a scaling generator L₀, one can argue that only massless states are possible since L₀ must annihilate these states! All states of the theory would be massless, not only those of fundamental particles as in conformally invariant theories to which twistor approach applies! This looks extremely beautiful mathematically but seems to be in conflict with reality already at single particle level!

The resolution of the objection is that thermodynamics is indeed in question.

1. Thermodynamics replaces the state of entire system with the density matrix for the subsystem and describes approximately the interaction with the environment inducing the entanglement of the particle with it. To be precise, actually a "square root" of p-adic thermodynamics could be in question, with probabilities being replaced with their square roots having also phase factors. The excited states of the entire system indeed are massless (see this).
2. The entangling interaction gives rise to a superposition of products of single particle massive states with the states of environment and the entire mass squared would remain vanishing. The massless ground state configuration dominates and the probabilities of the thermal excitations are of order O(1/p) and extremely small. For instance, for the electron one has p= M₁₂₇=2¹²⁷-1≈ 10³⁸.
3. In the p-adic mass calculations (see this and this), the effective environment for quarks and leptons would in a good approximation consist of a wormhole contact (wormhole contacts for gauge bosons and Higgs and hadrons). The many-quark state many-quark state associated with the wormhole throat (single quark state for quarks and 3-quark-state for leptons (see this).
4. In M⁸ picture (see this and this) tachyonicity is unavoidable since the real part of the mass squared as a root of a polynomial P can be negative. Also tachyonic real but algebraic mass squared values are possible. At the H level, tachyonicity corresponds to the Euclidean signature of the induced metric for a wormhole contact.

   Tachyonicity is also necessary: otherwise one does not obtain massless states. The super-symplectic states of quarks would entangle with the tachyonic states of the wormhole contacts by Galois confinement.

5. The massless ground state for a particle corresponds to a state constructed from a massive single state of a single particle super-symplectic representation (CP₂ mass characterizes the mass scale) obtained by adding tachyons to guarantee masslessness. Galois confinement is satisfied. The tachyonic mass squared is assigned with wormhole contacts with the Euclidean signature of the induced metric, whose throats in turn carry the fermions so that the wormhole contact would form the nearby environment.

   The entangled state is in a good approximation a superposition of pairs of massive single-particle states with the wormhole contact(s). The lowest state remains massless and massive single particle states receive a compensating negative mass squared from the wormhole contact. Thermal mass squared corresponds to a single particle mass squared and does not take into account the contribution of wormhole contacts except for the ground state.

6. There is a further delicate number theoretic element involved (see this and this). The choice of M⁴⊂ M⁸ for the system is not unique. Since M⁴ momentum is an M⁴ projection of a massless M⁸ momentum, it is massless by a suitable choice of M⁴⊂ M⁸. This choice must be made for the environment so that both the state of the environment and the single particle ground state are massless. For the excited states, the choice of M⁴ must remain the same, which forces the massivation of the single particle excitations and p-adic massivation.

These arguments strongly suggest that pure states, in particular the state of the entire Universe, are massless. Mass would reflect the statistical description of entanglement using density matrix. The proportionality between p-adic thermal mass squared (mappable to real mass squared by canonical identification) and the entropy for the entanglement of the subsystem-environment pair is therefore natural. This proportionality conforms with the formula for the blackhole entropy, which states that the blackhole entropy is proportional to mass squared. Also p-adic mass calculations inspired the notion of blackhole-elementary particle analogy (see this) but without a deeper understanding of its origin.

See the article Two objections against p-adic thermodynamics and their resolution or the chapter TGD as it is towards the end of 2021.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

Dark meiosis and the mystery of why different cells express the chromosomes of father and mother in different manner

Condensed matter physicists are discovering that the world of electrons at atomic level is govering by knotting and linking (this). This picture is just what TGD predicts but applies to all systems, not only electrons, and in all scales from hadron physics to cosmology. Besides particles there are magnetic flux tubes connecting them to a network. This is completely new from the perspective of quantum field theory based description.

Since 3-space is a surface in M⁴×CP₂ is 3-D, flux tubes and string world sheets accompanying them are necessarily linked and knotted: this distinguishes TGD from string models. This implies braiding and makes possible topological quantum computation (TQC) like activities at fundamental level, in particular in living matter and especially at the DNA level.

Since spacetime is 4-D, string world sheets and flux tubes can reconnect. This is a new element to TQC like activity. Reconnection is a fundamental aspect of the TGD inspired quantum biology.

Meiosis serves as a good example demonstrating how powerful predictions this vision leads to. Meiosis as a recombination of DNAs would be induced by a reconnection of the magnetic flux tubes. The reconnecting flux tubes, which accompany mother' and father's chromosomes, which control the ordinary DNA strands, carry "dark" genes with codons realized as dark proton triplets. Darkness means large effective Planck constant h_eff and high "IQ" therefore ability to control ordinary biomatter.

This leads to a solution of the mystery of why the gene expression, which selects either the allele for mother and father, does this differently in different cells (see this). The explanation is that dark meiosis, which yields a pair of different dark gametes for dark DNA, occurs already in cell replication for daughter cells and differently in each cell replication. Ordinary meiosis occurs only later and dark gamete serves as a controller and template for it. Since the dark gametes select whether the allele of mother or father is selected by resonance mechanism, dark meiosis effectively creates new descendants at cell level as far as transcription and replication are considered. 50 replications would mean 2⁵⁰ ≈ 10¹⁵ descendants living in the same body and expressing themselves genetically!

Natural selection would therefore occur already at the cell level and only those dark gametes, for which the cells controlled by them survive and have produced ordinary gametes as their images, have a change to participate in sexual production, which is like the finals in Olympics.

Second implication is that the two gametes produced in dark meiosis in cell replication and going to different cells are related by father ↔ mother symmetry and since XX chromosome pair characterizes female and XY chromosome pair male, sister and brother which are mirror images of each other emerge. Therefore cells have a well-defined sex!

This raises questions. Could same cellular sex dominate in organelles and even organs so that also these could be said to have a well-defined sex? Could the battle between sexes start already at the cell level and possibly lead to extinction of the other sex? Do cells have sexual relationships like us and tend to pair? Could possible multi-cellular structures with a well-defined sex have this kind of relationships? What comes into mind are epithelial layers consisting of two cell layers and various binary structures in the body and brain.

See the article Mysteries related to gene expression and meiosis or the chapter ZEO, adelic physics, and genes.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

About the number theoretic aspects of zero energy ontology

The interaction between number theoretic vision, ZEO, and the TGD view DNA enriches all of them. In this article the recent view about quantum measurements is discussed in light of the recent progress in the understanding of the number theoretic aspects of TGD.

By M⁸-H duality space-time regions would be determined by polynomials whose roots define in M^>4⊂ M⁸ 3-D mass shells providing the data for holography fixing the space-time surfaces. Whether product polynomials besides irreducible polynomials should be allowed has been an open question. The product polynomials could naturally correspond to free states unable to entangle. The functional composition was earlier interpreted as formation of many-particle states but perhaps a more natural interpretation is as a generation of sheets of the many-sheeted space-time with interactions having wormhole contacts as geometric correlates.

This modified picture leads to a re-analysis of state function reduction (SFR), in particular the notions of "big" SFR and "small" SFR from a number theoretic perspective. This leads to a more precise view about the notion of time and time evolution. The emerging picture can be applied to TGD inspired theory of consciousness, in particular various aspects related to the notion of time and memory.

See the article About the number theoretic aspects of ZEO or the chapter with the same title.

Mysteries associated with lightnings, ball lightnings and the electrosphere of Earth

Lightning and ball lightning are electrospheric phenomena involving several poorly understood aspects. Also the origin of the electrosphere of Earth is still a mystery. In the TGD framework it is possible to deduce information about magnetic and electric bodies of Earth (briefly MB and EB) by using empirical inputs and these phenomena.

1. Ball lightings are known to be real are not understood. Ball lightning-like phenomena can be created also artificially in microwave ovens using match. Matches contain organic material and this serves as a good hint.
2. There is a New Scientist article, which gives a popular representation of ball lightings (see this). The theory of Cameron (see this) is mentioned in the article. The theory assumes that lightnings are essentially phenomena associated with the electromagnetic radiation field alone and neglects the fact that plasma is very probably involved. The theory relies on exact solutions of Maxwell's equations and proposes that ball lightnings involve monochromatic electromagnetic fields which are knotted and linked making the field configurations topologically nontrivial. Both magnetic and electric field lines can be knotted. This does not however imply topological stability since the linearity of Maxwell's equations implies that these field configurations are unstable. The finding that lifetime is long enough for microwave lengths does not conform with the fact that visible light is involved. Another theory mentioned in the article is by Boerner and proposes that lightning comes from another dimension. What this could actually mean, is of course a highly non-trivial question.
3. The basic mystery is how ball lightning can survive for so long a time. An ordinary plasma ball is not expected to do so. This suggests that ball lightning obeys non-linear dynamics and is some kind of topological entity robust by their topological non-triviality.
4. A very natural expectation is that ball lightning is a self-organizing system consisting of plasma which radiates. Self-organization requires energy feed. It could come as a Coulombic energy from the electric field of Earth through which part of the plasma of ball lightning has arrived. Here one encounters a problem. The electric resistance of the atmosphere causes a dissipation of the energy so that the charged particles cannot accelerate to high energies. How could lightning avoid this?
5. Two problems are always better than one. The second puzzle is that ordinary lightnings involve relativistic electrons and gamma rays. This is impossible in standard physics due to the already mentioned electric resistance of the atmosphere. Could ball lightning involve a new phase of matter, for which the dissipation is very small. Perhaps because it interacts very weakly with the ordinary matter of the atmosphere?
6. The third mystery is that the surface of Earth carries a negative charge, which creates an electric field. This field is essential for the generation of lightning. The origin of this field is however not understood.
7. There is also a fourth problem. Dark matter exists but there is no generally accepted theory of dark matter. All experiments trying to detect proposed candidates for dark matter particles (the particle physicist's way to solve a problem is to propose a new particle) have failed. There is of course also the mystery of life but it is better to stop here.

In the sequel a TGD based model for electrosphere is deduced by using various empirical inputs and the TGD based view about dark matter and the model of quantum biology inspired by it. A model, which allows us to understand these phenomena in the TGD framework, is developed. The model relies on the TGD based model of dark matter residing at the flux tubes of the magnetic body. The gravitational magnetic bodies of both Earth and Sun are important.The notion of the electric body of Earth as an analog of the cell membrane acting as a generalized Josephson junction is developed. Lightning and ball lightning would be associated with the analog of action potential.

See the article Mysteries associated with lightnings, ball lightnings and the electrosphere of Earth or the chapter About Concrete Realization of Remote Metabolism.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

Quantum Gravitation and Topological Quantum Computation

The progress in the understanding of the role of quantum gravitation in quantum biology (see this), as it is understood in the TGD framework, leads to the questions about the role of quantum gravivation in topological quantum computation (TQC). I sketched the first TGD based vision about DNA as a TQCer for about 13 years ago. In particular, a model of the system consisting of DNA and nuclear/cell membrane system acting as a TQCer was discussed.

TGD has evolved a lot after this and there are several motivations for seeing what comes out from combining the recent view about quantum TGD and TGD inspired quantum biology with this model.

1. There is a rather detailed view about the role of dark matter as phases of ordinary matter with the effective Planck constant h_eff=nh₀. Large values of h_eff allow to overcome the problems due to the loss of quantum coherence.

   This leads to the notion of the dark DNA (DDNA), whose codons are realized as dark proton triplets and proposed to accompany the ordinary DNA. Also dark photon triplets are predicted and one ends up to a model of communications and control based on dark cyclotron resonance in which codons serve as addresses and modulation of the signal frequency scale codes the signal to a sequence of pulses. Nerve pulses could be one application.

2. Quite recently, also the understanding of the possible role of quantum gravitation in biochemistry, metabolism, bio-catalysis, and in the function of DNA has considerably increased. The gravitational variants of hydrogen bonds and valence bonds between metal ions having very large value of h_eff= h_gr, where h_gr=GMm/v₀ is the gravitational Planck constant originally introduced by Nottale, are in a key role in the model and explain metabolic energy quantum as gravitational energy liberated when dark protons "drops" from a very long gravitational flux tube in the transition h_gr → h. Also electronic metabolic energy quantum is predicted and there is empirical support for this.
3. A further motivation comes from the number theoretic vision of quantum TGD. Galois groups as symmetry groups represent new physics and the natural questions are whether Galois groups could give rise to number theoretic variants of anyons and what could the TGD counterparts of the condensed matter (effective) Majorana electrons proposed by Kitaev as anyon like states?

   The answer is that quantum superpositions of symmetric hydrogen bonded structures of form X..H-H+X-H...X are excellent candidates for the seats of dark (h_eff>nh₀>h) bi-localized electrons defining TGD analogs of condensed matter Majorana electrons.

   The Galois groups permute the roots of a polynomial, which determines a space-time region by M⁸-H duality. The roots correspond to mass squared values, in general algebraic numbers, and thus to mass hyperboloids in M⁴_c⊂ M⁸_c. The H images correspond to 3-hyperboloids with a constant value a=a_n of light-cone proper time. Therefore the Galois group can permute points with time-like separation. Note however that the real or rational parts of two values of a can be same.

   This looks very strange at first but actually confirms with the fact that time-like braidings defining TQC correspond in TGD time-like braidings (involving also reconnections) of string like objects defining string world sheets, which are not now time evolutions of space-like entities as physical state but correspond to time-like entities defining boundary data necessary for fixing holography completely. Their presence is forced by the small failure of the determinism of the action principle involved and is completely analogous to the non-determinism for soap films with frames serving as seats for the failure of determinism.

4. Braidings appear therefore at the level of fundamental TGD and correspond to string world sheets. They are possible only in 4-D space-time but not in string models.

   Also TQC-like processes appear automatically at the level of fundamental physics. In particular, the number theoretical state function reduction cascade for the Galois group following the time evolution induced by braiding can be regarded as a generalization of a decomposition of integers to primes: now primes are replaced by simple groups defining primes for finite groups. Nature is doing number theory!

5. Also zero energy ontology (ZEO) brings in new elements. The change of the arrow of time in "big" state function reductions (BSFRs) implies that dissipation with a reversed arrow of time provides an automatic error correction procedure. Also TQC in which the arrow of time varies for sub-modules, can be considered.

See the article Quantum Gravitation and Topological Quantum Computation or the chapter with the same title.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD. 


The newest anomaly of the cold dark matter scenario supports the TGD view of galactic dark matter

The newest anomaly of the cold dark matter model (ΛCDM) is discusses in the popular article "Space Has Invisible Walls Created by Mysterious 'Symmetrons,' Scientists Propose". It has been found that satellites galaxies of larger galaxies tend to move in planes whereas the ΛCDM predicts that the orbits are more or less random. Quite generally, ΛCDM fails in short scales. The proposed model is involves traditional kind of new physics: a new exotic particle and symmetry breaking producing galactic plane domain walls.

TGD predicts (see this , this , and this) a fractal network of very massive long cosmic strings which can locally thicken to flux tubes: this thickening involves transformation of dark energy and possible dark matter of cosmic string to ordinary matter giving rise to galaxies and other structures. Also stars would have thickened flux tube tangles insidde themselves. The model finds supports from the observation that galaxies form long strings as found decades ago (Zeldowich was one of the discoverers).

The TGD based model predicts the formation of planes in which objects in various scales move. The prediction is fractal: this applies to planets around stars, stars around galaxies, satellite galaxies arond larger galaxies,....

This model explains the newest anomaly and also the earlier anomalies if the galaxies are associated with the long "cosmic strings" predicted by TGD. They create a strong gravitational potential giving rise to a radial force in the plane orthogonal to the cosmic string. The motion along the string is free whereas the planar motion is rotation. The velocity spectrum is flat as required by the flatness of the galactic velocity spectrum. In the simplest model cosmic string is the carrier of galactic dark matter and dark energy. No dark matter halo and no exotic dark matter particles are needed.

Helical orbits are the most general orbits. If a concentration of matter occurs to a plane, it tends to catch objects moving freely in the direction of string to its vertical gravitational field and planar sheets such planetary systems, spiral galaxies, and the planar systems formed by satellite galaxies can form.

One can of course wonder whether there is something which serves as a seed for the concentration around particular plane. In TGD, space-time is a 4-surface in H=M⁴×CP₂ and also membrane like entities are predicted as 4-D minimal surfaces in H. For instance, objects M¹×X²×S¹ are predicted, where M¹ is time axis, X² is a piece of plane of E², and S¹ is a geodesic sphere of CP₂. Universe would be populated by these membrane-like objects. Cell membrane is one important example. These approximately planar objects orthogonal to the cosmic string could tend to gather the matter flowing along helical orbits along the cosmic string. These planes would accompany planetary, galactic, etc... planes.

Warped planes represent slightly more complex solutions (a thin metal foil or sheet of paper gets warped) for which the plane is deformed but still flat minimal surface. I am not sure whether the "warping" of the outer regions of galactic planes, which has received attention recently (see this and this) but has been detected already 1956, is really really warping that is vertical deformation, which depends only single coordinate varying along a straight line (2-D plane wave of membrane).

See the article Cosmic string model for the formation of galaxies and stars or the chapter with the same title.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

10 times too high amount of He-4 in atmosphere as evidence for cold fusion

I learned an interesting piece of fact related to nuclear physics anomalies. It has been found that the amount of ³He in the Earths' atmosphere is ten times higher than expected.

The result is not deduced by measuring the amount ³He but that of ⁴He. The amount of the latter is too high and since ⁴He produces ³He, the amount of ³He must be higher than normal if we believe in standard nuclear physics.

The first report by Fleischmann and Pons about "cold fusion" was the claim that ⁴He is produced by fusion of two deuterium nuclei. "Cold fusion" was labelled as pseudoscience first but now it has been accepted as a real science and cold fusion researchers are not regarded as science criminals anymore.

Could this extra ⁴He be produced by "cold fusion"? No extra ³He, not produced in "cold fusion", would be needed.

The TGD based model for cold fusion (see this, this, and this) relies on the notion of dark nuclei and one of the basic predictions is that heavier nuclei can be produced outside stellar cores at much lower temperatures than in the Sun. In the TGD framework, prestellar evolution would start by "cold fusion" and would lead eventually to such a high temperature that ordinary fusion would start.

"Cold fusion" solves many problems of the standard nuclear physics based view. For instance, the production of nuclei heavier and iron is poorly understood: the hypothesis that Supernovae might have produced them remains unproven. Also the abundances of many light nuclei, such as Lithium, are poorly understood. Also the model for solar fusion has an anomaly discovered a few years ago. There is also evidence that living matter produces nuclei such as Calcium by some unknown mechanism.

See the article Cold fusion again or the chapter with the same title.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

DMT experiences and hyperbolic geometry

I received a link to a highly inspiring talk about a modelling of DMT induced experiences in terms of 2-D and more generally 3-D hyperbolic geometry. The title of the talk was "DMT and Hyperbolic Geometry". The talk was by a person using the name "Algekalipso" and I understand that the person in question is Andres Gomez Emilsson. The organization in question is a non-profit organization known as Qualia Research Institute. There is also article with essentially the same content.

1. Can one characterize DMT experiences by using temperature like parameters?

The question posed in the beginning of the talk was whether there could exist parameters analogous to temperature allowing a general qualitative understanding of the nature of the DMT and more general psychedelic experiences. The proposal was that the DMT experience could be characterized by two parameters.

1. The first parameter characterizes how "hyperbolic" the visual field is and is identifiable as the curvature of the hyperbolic space. The idea is that during a DMT trip the experienced 3-space is not Euclidean but hyperbolic. This kind of geometry has been proposed as an effective statistical geometry of the brain in which functionally similar neurons distant from each other are close to each other.

   In the TGD framework, this effective geometry could correspond to a real hyperbolic geometry of 3-D hyperbolic space playing a key role in TGD and assignable naturally to the magnetic body (MB) (see this). What would be experienced would be the projection of objects of H³ to the usual Euclidean space E³.

   In the TGD framework, space-times are minimal surfaces apart from singularities analogous to frames of soap films and their basic aspect is local saddle point property possessed also by hyperbolic spaces (see this). Maybe DMT experiences make it possible to visually perceive 3-surfaces as objects in H³. Also the usual vision also corresponds to hyperbolic vision but with a small value of the H³ curvature.

2. The second parameter would characterize the complexity of the experience and could in the TGD framework correspond to algebraic complexity associated with the extension of rationals assignable to a given space-time region (see this and this).

   The value h_eff=nh₀ of the effective Planck constant, which can be larger than h, would correspond to the dimension n of the extension of rationals and serve as a universal IQ. Dark matter would correspond to phases of ordinary matter with h_eff ≠ h.

   As the IQ increases, the experience transforms from simple to complex and eventually chaotic since the experiencer is not able to make sense of it. Under some assumptions this would relate to the formation of Julia set type fractals (see this).

2. About hyperbolic spaces

First some mathematical background.

1. Hyperbolic 3-space H³ is a generalization of 1-D hyperbola of 2-D space-time as a curve defined by condition t²-x²= a² but with its metric being induced from the 2-D Minkowski metric ds²= dt²-dx² . By performing all possible rotations of this 1-D hyperbola one obtains H³.
2. In particle physics H³ corresponds to mass shell E²-p²= m² and in cosmology to cosmic time identifiable as a²=t^r-r² in M⁴ ⊂ M⁴× CP₂. a defines Lorentz invariant cosmic time and is therefore analogous to absolute time invariant under Lorentz boosts which do not affect the tip of the light-cone. It is not invariant under translations however.

   In the TGD framework H³ has a central role and plays a key role also in the model of the brain involving the notion of magnetic body (MB). One could say that cognitive and sensory representations are realized at the intersection of MB with H³.

3. The value of cosmic time a characterizes the curvature of H³. The curvature is proportional to 1/a² and the smaller the value of a, the larger the curvature and "hyperbolicity". As a decreases, one approaches the analog of the Big Bang with infinite curvature. As a increases, one approaches flat E³ in an infinite future. Cosmic evolution proceeds from the Big Bang to the future whereas DMT trip would be a travel towards the moment of Big Bang. One can of course ask whether trips could also be in the opposite time direction.
4. The lecture (see also the written version) contains a nice description of hyperbolic geometry. In particular, the volume of a ball in H³ increases exponentially as a function of its radius and this means that H³ has a lot of volume. This might be very relevant for memory storage. This can be easily understood from the visualization in terms of real hyperboloid.
5. The counterpart of plane E² of E³ in H³ is 2-D hyperbolic space H² and Poincare sphere gives a good view about what the projections of the tesselations of H² look like when projected to E². The radial size for the basic unit of tessellations decreases with the distance from the origin whereas the region around the origin looks like E².
6. The hyperbolic geometry H² embedded locally in E³ has the saddle property meaning that in one direction the observer is at the bottom of the valley and in another direction at the top of the hill. This property has analog also at the level of abstract geometry: geodesic lines diverge very rapidly since the curvature scalar is negative: for spheres they converge.
7. By their negative curvature, H³ and H² allow tessellations (analogs of lattices in E³ and E²) which are not possible in E³. For instance. 7-polygons are possible. The number of tessellations is infinite whereas in E² only 17 wall papers are possible.
8. Hyperbolic analogs of plants are mentioned as fractals.

3. A possible interpretation of DMT experiences

DMT experiences could reflect both the relationship between the geometries of hyperbolic 3-space and Euclidian 3-space represented as 3-surfaces of Minkowski space and the algebraic complexity assignable to the tesselations of H³.

3.1 DMT trip as travel backwards in cosmic time

It was already mentioned that the proper time parameter a and algebraic complexity characterized by extension of rationals could characterize DMT experience. The increased complexity in turn means approach to apparent chaos since it is not possible to comprehend too high complexity. The following description is what I understood from the representation of Emilsson. I have not personally made DMT trips except spontaneously decades ago. This experience was so impressive that I got a passion to understand conscious experience from a quantum physics point of view.

1. For small DMT does, the visual experiences correspond to patterns in plane E² ⊂ E³, which can be regarded as plane H²⊂ H³ for large value of a and thus small curvature.

   The 17 lattices of E², called wallpapers, serve as a background for the visual field. As if one would be perceiving two different worlds simultaneously. The lattices can be dynamical and pulsate. This kind of experience was part of the "Great Experience" decades ago.

2. As the DMT dose increases, the value of a decreases and one moves towards the Big Bang, so to say. In TGD and TGD inspired theory of consciousness, causal diamonds (CDs), identified as intersections of future and past directed light-cones, could be called correlates of perceptive fields. CD is analogous to a Big Bang followed by a Big crunch. The CDs form a fractal hierarchy.

   The visual field becomes more and more hyperbolic. What we would see is the projection of the patterns of H²_a⊂ H³_a⊂ M⁴₊ to E²_t⊂ E³_t⊂ M⁴₊, where a is cosmic time and t is the linear Minkowski time.

3. At the next step the 2-D patterns in H³ are replaced by patterns in H³ as hyperbolic analogous of curved surfaces in E³ and one can say that the dimension of the visual field becomes 3.
4. In TGD Universe space-time surfaces are minimal surfaces (see this) and analogous to 4-D soap films spanned by frames appearing as singularities where minimal surface property and also the determinism of field equations fail so that the frames are space-time correlates as seats of non-determinism. The saddle property of minimal surface could explain the appearance of the "hyperbolic plants" which Emilsson lists as part of DMT experience.

Do we really see a hyperbolic world or does the visual perception reflect only the statistical geometry of the brain? The TGD proposal is that these two views reflect real space-time surfaces. One can of course argue that since conscious experience itself is associated with quantum jumps in the TGD framework so that the experience is about becoming rather than about being in the physical sense.

3.2. Algebraic complexity of the experience as a second parameter

The second parameter discussed in the talk was meant to characterize what was called valence as a measure for the degree of "bliss" of the experience. TGD counterpart would be algebraic complexity associated with the extension of rationals defined by the polynomial defining the space-time region. The value of h_eff/h₀=n as dimension of extension would serve as the parameter . For large values of n the situation becomes too complex to comprehend or remember and the bliss is lost.

In the TGD framework more complex systems can be engineered as functional composites of polynomials and this leads to the increase of h_eff. One can interpret this also as a construction of many-particle states with each polynomial, which represents a particle-like entity (see this and this). When a fixed polynomial is iterated functionally, one obtains a fractal known as Julia set so that the connection with fractals is quite concrete (see this).

To sum up, the reports of Emilsson suggest a very concrete connection between DMT experience and TGD based views of space-time and number theoretical vision about quantum theory explaining dark matter as h_eff=nh₀ phases. DMT perception would be perceptions of both ordinary and dark matter simultaneously.

4. Possible implications for the interpretation of TGD

The proposed picture involving in an essential manner both H³ and E³ suggests some quite non-trivial implications concerning the physical interpretation of TGD.

4.1 H³ is ideal for information storage and holography

The hyperbolic radial distance r_H in H³ from origin is given by r_H= a arsinh(r_E/a) ≈ a log(r_E/a), where r_E is the Euclidean distance in E³. r_H depends logarithmically of r_E slowly. The area S=4π a²r² of the hyperbolic sphere of radius u projected to Euclidean sphere with r increases as function of u as S≈ 4π a²exp(2u/a). One can imbed a tree graph (say) m ranches in the node much more effectively than in the Euclidean case. One can think of the tree grapas a simple model for a neural network consisting of layers such that n:th layer has mⁿ nodes for

If a given node requires fixed area Δ S, the solid angle Δ Ω required by a node decreases as 1/r² whereas in E³ it remains constant, the number of these areas at sphere increases as S/Δ S= 4π exp(2u/a)/Δ S. In the Euclidean case it increases as S/ΔS= 4π r²/Δ S. This means that the geometric information storage capacity ofH³ is exponentially larger. Therefore the idea that the 3 surfaces associated with H³_a could serve as information storage is very attractive.

4.2 H³ and the origin of p-adic length scale hypothesis

p-Adic prime assignable to a region of the space-time surface is identified as the largests ramified prime associated with the polynomial defining the region of the space-time surface. p-Adic length scale hypothesis states that the physical preferred p-adic primes correspond to p-adic primes p≈ m^k, where m is a small integer: m=2 is the most important case.

I have proposed that there are two scales involved. The small p-adic length scale associated with m and the exponentially larger p-adic length scale proportional to p^1/2. The origin of these scales has remained a mystery.

Could the small scales correspond to the radial scales r_H and large scales to radial scales r_E?

1. H₃ allows tessellations playing a key role in TGD framework and the size scale of the cell of the tesselation defines a natural length scale unit Δ r_H= aX, which could define the small scale and scales would be expressible in terms of this unit.
2. In E³ the natural scale would correspond to Euclidean lattices with constant cell size Δ r_E. For r_H= Δ r_H, r_E = a sinh(r_H/a) ≈ aexp(r_H/a) would give r_E ≈ aexp(nX= a m^{Δ X/log(m)}.
3. r_E=L_p= p^1/2R would give p^1/2R = am^{Δ Xlog(a)/log(m)}. p-Adic length scale hypothesis p≈ m^k requires X= klog(m)/2log(a/R).

   Note that there would be a logarithmic dependence of the p-adic length scale on the a, which would have an interpretation as a renormalization of the p-adic length- and mass scales.

See the article DMT experience and hyperbolic geometry or the chapter Magnetic Sensory Canvas Hypothesis.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.