Monday, June 01, 2020

New resuls on M8-H duality

M8-H duality (H=M4× CP2) has taken a central role in TGD framework. M8-H duality allows to identify space-time regions as "roots" of octonionic polynomials P in complexified M8 - M8c - or as minimal surfaces in H=M4× CP2 having 2-D singularities.

Remark:Oc,Hc,Cc,Rc will be used in the sequel for complexifications of octonions, quaternions, etc.. number fields using commuting imaginary unit i appearing naturally via the roots of real polynomials.

Space-time as algebraic surface in M8c regarded complexified octonions

The octonionic polynomial giving rise to space-time surface as its "root" is obtained from ordinary real polynomial P with rational coefficients by algebraic continuation. The conjecture is that the identification in terms of roots of polynomials of even real analytic functions guarantees associativity and one can formulate this as rather convincing argument. Space-time surface X4c is identified as a 4-D root for a Hc-valued "imaginary" or "real" part of Oc valued polynomial obtained as an Oc continuation of a real polynomial P with rational coefficients, which can be chosen to be integers. These options correspond to complexified-quaternionic tangent- or normal spaces. For P(x)= xn+.. ordinary roots are algebraic integers. The real 4-D space-time surface is projection of this surface from M8c to M8. One could drop the subscripts "c" but in the sequel they will be kept.

M4c appears as a special solution for any polynomial P. M4c seems to be like a universal reference solution with which to compare other solutions.

One obtains also brane-like 6-surfaces as 6-spheres as universal solutions. They have M4 projection, which is a piece of hyper-surface for which Minkowski time as time coordinate of CD corresponds to a root t=rn of P. For monic polynomials these time values are algebraic integers and Galois group permutes them.

One cannot exclude rational functions or even real analytic functions in the sense that Taylor coefficients are octonionically real (proportional to octonionic real unit). Number theoretical vision - adelic physics suggests that polynomial coefficients are rational or perhaps in extensions of rationals. The real coefficients could in principle be replaced with complex numbers a+ib, where i commutes with the octonionic units and defines complexifiation of octonions. i appears also in the roots defining complex extensions of rationals.

Brane-like solutions

One obtains also 6-D brane-like solutions to the equations.

  1. In general the zero loci for imaginary or real part are 4-D but the 7-D light-cone δ M8+ of M8 with tip at the origin of coordinates is an exception. At δ M8+ the octonionic coordinate o is light-like and one can write o= re, where 8-D time coordinate and radial coordinate are related by t=r and one has e=(1+er)/\sqrt2 such that one as e2=e.

    Polynomial P(o) can be written at δ M8+ as P(o)=P(r)e and its roots correspond to 6-spheres S6 represented as surfaces tM=t= rN, rM= \sqrtrN2-rE2≤ rN, rE≤ rN, where the value of Minkowski time t=r=rN is a root of P(r) and rM denotes radial Minkowski coordinate. The points with distance rM from origin of t=rN ball of M4 has as fiber 3-sphere with radius r =\sqrtrN2-rE2. At the boundary of S3 contracts to a point.

  2. These 6-spheres are analogous to 6-D branes in that the 4-D solutions would intersect them in the generic case along 2-D surfaces X2. The boundaries rM=rN of balls belong to the boundary of M4 light-cone. In this case the intersection would be that of 4-D and 3-D surface, and empty in the generic case (it is however quite not clear whether topological notion of "genericity" applies to octonionic polynomials with very special symmetry properties).
  3. The 6-spheres tM=rN would be very special. At these 6-spheres the 4-D space-time surfaces X4 as usual roots of P(o) could meet. Brane picture suggests that the 4-D solutions connect the 6-D branes with different values of rn.

    The basic assumption has been that particle vertices are 2-D partonic 2-surfaces and light-like 3-D surfaces - partonic orbits identified as boundaries between Minkowskian and Euclidian regions of space-time surface in the induced metric (at least at H level) - meet along their 2-D ends X2 at these partonic 2-surfaces. This would generalize the vertices of ordinary Feynman diagrams. Obviously this would make the definition of the generalized vertices mathematically elegant and simple.

    Note that this does not require that space-time surfaces X4 meet along 3-D surfaces at S6. The interpretation of the times tn as moments of phase transition like phenomena is suggestive. ZEO based theory of consciousness suggests interpretation as moments for state function reductions analogous to weak measurements ad giving rise to the flow of experienced time.

  4. One could perhaps interpret the free selection of 2-D partonic surfaces at the 6-D roots as initial data fixing the 4-D roots of polynomials. This would give precise content to strong form of holography (SH), which is one of the central ideas of TGD and strengthens the 3-D holography coded by ZEO alone in the sense that pairs of 3-surfaces at boundaries of CD define unique preferred extremals. The reduction to 2-D holography would be due to preferred extremal property realizing the huge symplectic symmetries and making M8-H duality possible as also classical twistor lift.

    I have also considered the possibility that 2-D string world sheets in M8 could correspond to intersections X4∩ S6? This is not possible since time coordinate tM constant at the roots and varies at string world sheets.

    Note that the compexification of M8 (or equivalently octonionic E8) allows to consider also different variants for the signature of the 6-D roots and hyperbolic spaces would appear for (ε1, εi,..,ε8), epsiloni=+/- 1 signatures. Their physical interpretation - if any - remains open at this moment.

  5. The universal 6-D brane-like solutions S6c have also lower-D counterparts. The condition determining X2 states that the Cc-valued "real" or "imaginary" for the non-vanishing Qc-valued "real" or "imaginary" for P vanishes. This condition allows universal brane-like solution as a restriction of Oc to M4c (that is CDc) and corresponds to the complexified time=constant hyperplanes defined by the roots t=rn of P defining "special moments in the life of self" assignable to CD. The condition for reality in Rc sense in turn gives roots of t=rn a hyper-surfaces in M2c.
Explicit realization of M8-H duality

M8-H duality allows to map space-time surfaces in M8 to H so that one has two equivalent descriptions for the space-time surfaces as algebraic surfaces in M8 and as minimal surfaces with 2-D singularities in H satisfying an infinite number of additional conditions stating vanishing of Noether charges for super-symplectic algebra actings as isometries for the "world of classical worlds" (WCW). Twistor lift allows variants of this duality. M8H duality predicts that space-time surfaces form a hierarchy induced by the hierarchy of extensions of rationals defining an evolutionary hierarchy. This forms the basis for the number theoretical vision about TGD.

M8-H duality makes sense under 2 additional assumptions to be considered in the following more explicitly than in earlier discussions.

  1. Associativity condition for tangent-/normal space is the first essential condition for the existence of M8-H duality and means that tangent - or normal space is quaternionic.
  2. Also second condition must be satisfied. The tangent space of space-time surface and thus space-time surface itself must contain a preferred M2c⊂ M4c or more generally, an integrable distribution of tangent spaces M2c(x) and similar distribution of their complements E2c(x). The string world sheet like entity defined by this distribution is 2-D surface X2c⊂ X4c in Rc sense. E2c(x) would correspond to partonic 2-surface.

    One can imagine two realizations for this condition.

    Option I: Global option states that the distributions M2c(x) and E2c(x) define slicing of X4c.

    Option II: Only discrete set of 2-surfaces satisfying the conditions exist, they are mapped to H, and strong form of holography (SH) applied in H allows to deduce space-time surfaces in H. This would be the minimal option.

    How these conditions would be realized?

    1. The basic observation is that X2c can be fixed by posing to the non-vanishing Hc-valued part of octonionic polynomial P condition that the Cc valued "real" or "imaginary" part in Cc sense for P vanishes. M2c would be the simplest solution but also more general complex sub-manifolds X2c⊂ M4c are possible. This condition allows only a discrete set of 2-surfaces as its solutions so that it works only for Option II.

      These surfaces would be like the families of curves in complex plane defined by u=0 an v= 0 curves of analytic function f(z)= u+iv. One should have family of polynomials differing by a constant term, which should be real so that v=0 surfaces would form a discrete set.

    2. One can generalize this condition so that it selects 1-D surface in X2c. By assuming that Rc-valued "real" or "imaginary" part of quaternionic part of P at this 2-surface vanishes. one obtains preferred M1c or E1c containing octonionic real and preferred imaginary unit or distribution of the imaginary unit having interpretation as complexified string. Together these kind 1-D surfaces in Rc sense would define local quantization axis of energy and spin. The outcome would be a realization of the hierarchy Rc→ Cc→ Hc→ Oc realized as surfaces.

      This option could be made possible by SH. SH states that preferred extremals are determined by data at 2-D surfaces of X4. Even if the conditions defining X2c have only a discrete set of solutions, SH at the level of H could allow to deduce the preferred extremals from the data provided by the images of these 2-surfaces under M8-H duality. Associativity and existence of M2(x) would be required only at the 2-D surfaces.

    3. I have proposed that physical string world sheets and partonic 2-surfaces appear as singularities and correspond to 2-D folds of space-time surfaces at which the dimension of the quaternionic tangent space degenerates from 4 to 2. This interpretation is consistent with a book like structure with 2-pages. Also 1-D real and imaginary manifolds could be interpreted as folds or equivalently books with 2 pages.

      For the singular surfaces the dimension quaternionic tangent or normal space would reduce from 4 to 2 and it is not possible to assign CP2 point to the tangent space. This does not of course preclude the singular surfaces and they could be analogous to poles of analytic function. Light-like orbits of partonic 2-surfaces would in turn correspond to cuts.

    Does M8-H duality relate hadron physics at high and low energies?

    During the writing of this article I realized that M8-H duality has very nice interpretation in terms of symmetries. For H=M4× CP2 the isometries correspond to Poincare symmetries and color SU(3) plus electroweak symmetries as holonomies of CP2. For octonionic M8 the subgroup SU(3) ⊂ G2 is the sub-group of octonionic automorphisms leaving fixed octonionic imaginary unit invariant - this is essential for M8-H duality. SU(3) is also subgroup of SO(6)== SU(4) acting as rotation on M8= M2× E6. The subgroup of the holonomy group of SO(4) for E4 factor of M8= M4× E4 is SU(2)× U(1) and corresponds to electroweak symmetries. One can say that at the level of M8 one has symmetry breaking from SO(6) to SU(3) and from SO(4)= SU(2)× SO(3) to U(2).

    This interpretation gives a justification for the earlier proposal that the descriptions provided by the old-fashioned low energy hadron physics assuming SU(2)L× SU(2)R and acting acting as covering group for isometries SO(4) of E4 and by high energy hadron physics relying on color group SU(3) are dual to each other.

    See the article About p-adic length scale hypothesis and dark matter hierarchy or the chapter TGD view about McKay Correspondence, ADE Hierarchy, Inclusions of Hyperfinite Factors, M8-H Duality, SUSY, and Twistors.

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

    Articles and other material related to TGD.

Thursday, May 28, 2020

About p-adic length scale hypothesis and dark matter hierarchy

The following represents an introduction to an article summarizing my recent understanding of p-adic length scale hypothesis and dark matter hierarchy. These considerations lead to more detailed proposals. In particular, a proposal for explicit form of dark scale is made.

p-Adic length scale hypothesis

In p-adic mass calculations real mass squared is obtained by so called canonical identification from p-adic valued mass squared identified as analog of thermodynamical mass squared using p-adic generelization of thermodynamics assuming super-conformal invariance and Kac-Moody algebras assignable to isometries ad holonomies of H=M4× CP2. This implies that the mass squared is essentially the expectation value of sum of scaling generators associated with various tensor factors of the representations for the direct sum of super-conformal algebras and if the number of factors is 5 one obtains rather predictive scenario since the p-adic temperature Tp must be inverse integer in order that the analogs of Boltzmann factors identified essentially as pL0/Tp.

The p-adic mass squared is of form Xp+O(p2) and mapped to X/p+ O(1/p2). For the p-adic primes assignable to elementary particles (M127=2127-1 for electron) the higher order corrections are in general extremely small unless the coefficient of second order contribution is larger integer of order p so that calculations are practically exact.

Elementary particles seem to correspond to p-adic primes near powers 2k. Corresponding p-adic length - and time scales would come as half-octaves of basic scale if all integers k are allowed. For odd values of k one would have octaves as analog for period doubling. In chaotic systems also the generalization of period doubling in which prime p=2 is replaced by some other small prime appear and there is indeed evidence for powers of p=3 (period tripling as approach to chaos). Many elementary particles and also hadron physics and electroweak physics seem to correspond to Mersenne primes and Gaussian Mersennes which are maximally near to powers of 2.

For given prime p also higher powers of p define p-adic length scales: for instance, for electron the secondary p-adic time scale is .1 seconds characterizing fundamental bio-rhythm. Quite generally, elementary particles would be accompanied by macroscopic length and time scales perhaps assignable to their magnetic bodies or causal diamonds (CDs) accompanying them.

This inspired p-adic length scale hypothesis stating the size scales of space-time surface correspond to primes near half-octaves of 2. The predictions of p-adic are exponentially sensitive to the value of k and their success gives strong support for p-adic length scale hypothesis. This hypothesis applied not only to elementary particle physics but also to biology and even astrophysics and cosmology. TGD Universe could be p-adic fractal.

Dark matter as phases of ordinary matter with heff=nh0

The identification of dark matter as phases of ordinary matter with effective Planck constant heff=nh0 is second key hypothesis of TGD. To be precise, these phases behave like dark matter and galactic dark matter could correspond to dark energy in TGD sense assignable to cosmic strings thickened to magnetic flux tubes.

There are good arguments in favor of the identification h=6h0. "Effective" means that the actual value of Planck constant is h0 but in many-sheeted space-time n counts the number of symmetry related space-time sheets defining space-time surface as a covering. Each sheet gives identical contribution to action and this implies that effective value of Planck constant is nh0.

M8-H duality

M8-H duality (H=M4× CP2) has taken a central role in TGD framework. M8-H duality allows to identify space-time regions as "roots" of octonionic polynomials in complexified M8. The polynomial is obtained from ordinary real polynomial P with rational coefficients by algebraic continuation. One obtains brane-like 6-surfaces as 6-spheres as universal solutions. They have M4 projection which is piece of hyper-surface for which Minkowski time as time coordinate of CD corresponds to a root t=rn of P. For monic polynomials these time values are algebraic integers and Galois group permutes them.

M8-H duality allows to map space-time surfaces in M8 to H so that one has two equivalent descriptions for the space-time surfaces as algebraic surfaces in M8 and as minimal surfaces with 2-D singularities in H satisfying an infinite number of additional conditions stating vanishing of Noether charges for super-symplectic algebra actings as isometries for the "world of classical worlds" (WCW). Twistor lift allows variants of this duality. M8H duality predicts that space-time surfaces form a hierarchy induced by the hierarchy of extensions of rationals defining an evolutionary hierarchy. This forms the basis for the number theoretical vision about TGD.

During the writing of this article I realized that M8-H duality has very nice interpretation in terms of symmetries. For H=M4× CP2 the isometries correspond to Poincare symmetries and color SU(3) plus electroweak symmetries as holonomies of CP2. For octonionic M8 the subgroup SU(3) ⊂ G2 is the sub-group of octonionic automorphisms leaving fixed octonionic imaginary unit invariant - this is essential for M8-H duality. SU(3) is also subgroup of SO(6)== SU(4) acting as rotation on M8= M2× E6. The subgroup of the holonomy group of SO(4) for E4 factor of M8= M4× E4 is SU(2)× U(1) and corresponds to electroweak symmetries. One can say that at the level of M8 one has symmetry breaking from SO(6) to SU(3) and from SO(4)= SU(2)× SO(3) to U(2).

This interpretation gives a justification for the earlier proposal that the descriptions provided by the old-fashioned low energy hadron physics assuming SU(2)L× SU(2)R and acting acting as covering group for isometries SO(4) of E4 and by high energy hadron physics relying on color group SU(3) are dual to each other.

Number theoretic origin of p-adic primes and dark matter

There are several questions to be answered. How to fuse real number based physics with various p-adic physics? How p-adic length scale hypothesis and dark matter hypothesis emerge from TGD?

The properties of p-adic number fields and the strange failure of complete non-determinism for p-adic differential equations led to the proposal that p-adic physics might serve as a correlate for cognition, imagination, and intention. This led to a development of number theoretic vision which I call adelic physics. A given adele corresponds to a fusion of reals and extensions of various p-adic number fields induced by a given extension of rationals.

The notion of space-time generalizes to a book like structure having real space-time surfaces and their p-adic counterparts as pages. The common points of pages defining is back correspond to points with coordinates in the extension of rationals considered. This discretization of space-time surface is in general finite and unique and is identified as what I call cognitive representation. The Galois group of extension becomes symmetry group in cognitive degrees of freedom. The ramified primes of extension are exceptionally interesting and are identified as preferred p-adic primes for the extension considered.

The basic challenge is to identify dark scale. There are some reasons to expect correlation between p-adic and dark scales which would mean that the dark scale would depend on ramified primes, which characterize roots of the polynomial defining the extensions and are thus not defined completely by extension alone. Same extension can be defined by many polynomials. The naive guess is that the scale is proportional to the dimension n of extension serving as a measure for algebraic complexity (there are also other measures). Dark p-adic length scales Lp would be proportional nLp, p ramified prime of extension? The motivation would be that quantum scales are typically proportional to Planck constant. It turns out that the identification of CD scale as dark scale is rather natural. In the article p-adic length scale hypothesis and dark matter hierarchy are discussed from number theoretic perspective. The new result is that M8 duality allows to relate p-adic length scales Lp to differences for the roots of the polynomial defining the extension defining "special moments in the life of self" assignable causal diamond (CD) central in zero energy ontology (ZEO). Hence p-adic length scale hypothesis emerges both from p-adic mass calculations and M8-H duality. It is proposed that the size scale of CD correspond to the largest dark scale nLp for the extension and that the sub-extensions of extensions could define hierarchy of sub-CDs.

See the article About p-adic length scale hypothesis and dark matter hierarchy.

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

Articles and other material related to TGD.

Tuesday, May 12, 2020

Rejuvenation and zero energy ontology


Biologist Harold Katcher (see this) claims that the epigenetic age (there are several measures for it such as methylation level of DNA) of rats has been reduced up to 50 percent. The theory goes that epigenetic age of molecules would be controllable by hormonal signalling globally.

I have been just working with the view about state function reduction in zero energy ontology of TGD providing a theory of quantum measurement free of its basic paradox and having profound implications in the understanding of mysteries of life and death.

For ordinary "big" state function reductions (BSFRs) the arrow of time changes. BSFR would mean death of conscious entity and its reincarnation with opposite arrow of time. The system would rejuvenate in the transition starting a new life in opposite time direction from childhood so to say- rejuvenation would be in question. Doing this twice would lead to life with original arrow of time but starting in rejuvenated state.

Returning cells to the stem cell state inducing de-differentiation as reversal of differentiation would be one example of rejuvenation. The claims of the group suggests that living matter is doing this systematically using hormonal control.

See the article When does "big" state function reduction as universal death and re-incarnation with reversed arrow of time take place?.

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

Articles and other material related to TGD.

Monday, May 04, 2020

When does "big" state function reduction as universal death and re-incarnation with reversed arrow of time take place?

In ZEO based view about quantum measurement theory as theory of consciousness one has two kinds of state function reductions (SFRs) ( see this and this). The ordinary "big" SFRs (BSFRs) and "small" SFRs (SSFRs) (see this). BSFR changes the arrow of geometric time and is identified as death of self identified as a sequence of SSFRs, which do not change arrow of time but increase the size of self by keeping passive boundary in place and states at it unaffected but increasing the size of CD by shifting the upper boundary towards future. Both boundaries increase in size. The 3-surfaces at the active boundary form a kind of log file about events in the life of self and - contrary to expectations - the memories are stored to geometric future.

Under what conditions does "big state function reduction (BSFR) changing the arrow of time take place? I have proposed several ad hoc guesses about this. One example is following. If the heff=n× h0 assignable to the CD or its active boundary does not change in SSFRs, the entanglement can become such that the diagonalized density matrices does not have eigenvalues in the extension of rationals considered and one can argue that BSFR is forced to occur. The proposal for how the sequence of SSFR could in special case correspond to a sequence of iterations for a polynomial of degree n (see this) is however in conflict with the constancy of n.

The hypothesis is that BSFR corresponds to the death of self followed by re-incarnation with opposite arrow of geometric time in universal sense. This suggests that one should look what one can learn from what happens in the death and birth of biological organism, which should now take in opposite arrow of time.

  1. Death certainly occurs if there is no metabolic energy feed to the system. Metabolic energy feed is guaranteed by nutrition using basic molecules as metabolites. Since the increase of heff quite generally requires energy if other parameters are kept constant and since the reduction of heff can take spontaneously, the metabolic energy is needed to keep the distribution of values of heff stationary or even increase it - at least during the growth of organism and perhaps also during the mature age when it would go to increase of heff at MB.

    If the size of CD for at least MB correlates with the maximum value of heff or its average, the size of CD cannot grow and can be even reduced if the metabolic energy feed is too low. The starving organism withers and its mental abilities are reduced. This could correspond to the reduction of maximum/average value of heff and also size of CD.

    One can argue that if the organism loses metabolic energy feed or is not able to utilize the metabolic energy death and therefore also BSFR must take place.

  2. In ZEO self-organization reduces to the second law in reversed direction of geometric time at the level of MB inducing effective change of arrow of time at the level of biological body (see this)). The necessary energy feed correspond to dissipation of energy in opposite time direction. In biological matter energy feed means its extraction from the metabolites fed to the system. One could say that system sends negative energy to the systems able to receive it. A more precise statement is that time reversed subs-system dissipates and metabolites receive the energy but in reversed time direction.

    In living matter sub-systems with non-standard arrow of time are necessary since their dissipation is needed to extract metabolic energy. The highest level dissipates in standard time direction and there must be a transfer of energy between different levels. This hierarchy of levels with opposite arrows of geometric time would be realized at the level of MB.

These observations suggest that one should consider the reincarnation with opposite arrow of time with wisdom coming from the death of biological systems.
  1. We know what happens in death and birth in biological systems. What happens in biological death should have analogy at general level. In particular, in death the decay of the system to components should occur. Also the opposite of this process with reversed arrow of time should take place and lead at molecular level to the replication of DNA and RNA and build-up of basic biomolecules and at the cell level to cell replications and development of organs. How these processes could correspond to each other?

  2. The perceived time corresponds to the hyperplane t=T/2 of CD, where T is the distance between the tips of CD and therefore to maximal size of temporal slice of CD. The part of CD above it shifts towards future in SSFRs. In BSFR part of the boundary of space-time surfaces at the active boundary of CD becomes unchanging permanent part of re-incarnate - kind of log file about the previous life. One can say that the law of Karma is realized.

    If CD decreases in size in BSFR the former active boundary keeps its position but its size as distance between its tips is scaled down: T → T1≤ T. The re-incarnate would start from childhood at T-T1/2 and would get partially rid of the permanent part of self-hood so that new permanent part would be between T/2 and T-T1/2 . Reincarnate would start almost from scratch, so to say. The part between T-T1/2 and T would be preserved as analog of what was called BIOS in personal computers.

  3. At the moment of birth CD possibly would thus decrease in size and the former passive boundary between t=T/2 hyperplane and lower tip of new CD at T-T1 would becomes active and the seat of sensory experience. Where the analog of biological decay is located? The region of CD above T/2 and T-T1/2 is the only possible candidate. This region is also the place, where the events related to birth in opposite time direction should take place.

    The decay of previous organism should correspond to the development and birth of re-incarnated organism. The decay of organism dissipates energy in standard time direction: this energy could used by the re-incarnate as metabolic energy.

    This vision might be tested. The replication of DNA and RNA and build-up of various bio-molecules should be time-reversals for their decays. The same applies to the replication of cells and generation of organs. Replication of DNA is self-organization process in which second DNA strand serves as a template for a new one. The decay of DNA should therefore involve two DNA strands such that the second DNA strand serves as a template for the time reversed replications. The double strand structure indeed makes possible for the other strand to decay first. One could even ask whether the opposite inherent chiralities of DNA strands correspond to opposite arrows of time. Maybe this could be seen as a kind of explanation for the double strand structure of DNA.

    In biology pairs of various structures often occur and maybe they could correspond in some sense to time reversals of each other. Also cell replication should use another cell as replicate and same would happen in the cell decay.

  4. Eastern philosophies talk about the possibility of liberation from Karma's cycle. Can one imagine something like this? The above picture would suggest that in this kind of process the reduction of the size of CD does not occur at all and therefore there would be no decay process equivalent to the growth of time reversed organism. This would serve as an empirical signature for the liberation if possible at all. CD would continue to increase in size or perhaps keep its size. It would seem that a new kind of non-biological source of metabolic energy is needed.

  5. Mental images should correspond to sub-selves and therefore sub-CDs of CD. The idea that the re-incarnations of mental images correspond to re-incarnations with a reversed arrow of time is very attractive. After images is the basic example. Only the after images with standard arrow of time would be experienced by us. Are the after images sensory memories of subjective past involving communication with re-incarnated visual mental image?

    The original, rather natural, proposal was that the after image is in the geometric past but according to the new view it would be shifting with the active boundary of CD towards geometric future at the active boundary of CD as a kind of log file. To remember it as sensory mental image requires communication with it along active boundary involving both future and past directed signals.

    One can imagine also more mundane explanation for after images in terms of propagation of dark photon signals along closed magnetic loops giving rise to periodically occurring mental images.

See either the article Some comments related to Zero Energy Ontology (ZEO), the article When does "big" state function reduction as universal death and re-incarnation with reversed arrow of time take place?, or the chapter Life and Death and Consciousness.

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

Articles and other material related to TGD.

Saturday, May 02, 2020

Could Universe could have North-South direction: How?


Wes Johnson gave ) told about very interesting observations suggesting that cosmology has North-South (N-S) axis in the sense that fine structure constant has N-S variation with respect to this axis. See the popular article. Here is the abstract of the article of Webb et al.

Observations of the redshift z = 7.085 quasar J1120+0641 are used to search for variations of the fine structure constant, a, over the redshift range 5.5 to 7.1. Observations at z = 7.1 probe the physics of the universe at only 0.8 billion years old. These are the most distant direct measurements of a to date and the first measurements using a near-IR spectrograph. A new AI analysis method is employed. Four measurements from the X-SHOOTER spectrograph on the Very Large Telescope (VLT) constrain changes in a relative to the terrestrial value (α0). The weighted mean electromagnetic force in this location in the universe deviates from the terrestrial value by Δ α/α = (αz- α0)/α0= (-2.18 ± 7.27) × 10-5, consistent with no temporal change. Combining these measurements with existing data, we find a spatial variation is preferred over a no-variation model at the 3.9 σ level.

To repeat: the difference from earthly value of α is small and consistent with no temporal change. If the measurements are combined with existing data, one finds that the model assuming spatial variation in north-south direction is preferred over no-variation model at 3.9 sigma level.

This kind of variation was reported years ago (see this). Thanks for Richard Ruquist for the link. I also wrote about the claim (see this).

The findings are very strange and counterintuitive and the effect probably disappears: there are many uncertainties involved since data from several experiments are combined. If the effect is real, there is challenge to understand it so that one cannot avoid the temptation for intellectual exercise.

In TGD framework many-sheeted space-time serves as a starting point.

  1. The notion of space-time sheet requires that the M^4 projection of space-time surfaces is 4-D: I call these space-time sheets Einstenian. This was not true in primordial cosmology during which cosmic strings with 2-D M4 projection dominated (2-D in good approximation) - space-time was not Einsteinian yet. During the analog of inflationary period cosmic strings thickened to flux tubes and liberated energy giving rise to ordinary particles. Transition to radiation dominated cosmology took place during this period.

  2. The fluctuations in the density of matter tell that this transition did not take at exactly the same value of cosmic time T but there are fluctuations of order ΔT/T ≈ 10-5. This happens to be same order of magnitude as the reported value of Δα/α along North-South direction, which puts bells ringing. Could same cosmic parameter determine fluctuation amplitude ΔT/T and the relative change Δα/α along N-S direction?

    Could it be that the transition to radiation dominated cosmology took place in a wave propagating in North-South (N-S) direction so that there would be a gradient of T along N-S direction: ΔT/T - not fluctuation. This does not require gradient in fluctuations Δ T/T and Δ ρ/ρ. Could this gradient also explain the gradient in α along N-S direction?

How the N-S gradient in α could be understood?
  1. At QFT limit particle experiences the sum of induced gauge fields assignable to the space-time sheets which it necessarily touches because it has same size of order CP2size as the sheets on top of each other in CP2directions. Standard model gauge fields can be indeed defined as sums of these induced gauge fields. Same applies to gravitational field identified in terms of metric of Einsteinian space-time having 4-D M4 projection.

  2. The many-sheeted space-time was not quite the same thing in today and in ancient universe. The number of space-time sheets could have been different. Space-time sheets carried also induced classical fields with different strength.

    Monopole flux tubes created during the analog of inflationary period from cosmic strings indeed evolve during cosmic evolution. Their thickness increases in rapid jerks and in average sense this corresponds to a smooth cosmic expansion. This conforms with the fact that astrophysical objects do not seem to expand themselves in cosmic expansion although they co-move as particles in this expansion.

    The increase of the thickness of monopole magnetic flux tube reduces its magnetic field strength since monopole flux is conserved. This in turn reduces the contribution of this space-time sheet to the classical em field experienced by a charged particle. In particular, this would affect the binding energies of atoms slightly.

  3. Could this together with the wave like progression of the transition to radiation dominated cosmology be responsible for the dependence α on N-S direction with the increase Δα/α ≈ 10-5?

See the chapter More TGD inspired cosmology.

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

Articles and other material related to TGD.

Thursday, April 30, 2020

Could brain be represented by a hyperbolic geometry?

There are proposals (see this) that the lattice-like structures formed by neurons in some brain regions could be mapped to discrete sets of 2-D hyperbolic space H2, possibly tesselations analogous to lattices of 2-D plane. The standard representations for 2-D hyperbolic geometry are 2-D Poincare plane and Poincare disk. The map is rather abstract: the points of tesselation would correlate with the statistical properties of neurons rather than representing their geometric positions as such.

Remark: There is a painting of Escher visualizing Poincare disk. From this painting one learns that the density of points of the tesselation increases without limit as one approaches the boundary of the Poincare disk.

In TGD framework zero energy ontology (ZEO) suggests a generalization of replacing H2 with 3-D hyperbolic space H3. The magnetic body (MB) of any system carrying dark matter as heff=nh0 provides a representation of any system (or perhaps vice versa). Could MB provide this kind of representation as a tesselation at 3-D hyperboloid of causal diamond (cd) defined as intersection of future and past directed light-cones of M4? The points of tesselation labelled by a subgroup of SL(2,Z) or it generalization replacing Z with algebraic integers for an extension of rationals would be determined by its statistical properties.

The positions of the magnetic images of neurons at H3 would define a tesselation of H3. The tesselation could be mapped to the analog of Poincare disk - Poincare ball - represented as t=T snapshot (t is the linear Minkowski time) of future light-cone. After t=T the neuronal system would not change in size. Tesselation could define cognitive representation as a discrete set of space-time points with coordinates in some extension of rationals assignable to the space-time surface representing MB. One can argue that MB has more naturally cylindrical instead of spherical symmetry so that one can consider also a cylindrical representation at E1× H2 so that symmetry would be broken from SO(1,3) to SO(1,2).

M8-H duality would allow to interpret the special value t=T in terms of special 6-D brane like solution of algebraic equations in M8 having interpretation as a "very special moment of consciousness" for self having CD as geometric correlate. Physically it could correspond to a (biological) quantum phase transition decreasing the value of length scale dependent cosmological constant Λ in which the size of the system increase by a factor, which is power of 2. This proposal is extremely general and would apply to cognitive representations at the MB of any system.

See the article Could brain be represented by a hyperbolic geometry?.

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

Articles and other material related to TGD.


Thursday, April 23, 2020

Decapitated wasp grasping its head and flying away


Runcel Arcaya gave a link to very interesting popular article telling about the rather surreal behavior of decapitated wasps. The wasp just grabs its head and flies away! Also decapitated hen can fly and I remember the story that some decapitated animals start to move towards nearby water.

The standard explanation for the ability of insect to move would be that insect brain is far from being so important than brains in higher animals. Ganglions in their spine take care of motor control. This looks reasonable.

One can of course wonder how the insect can fly if it does not see - eyes are in the head which it lost. Flying could be of course completely random.

These findings force to challenge the belief that brain is the seat of consciousness. Actually one must challenge also the belief that biological body is the seat of consciousness.


  1. The notion of magnetic body (MB) is more or less forced by the fact that brain codes information to EEG and sends it to space: the waste of metabolic energy in this manner makes no sense if there is no receiver. Also the sensory data is fraction of second old: this finds explanation since it takes some time to communicate it from brain to MB. This allows to estimate the size of MB and it has layers of size scale of Earth and even bigger.

  2. The macroscopic coherence of biological body is not possible without macroscopic coherence at control level and standard quantum mechanics does not provide it: Planck constant is simply too small. Hence dark matter at MB.
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  3. Even further, the idea that consciousness is a property of physical system must be challenged at fundamental level. Conscious experience is in quantum jump replacing the quantum state with a new one, between the old and new world, in a moment of creation. This picture solves the logical paradoxes of physicalistic and idealistic paradigms.

TGD based view about quantum jump provides another view about the situation.
  1. "Big" (ordinary) state function reductions in zero energy ontology change the arrow of time. This is essential for the new view about self-organization apparently breaking second law. Time evolution obeying second law in non-standard time direction looks in standard time direction like self-organization generating order and coherence and dissipation of energy looks in standard time direction like extracting energy from environment - feed of metabolic energy.

  2. This explains Libet's experiments apparently showing that experience of free will is caused by neural activity. The macroscopic quantum jump would correspond to this experience and the time evolutions starting from the final state would lead to geometric past and cause brain activity.

  3. Motor actions would be realizations of free will induced by "big" (ordinary) quantum jumps at MB carrying dark matter as heff=n×h0 phases and inducing coherent actions at the level of ordinary matter.Also effective change of arrow of time would be induced at the level of ordinary bio-matter.

  4. In the case of decapitated insect motor actions would involve similar macrossopic quantum jumps. The effects of motor activity propagating backwards time would start from the level of body but would not reach the brain but this would not be a problem!

  5. In TGD framework one can wonder whether eyes still see and the information about visual percepts still goes to the magnetic body (MB) of the insect, which controls the biological body? It would be enough to keep the head and just this the wasp does!

See the article Getting philosophical: some comments about the problems of physics, neuroscience, and biology.

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

Articles and other material related to TGD.