The last year has been a period of progress in TGD (as also the previous years actually). In the following I try to summarize key points concerning theoretical advances and applications to various findings challenging the standard views.
What the notion of space-time supersymmetry (SUSY) could mean in TGD has been a longstanding problem and I have made several attempts to identify SUSY.
- TGD allows super-conformal invariance at the level of WCW geometry but it has not been clear whether something analogous to SUSY could emerge. The notion of super-space is conceptually extremely elegant although it could be blamed to be very formal and have no real geometric content. Is it possible to generalize this notion to TGD framework.
The basic technical problem is that Majorana spinors do not make sense in TGD since fermion number is conserved. In the scenario considered hitherto both quark and lepton numbers - are conserved and correspond to different chiralities of H-spinor fields.
- The dramatic step in progress occurred with the realization that the notion of super-field can be generalized and naturally leads to a scenario in which leptons can be seen as local composites of quarks so that quarks would be the only fundamental fermions. SUSY would have been staring us directly to face for almost century. This also led to a dramatic simplification of the model for the elementary particles meaning return to almost the original picture in which particles correspond to Euclidian regions of space-time surface - so called CP2 type extremals.
- There are still open questions. Are elementary particles - maybe even graviton - wormhole contacts connecting two space-time sheets with Minkowskian signature or just Euclidian inside Minkowskian ones as the first model formulated long time ago assumed. It is clear that quarks carry non-trivial homology charge identifiable as effective magnetic charge and it has important role in colof confinement. Leptons and gauge bosons need not have homology charge. Does the monopole flux loop run along single space-time sheet or does it form flattened square type loop running between two space-time sheets through wormhole contact?
The king idea behind twistor lift of TGD is simple.
- If the 12-D twistor space assignable to imbedding space has twistor space allowing Kähler structure allowing it is possible to define 6-D Kähler action. This is possible only for H=M4×CP2 and M8 and leads to the introduction of the analog of Kähler structure for M4 predicting CP breaking. Poincare invariance is not lost at the level of moduli space and different octonionic structures for M8 correspond to various Kähler structures for M4
(or actually DD).
- The earlier proposal was that the "geometric" twistor space of M4 is simply M4xS2. It turned out that the standard identification is correct and the scale of the twistor space of M4 endowed with metric (projective space allows metric) corresponds to the scale of CD. It seems that one can assign twistor space also with the Cartesian factors of M8= M4× E4 and perhaps even with M8. These twistorializations seem provide alternative descriptions of physics.
- Already earlier it had become clear that cosmological constant emerges naturally in the dimensional reduction for the 6-D Kähler action of 12-D twistor space to 4-D Kähler action plus volume term. The dimensional reduction is necessary in order to induce twistor structure to space-time surface (6-D surface must have structure of S2 bundle).
The challenge has been to understand the value of the coefficient of volume term - counterpart of cosmological constant Λ - and the new idea is that Λ is determined by the scale of causal diamond (CD) so that a connection with ZEO emerges. Λ thus characterizes the size of CD and thus of space-time surfaces associated with CD.
- The value of Λ should be determined by preferred extremal property and p-adic length scale hypothesis strongly suggests that quantization of cosmological constant as proportional to 1/L(k)2, p≈ 2^k. If p-adic length scale corresponds to ramified prime of extension of rationals, cosmological constant is determined by the extension and one has discrete evolution of Λ. Λ in turn takes the role of length in ordinary coupling constant evolution and induces the evolution of various coupling constants as function of p-adic length scale.
- When the notion of local cosmological constant is combined with the idea about cosmic strings thickened to flux tubes carrying dark matter as heff=nh0 phases and forming a fractal hierarchy, one ends up to a rather detailed view about the formation of galaxies and stars as tangles of cosmic strings. In particular, a concrete model for blackhole like objects emerges. This picture predicts that flux tubes thicken in rather rapid phase transitions increasing the size of CD and reducing the value of cosmological constant. This gives rise to accelerated expansion stopping when the increase of volume compensates the reduction of magnetic part of action.
See the articles
- Twistor lift of TGD for M4× CP2 should be dual to the description in terms of M8 which could allow its own twistor lift. Since the dynamics is algebraic at the level of M8 (Λ is replaced with CD size), it is clear that the dynamics determined by partial differential equations at the level of H must involve additional constraints guaranteeing preferred extremal property (analog of Bohr orbit). The condition that extremal of both Kähler action and minimal surface with 2-D string world sheets and partonic 2-surfaces as singularities guarantees this. At string world sheets the quaternionic tangent space would degenerate to 2-D one. There are also other formulations for the preferred extremal property.
A cosiderable progress occurred on both theoretical and experimental side. ZEO based view about generalizes quantum measurement theory to a theory of consciousness. There are two kinds of state function reduction and they are universal rather than assigned only to laboratory quantum measurements. Ordinary - "big"- state function (BSFR) changes the arrow of time whereas "small" state function reduction (SSFR) as counterpart of "weak" measurement very preserved it and is analogous to classical measurement. The life cycle of self consists of a sequences of SSFRs and self dies and reincarnates with opposite arrow of time in BSFR.
- What happens for CD - or rather to the wave function in the moduli space of CDs localized around single CD - in BSFR has not been quite clear. Does CD size continue to increase in statistical sense from the size already achieved or is its size reduce so that self would have childhood also in the time reversed life. The latter option looks the only reasonable one. This allow the possibility that the size of CD remains below upper limit and predicts that the objects in the very early universe look like their modern counterparts. Cosmology indeed shows time anomalies such as stars older than the Universe and modern abundances of nuclei in very early Universe.
- Also progress in the understanding of the details related to SSFR has occurred. The complete localization of space-time surfaces inside CD in given SSFR breaks Poincare invariance at quantum level although this symmetry is unbroken classically. Can one require complete localization? Should one allow wave functions in the moduli space of CDs defined by Poincare transforms of the active boundary of CD and consider analogs of Gaussian wave packets having minimal uncertainties with respect to energy and temporal position of active boundary of CD?
This question leads to a proposal in which the unitary evolutions of wave functions in the moduli space of CDs followed by SSFR are adiabatic in the sense that the coefficients of the state as superposition of analogs of energy energy eigenstates remain invariant although the basic states themselves change. Also an analog of cosmic temperature decreasing during evolution emerges and is inversely proportional to the average size of CD.
- The increase of heff while keeping other parameters constant requires energy. The value of heff also tends to be reduced spontaneously. This leads to the idea that in living matter metabolic energy is needed to increase heff and increase the scale of quantum coherence and also to preserve it.
Quite generally, self-organization requires feed of energy needed to increase the scale of coherence. This inspires the idea that dark matter at magnetic body of the system serving as master for ordinary matter quite generally is responsible for self-organization in presence of energy feed. Self-assembly aspect of self-organization could be understood as dissipation with non-standard arrow of time and evolutionary aspect due to BSFRs increasing the dimension n= heff/h0 of algebraic extension and evolutionary level in statistical sense.
See the articles
What about experimental support for ZEO?
- Concerning the experimental side, a breakthrough came from the strange findings of Minev et al on state function reduction in atomic systems. If the recent experimental findings by Minev et al are replicable, one is forced to challenge the basic assumption of the standard quantum measurement theory stating that state function reductions occur completely randomly and instantaneously. Rather, state function reduction (SR) looks like a continuous, deterministic process. The findings even suggest that SR gives a detectable warning signal and can be prevented: this would be like Zeno effect.
Zero energy ontology (ZEO) based view about quantum measurement and the relationship between geometric subjective time could explain why state function reduction looks like a deterministic process and one can apparently anticipate it in TGD framework: this is however an illusion.
The fact that the absence of the signal inducing quantum jump does not affect the occurrence of quantum jump suggests that the "flight" period indeed represents the classical evolution after the quantum jump in the reversed direction of time so that the absence of the external signal would not anymore affect the situation.
The most plausible interpretation for the control signal apparently stopping the reduction process is that it induces the reversal of the quantum jump already occurred. A careful analysis to distinguish between subjective and geometric time and arrows of time for the observer and atom would be needed. Interestingly, the Libet's findings that conscious decision is preceded by neural activity could be interpreted in the same manner.
- The possibility of macroscopic quantum jumps combined with ZEO predicts macroscopic time anomalies analogous to that found by Minev.
Earthquakes and volcanic eruptions are found to exhibit such anomalies and the ZEO interpretation could be as macroscopic quantum jumps "big" (ordinary) state function reductions as opposed to "small" state function reductions identified as counterparts of weak measurements . The occurrence of these phenomena correlates strongly with sunspot minima, cosmic rays seem to induce them but quite too deep below the Earth's surface, and electromagnetic activity in upper atmosphere precedes rather than follows these phenomena as one might expect.
See the articles
Number theoretic vision is complementary to the geometry based approach to TGD and involves several aspects. p-Adic number fields and their extensions as correlates of cognition is one aspect: this leads to adelic physics. Classical number fields and M8-H duality is second aspect. Infinite primes represent the third aspect.
The p-adic aspects of number theoretical vision are formulated in terms of adelic physics. Adele is obtained as analog of Cartesian product of real number fields and various p-adic number fields. The extensions of rationals lead to a hierarchy of adeles with extension of p-adic number fields induced by extension K of rationals. The hierarchy of extensions defines an evolutionary hierarchy and evolution as increase of the dimension of extension in statistical sense is unavoidable in ZEO. BSFRs would give rise to the increase of the dimension of extension.
Consider the basic aspects of the adelic vision.
- Hierarchy of Planck constants of effective Planck constants heff=n×h0 is the basic prediction. Here n is the dimension of the extension of rationals involved.
- The conjecture is that the preferred p-adic primes appearing in p-adic length scale hypothesis correspond to ramified primes of extension of rationals considered.
- The dimension of extension of rationals can change in BSFRs and is bound to increase in statistical sense. This implies evolution. One can even speak number theoretical fight for survival. Extensions for which cognitive representations are especially larger could be winners and therefore also corresponding preferred primes as ramified primes of extension.
- Prime extensions, which are not extensions of extension could be seen as analogs of genes and the connection with genes could be even more concrete.
Cognitive representations defined as intersections of real and various p-adic space-time sheets and consisting of space-time points with imbedding space coordinates having values in the extension K are the key element of adelic physics. Cognitive representation is highly unique at the level of M8 since the octonionic structure involves a choice of coordinates unique moduli translations in the real coordinate of M8 identifiable as M4 time coordinate.
Cognitive representation are unique for given extension modulo these time translations, which means universal discretization defined by physics itself. Cognitive representations at the level of H are identified as points of space-time surface X4⊂ M4× CP2 having imbedding space coordinates in the extension of rationals defined by the polynomial defined by the M8 pre-image of X4 under M8-H correspondence. The optimal situation would be that in preferred coordinates for H the map by M8-H duality preservesextension and cognitive representation property.
The challenge of identifying cognitive representations for an arbitrary surface looks like a formidable but the physical picture helps considerably.
- Finding the cognitive representation for given space-time surface reduces to a classical problem of algebraic geometry. Kim has proposed new ideas in this respect- in particular, the one should consider large number of the counterparts of cognitive representation and that symmetries transforming these representations to each other might play a role in the problem. It seems that these idea fit very nicely with TGD picture. A subgroup of symplectic isometries of δ M4_+ × CP2 act as symmetries and produces new cognitive representations from a given one so that one can speak of an orbit of cognitive representation.
- The preferred extremal property and strong form of holography (SH) suggest that cognitive representations can be restricted to partonic 2-surfaces and string world sheets. This give hopes that one can say something non-trivial about them.
- One can argue that number theoretic evolution as increase of the dimension of the extension of rationals favors space-time surfaces with especially large cognitive representations since the larger the number of points in the representation is, the more faithful the representation is. By SH it would be enough to consider cognitive representations restricted to partonic 2-surfaces and string world sheets.
What kind of 2-surfaces are the cognitively fittest one? It would not be surprising if surfaces with large symmetries acting in extension were favored and elliptic curves with discrete 2-D translation group indeed turn out to be assignable string world sheets as singularities and string like objects. In the case of partonic 2-surfaces geodesic sphere of CP2 is similar object.
M8-H duality emerged from the observation that complexified M8 allows octonionic structure. Also H allows number theoretic interpretation, for instance SU(3) as automorphisms of octonions. Space-time surfaces in H obeying dynamics dictated by partial differential equations plus infinite number of analogs of gauge condition expressing preferred extremely property. This lead to the idea of M8-H duality stating that this dynamics is an image of purely algebraic dynamics at the level of M8.
The conjecture is that this dynamics is determined by a simple condition stating the the real or imaginary in quaternionic sense for an octonionic polynomial obtained by algebraically continuing a real polynomial with rational coefficients gives the dynamics at the level of M8 as purely algebraic dynamics involving no partial differential equations.
General vision about M8-H duality is discussed in the following articles. See the articles
- TGD view about McKay Correspondence, ADE Hierarchy, Inclusions of Hyperfinite Factors, M8-H Duality, SUSY, and Twistors
- TGD view about McKay Correspondence, ADE Hierarchy, and Inclusions of Hyperfinite Factors
- New results related to M8-H duality
M8-H duality means that one one describe particles as having light-like M8-momentum. 8-D light-likeness is essential for the generalization twistor approach so that it applies also to particles massive in M4 sense. 4-D mass would depend on this choice. The basic condition would be that the spectra of CP2-mass squared and E4 mass squared are same and this fixes the choice of M4 to high degree.
For a given massive state one can make M4 mass vanishing by a suitable choice of M4? It seems hower that this change of M4 must be accompanied by a spectral flow shifting the conformal weights by a negative vacuum conformal weight necessary for p-adic mass calculations. Can one consider the possibility that the choice of M4 depends on particle? These are still open questions.
M8-H-duality led to a discovery of a further aspect of ZEO.
- At M8 level the equations determining a given region of space-time surface are algebraic equations stating that either the real or imaginary part (in quaternionic sense) of octonionic polynomial obtains as algebraic continuations of a real polynomial with rational coefficients vanishes (one can consider also coefficients in given extension of rationals).
- These equations allow besides 4-D surfaces also exceptional solutions, which are 6-spheres and analogs of branes. They have the ball defined by the intersection of M4 time t= constant plane with CD as M4 projection and one has almost fiber space with fiber which is 3-sphere contracting to a point at light-like boundaries of CD. The value of t is given by a root t=rn of the real polynomial so that the number of these moments is finite and equal to the degree of the polynomial.
- These 6-spheres provide maximal cognitive representations. Their intersections with 4-D solutions are partonic 2-surfaces and by strong form of holography (SH) these partonic 2-surfaces and string world sheets are expected to carry the data - cognitive representation - determining the space-time surface in question. From the point of view of consciousness theory, the intersections of 4-surfaces with t=rn branes - analogs of vertices at which 4-D surfaces meet - would define "very special moments in the life of self", kind of eureka moments, one might say.The life cycle of self would be characterize partially by this sequence.
"Cold fusion" (transmutations of elements) is a phenomenon not accepted by the mainstream but the pioneers have continued their work and nowadays these people are not regarded as crackpots anymore.
"Cold fusion" is not the only problem of nuclear physics. For about 10 years ago Asplund et al discovered that solar abundances deduced from those outside Sun or at surface of Sun are lower than the abundance deduced from sound wave propagation in solar interior.
TGD based model for "cold fusion" generalizes to a model of nuclear reactions modifying dramatically the standard model.
- TGD based model of "cold fusion" relies on the notion of dark nucleus identified as dark proton sequence at magnetic flux tube. This kind of dark nuclei would be formed in Pollack effect in which charge separation leads to formation of negatively charged regions as protons go somewhere. Charge separation is generated by a feed of energy and IR light is the most effective manner to achieve Pollack effect.
- Dark nuclei have scaled down nuclear binding energy inversely proportional to the p-adic length scale characterizing the transversal thickness of the flux tube and distance between dark protons. The experimental findings about "cold fusion" suggest that the dark nucleons in these experiments have size scale of electron and binding energy in keV range. Also other scales are possible and in Pollack's experiments size scale would be considerably larger. Dark nuclei would also realized genetic code at fundamental level with 3-proton unit determining the code word. All basic bio-molecules have dark analogs of this kind.
- The transformation of dark nuclei to ordinary nuclei would liberate essentially all nuclear binding energy and explain heat production in dark fusion. It is quite possible that most of the energy leaks out along dark flux tubes. This process can take place at low temperatures and therefore also outside stellar cores. The generation of ordinary nuclei in this manner could solve why the abundances of Li, B, and Be are much larger than predicted by the standard nuclear physics. Same applies to nuclei heavier than Fe.
- Standard model for hot fusion occurring inside solar core assumes tunnelling as a basic step of fusion occurring in solar core. TGD suggests that the model for "cold fusion" generalize to all nuclear reactions. The formation of dark nuclei would the intermediate step instead of tunnelling and dark nuclear reactions would occur first and produce dark nuclei transforming to ordinary ones. The presence of dark nuclei in stellar interior could explain the findings of Asplund et al. Also the picture about pre-stellar evolution would change: elements could be produced already during this era.
Cosmology is in crisis as the number of anomalies is steadily increasing. To mention only few of them.
- Cosmological constant is predicted to be huge but is non-vanishing and extremely small and gives rise to accelerated expansion.
- The mysteries of dark matter and dark energy are known for decades. The halo model of galactic dark mater is plagued by anomalies and the predicted dark particles have not been found.
- There is also the problem of two Hubble constants.
TGD suggests a solution of these problems.
- Twistor lift of TGD leads to the notion of length scale dependent cosmological constant and cosmic expansion would be a sequence of phase transition increasing the size scale of CD and reducing cosmological constant. Each step would involve accelerated period followed by slowing down of the expansion.
- TGD leads to a general model of cosmology in which primordial period would be cosmic string dominated - the M4 projection of space-time surfaces was 2-D string world sheet rather than 4-D piece of M4 defining Einsteinian space-time at QFT limit. In later evolution cosmic strings would thicken and GRT based cosmology would give a reasonable description in long length scales.
Cosmic strings thickened to flux tubes would appear in all length scales and one can say that they permeate through entire physics. Gravitation alone would not determine cosmology and astrophysics. Also Electric Universe hypothesis claims this and even that electromagnetism is all that is needed. This is unrealistic hypothesis.
Cosmic strings thickened to flux tubes would represent deviation from GRT.
- The energy of cosmic strings and dark matter at them would explain dark matter and energy. Flat velocity spectrum for distant stars of galaxies is predicted without further assumptions. Quantum classical correspondence suggests that dark energy could be actually classical space-time correlate of dark matter identified as heff=nh0 phases at magnetic flux tubes resulting in the thickening of cosmic strings.
- Cosmic strings carrying monopole flux need no currents to maintain the magnetic field. This would explain the presence of magnetic fields even in cosmological scales. Also Earth's magnetic field would have two components corresponding to flux tubes carrying monopole flux and Maxwellian flux. This would also explain why magnetic field of Earth has not disappeared long time ago and also the finding that Mars has surprisingly strong magnetic field which is however visible only via auroras (only the monopole component is present).
- One can understand the formation of galaxies and stars and even planets and smaller structures as a generation of tangles to long cosmic strings, which have topology of dipole magnetic field in the simplest situation. One ends up to a replacement of blackholes with volume filling flux tube tangles. White hole would be time reversal of blackhole. Even ordinary stars could be seen as blackhole like entities in this sense.
Quantum consciousness, and quantum biology and neuroscience are applications of TGD. The macroscopic quantum coherence made possible by heff=nh0 hierarchy labelling dark matter as phases of ordinary matter, the notion of magnetic body, and zero energy ontology (ZEO) are key elements of TGD inspired vision. Magnetic body (MB) carrying dark matter serves as master and ordinary bio-matter as slave. The coherence of ordinary bio-matter is not quantum coherence but coherence induced by the quantum coherence of dark matter at MB.
- The basic problem of quantum biology based on standard quantum mechanics is that Planck constant is too small. TGD view obviously solves this problem. In particular, one ends up to a model for magneto-reception and circadian rhythm based on the notion of quantum compass defined by magnetic flux tubes with large value of heff.
- Dark proton sequences - dark nuclei - allow a realization of genetic code and basic biomolecules. Codon corresponds to dark proton triplet. The numbers DNA,RNA,tRNA, and amino-acids are predicted correctly if they correspond to "shadow" of their dark counterparts. Also the number of codons coding for given amino-acid are predicted correctly.
Second realization of genetic code would be in terms dark photon triplets whose frequencies define the analog of 3-chord. This allows communications utilizing genetic code. The geometries of icosahedron and tetrahedron lead to a model of genetic code predicting correctly the numbers of codons coding or given amino-acid. The model predicts large number of collections of 3-chords defining harmonies. Harmony would define emotional intelligence as holistic aspect of intelligence whereas codons would triplet 6-bits units.
- Standard cosmology has a problem. Although various astrophysical objects participate in cosmic expansion, they do not seem to expand themselves. In TGD the expansion would take place even for astrophysical objects as jerks as cosmological constant is reduces and the thickness of flux tube increase. This leads to TGD variant of Expanding Earth Model in which Earth radius would have increased by a factor of 2 during relatively short period at the time of Cambrian Explosion. This would have caused the bursts of underground oceans and intra-terrestial multicellular life to the surface of Earth. There are indications that also Mars has oceans in its interior. Mars has also magnetic field and this could correspond to monopole flux tubes. Could this make possible multicellular life in the intra-Martial oceans?
- The basic prediction of TGD inspired biology is the existence of networks formed by magnetic flux tubes. It has been known for a long time that viruses can be multi-local in the sense that their parts are shared by several host cells. A possible interaction is that the parts of these multi-local viruses are connected by magnetic flux tubes. Bacterial colonies form tight structures analogous to multi-cellulars when metabolic resources are scarce. This could have led to multi-cellulars. These structures indeed resemble multicellular embryos.