Following a news article from Stanford, slashdot has followed up with a report on observed changes in decay rates of radioactive elements caused by solar flares. This is not really new and follows other claims that nuclear decay rates change by about 0.1% on an annual cycle (or other longer cycles corresponding to various forms of solar activity) of course Motl has reported it two years ago.

The explanation for the effect offered by the scientists involved is that it is caused by changes in neutrino fluxes from the Sun. There *are* small variations in beutrino flux of this sort but the effect on deacy rates seems unlikely because neutrino interactions as we know them are too weak for this to happen. It would have to be something far outside the standard model that has somehow avoided detection in very sensitive experiments such as Super-Kamiokande. If not neutrinos then the next suggestion is some as-yet-unknown particle. It is an appealing idea but it is still unlikely that something like that could affect nuclear decay rates without being observed in different ways in other experiments.

Could the effect be caused by something more basic such as changes in electric or magnetic fields or even temperature in the environment of the experiment? If such dramatic effects on decay rates could be caused in these ways it would have been observed in controlled experiments a long time ago, so this can be ruled out. Environmental effects on the measuring apparatus are another matter, so suspicions immediately arise.

Putting aside the solar flare result for the moment, it turns out that someone has already done some more careful experiments to look for annual variations of decay rates and found nothing (See Evidence against correlations between nuclear decay rates and Earth–Sun distance) here is one of their plots. I have chosen the one that looks like it comes closest to showing some effect to my eye but it is nowhere near the claimed effect shown by the sine curve and is not statistically significant.

Could there be some effect seen better with solar flares? The trouble is that solar flares are relatively brief. One claim was for an effect that lasted 43 minutes. The studies of annual variations were performed over a period of two years and still the statistical errors are just a little below the expected effect. If solar flares caused an effect observable over 43 minutes it would surely have to be much larger to stand out from the noise.

Sadly then, the warning signs are not aligning in favour of these results, but ruling out an effect conclusively might require more experiments.

I have also written about tritium beta decay anomaly and suggested also an explanation for the annual variation of nuclear rates. See see this.

In TGD inspired nuclear string model nucleons inside nuclei are connected by color bonds having quark and antiquark at their ends to form a string like structure. The color bonds can be both neutral and charged and this predicts a lot of exotic new states. Thus color would be highly relevant also for nuclear physics. p-Adic length scale hypothesis allows light variants of ordinary quarks and this might be also relevant (note however that masses are in any case in MeV range for u and d).

For instance, the very hard to understand and debated tetra neutron would be alpha particle (two proton and two neutrons) with two negatively charged color bonds.

The energy scale for the states with apparently same proton and neutron numbers could be in keV range by naive estimate of Coulomb energy. If so, X rays from flares and also the standard X ray background varying like 1/r^2, r the distance to the Sun, could induce transitions between ordinary and exotic nuclei and affect the equilibrium between genuinely standard ground states and their exotic variants. This would lead to an apparent variation of nuclear reaction rates. Only apparent variation would be of course in question. Exotic states could be highly relevant also for cold fusion which is now taken much more seriously than earlier since direct detection of highly energetic protons form electrolyte is possible.

Maybe a new branch of physics is patiently waiting for its discovery;-) . Unfortunately, nuclear physicists are too tightly bound to the reductionistic text book wisdom and take quite too seriously what Big Brothers (particle physicists) tell to them.

This is the sort of physics I hate to see come about, and when it does I prefer that it goes away. I took a couple of courses from E. Fischbach, and the guy is curious to say the least. Back then he was all over the map over the “fifth force,” which has faded away like the morning fog. Much the same might happen here. Fischbach is attracted to the quirky aspects of physics. He is intrigued by these oddities, for there is always a chance something might come about that changes everything. That is what we have going on here.

From at least a first glance this simply does not make any sense. There can be all sorts of complicated stuff with solar physics and variations in nuclear processes and neutrino production. How this could causally affect the nuclear or weak interaction forces is utterly implausible. My only hunch is that if something is really going on that there is some quantum entanglement involving the quantum fields of these forces that is somehow set up. I am not going to put any bet on this, for even still this is an extreme dark horse prospect. Neutrinos produced in the core of the sun interact so weakly with anything sitting on a lab bench, whether that being a neutrino detector or an isotope of some element, that it is difficult to imagine there being some causal process going on here.

Lawrence is right that this does not make sense if one believes that recent day theoretical prejudices provide the final description of the universe. History of science has again and again demonstrated that it does not care about our text book beliefs and it is course is totally implausible that physics would be fully understood down to intermediate boson length scale only 500 years after Newton. Therefore one should try to avoid negative emotional attitudes and remain curious.

The example mentioned here is just one example of many well-documented anomalies in nuclear physics coming from respectable research groups doing lab experiments. Russian physicist Shnoll has done a whole lifework in in demonstrating that nuclear rates vary with periods which are astrophysical time scales. For this and related anomalies see this and this.

Quite recently an anomaly in Lamb shift of muonic atom suggesting that proton’s charge radius is 4 per cent smaller than in hydrogen atom was discovered (see this. This result published in Nature is sensational taking into account the accuracies involved and has no sensible explanation if one sticks in standard model. But the anomaly will be forgotten because text books know better and the recent day theoretic belief system cannot say anything interesting about the finding.

A dramatic example about the power of prejudice comes from biology: water memory assigned with homeopathy has been one of the basic targets of ridicule by skeptics. Top biologist Benveniste was doomed to be a swindler when he published an article supporting the phenomenon in Nature.

He and his group continued to work and developed a working device demonstrating water memory and based on what can be interpreted as electromagnetic representation of the biologically relevant aspects of biomolecules. For year ago the research group led by HIV Nobelist demonstrated in a very detailed manner the reality of phenomenon and much more and really fascinating things. [L. Montagnier, J. Aissa, S. Ferris, J.-L. Montagnier, and C. Lavall’e (2009).

Electromagnetic Signals Are Produced by Aqueous Nanostructures Derived from Bacterial DNA Sequences. Interdiscip. Sci. Comput. Life Sci. See this]. A complete silence surrounds also these findings.

The problem is that most theoreticians are stuck to the reductionistic belief system. Second closely related problem is that most theoreticians know practically nothing about experimental discoveries outside their own specialization (and couldn’t be less interested). The reductionistic belief is of course completely irrational and based on fear of authority and intellectual laziness. That it is also deadly wrong is suggested by the fact that the theoretical bridges from quarks to nucleons, from nucleons to nuclei, from atoms to molecules, and from molecules to biomolecules do not actually exist

except as wishful thoughts. I am convinced that fractal view about Universe at fundamental level is the only cure to the dead situation in theoretical physics.

Matti,

I am not trying to argue that textbook physics is somehow absolute. However, if something like general relativity or quantum mechanics might fail in the future I would prefer that it do so “gracefully.” Newtonian mechanics failed gracefully, where outside its proper domain of applicability we now know it failed to describe nature. Yet we still use Newtonian mechanics to send spacecraft to Saturn and so forth. A catastrophic failure might have been if some strange class of asteroids had been found in the 1840s or so that utterly defied Newtons’s second law of motion or if gravity force had been F = GMm/r^{2.7} or some other very odd occurrence was found. This data suggests something like a catastrophic failure, at least with respect to concepts of causality.

This putative discovery so far does not seem to have a great follow on of empirical support. So right away we might suspect some instrument or analytical bias of one sort or the other. It could be the old fashioned file-drawer effect. Since E. Fischbach has inspired these efforts, that is something I suspect. He based his idea of the fifth force on Eotvos’ data on the equivalency of gravitational and inertial mass, which was odd for there was much more recent data of far greater accuracy. Some sort of data-bias set in. The E.F. et al paper also references data from old experiments. So my first inclination is to say this is an example of what I would call the Fischbach effect.

Now let us suppose there is actually something here. This raises some troublesome problems, for clearly neutrinos flying out from the sun do not interact strongly enough to have a causal influence of this magnitude. Again, if theories fail I expect them to do so gracefully, and so I don’t expect our theories of weak interactions to operate with super-Kamiokande detection of neutrinos, but with some odd exceptions for various isotopes on a lab bench that are examined by E. Fischbach. This is too much like the fictional case of exceptional asteroids above. So a causal theory of this is difficult to defend, for if there really was such a causal effect with respect to neutrinos I would expect a similar observation from the super-K. I would expect the super-K to measure some cyclical variation in the interaction strengths of neutrinos that is commensurate with these nuclear and beta decay data.

So if this is real then it might indicate something very deep is going on. I would be tempted to say that it would be some quantum entanglement physics of a new variety. It might then be a case of where the quantum field physics of the strong or weak interactions are by some means capable of entering into large scale entanglements without some prior interaction. Normally to get electrons into entangled states they have to be brought to within their Compton wavelengths, which then sets up the entanglement that in principle can exist over arbitrary distances. So if this physics turns out to be real, the data is reproduced and the nuclear experimental community comes out with a conclusive, “Yes this is real,” then we are faced with new physics of some sort. My sense is it would involve the entanglement of states of nuclear and weak interactions by other means, maybe gravity.

This would lead to a new break through if it all works out. Yet we have to be careful, for my suspicions are pretty high with regards to this. At this time my bet would be this will burn off like the morning fog.

Lawrence,

Fesbach is not alone. As I mentioned this is only one of the many nuclear physics anomalies. I learned just yesterday about new evidence for 33 days period in nuclear rates and assigned with the rotation of the solar core and possible new exotic particles from Sun. See this. It is very unfair that the pioneering work of Shnoll (30 years or so now if he is still continuing it) is not mentioned at all in western media. If someone is interested about it he can use the following reference:

S. E. Shnoll et al (1998), Realization of discrete states during fluctuations in macroscopic processes, Uspekhi Fisicheskikh Nauk, Vol. 41, No. 10, pp. 1025-1035.

Concerning Newtonian gravitation, the expected anomalous effects are tiny. Allais effect is excellent example and I mentioned it in earlier discussion about energy conservation. This kind of effects are precious gifts for a theoretician -much more valuable than tons of data supporting existing theory – and for century ago they would have received the attention they deserve. Nowadays they disappear in the flood of irrelevant information and hype. I am amazed that leading string theorists give no attention for an effect like this and stubbornly continue to claim that string theory is the only logical possibility.

Returning to the topic: there is no need to assume that neutrinos cause the effect. My own proposal is based on prediction of what I call nuclear string model which I briefly described in the earlier posting. X rays from Sun would induce transitions between standard states and exotic states of nuclei. In exotic states one proton (say) is replaced with neutron and neutral color bond connecting nucleons with quark and antiquark at its ends has been replaced with positively charged one. This involves besides the absorption of X ray also W boson emission from quark of color bond absorbed by quark inside proton and tranforming it to neutron. A weak process is in question and the rate might be of course too low to induce appreciable effect, which would be due to the different nuclear properties of the ordinary and exotic nucleus so that the average. As a reference one might take the life time of neutron and nuclear life times varying in huge range.

The hierarchy of Planck constants is also a basic prediction of TGD. The general prediction is the existence of scaled up variants of also weak gauge bosons with scaled up Compton lengths. If weak process occurs in scale below this length scale, weak bosons are effectively massless and the rates are of same order of magnitude as those for electromagnetic process. Addition of p-adic length scale hypothesis allows to develop suprisingly detailed and even quantitative models for quantum biology based on this vision.

P. S. Here is a list of references about nuclear rate anomalies.

H. J. Assenbaum, K. Langanke and C. Rolfs (1987),

Z. Phys. A 327, 461.

C. Rolfs and W. S. Rodney (1988), Cauldrons in the Cosmos (Chicago, IL: Universy of Chicago Press).

C. Rolfs et al (2006), High-Z electron screening, the cases ^{50V(p,n)^{50Cr and ^{176Lu(p,n), J. Phys. G: Nuclear. Part Phys. 32 489. Eur. Phys. J. A 28, 251-252.

C. Rolfs et al (2006), First hints on a change of the {^22Na beta decay half-life in the metal Pd, Eur. Phys. J. A 28, 251.

S. E. Shnoll et al (1998), Realization of discrete states during fluctuations in

macroscopic processes, Uspekhi Fisicheskikh Nauk, Vol. 41, No. 10, pp. 1025-1035.

J. H. Jenkins et al (2008), Evidence for Correlations Between Nuclear Decay Rates and Earth-Sun Distance. arXiv:0808.3283v1 [astro-ph], http://arxiv.org/abs/0808.3283.

J. H. Jenkins and E. Fischbach (2008)

Perturbation of Nuclear Decay Rates During the Solar Flare of 13 December 2006, arXiv:0808.3156v1 [astro-ph].

GOES X-ray flux plot. http://www.swpc.noaa.gov/rt_plots/xray_5m.html.

GSI collaboration (2008), Observation of Non-Exponential Orbital Electron Capture Decays of Hydrogen-Like ^{140Pr and ^{142Pm Ions. http://xxx.lanl.gov/abs/0801.2079.

Jester. Hitchhikers-guide-to-ghosts-and-spooks in particle physics. Blog posting.

http://resonaances.blogspot.com/2008/11/hitchhikers-guide-to-ghosts-and-spooks.html.

Sun activity also has some effectson health and psyche. Maybe it is the nuclear link that achieve that?

I have read about earthquakes as instance, and they are linked to an elevated Rn-level in the atmosphere. Also other catastrophes get that effect. This has been linked to hallucination rate of pilots and errors made. It also has a link to observations of UFOs.

Rn is a gas in the earth, and movements of the crust release it. Would this mean that the sun activity works on the movements of the Earth crust?

In biological systems there is a diurnal rhythm in metabolic rates and mitotic rates due to changes in the EM-field or Ca-resonancies, possibly also other metals as Fe-resonancies? This is wellknown from cancer research etc.

Light invokes on melatonin (epiphyse), thyroxine etc. hormones and cholesterol, and coorporate with other metals.

NEW INSIGHTS INTO MELATONIN REGULATION OF CANCER GROWTH

… Sauer, RT Dauchy, EW Holowachuk, MS … – Melatonin after four …, 1999 – books.google.com – as instance.

This is somewhat off topic but talks in favour of an changing rate of decay, maybe not only for radionucleotides? Everything almost change a bit. One longstanding problem is the diurnal rhythm in cell mitosis in in vitro cell cultures. It depends on EM-waves?

For myself I think it is best to “watch and wait.” If something comes of this then fine. The whole business seems too muddled. Theories might languish for a time, but experimental data should usually shout and rise forth quickly. I tend to be cautious about experimental claims that remain in a semi-submerged state.

As for X-rays inducing quark transitions, say u –> d, that is on the order of a 10MeV energy transition. A photon might of course do this,

γ + u – -> d + e + bar-ν

is certainly possible. In fact near the EW realm this is quite common and the photon can by interchanged with the Z^0. However, consider the energy here. These photons are not X-rays, but gamma rays. The are also high energy gamma rays, far more energetic than most photons from the sun. So I think this is an unlikely process. It could also be removed with sufficient shielding.

I do not believe in ad hoc model building to explain anomalies. Various X-ino explanations for dark dark matter belong to this category if explanations. Genuinely new theory usually predicts a lot of unexpected experimental effects and TGD especially so because fractal hierarchies are its basic prediction. The prediction is not prediction of some exotic particle but hierarchies of scaled variants of standard model physics and interpreted in terms of dark matter.

Concerning the rates the low energy of X-rays might well make too slow the process transforming nuclei between their exotic states. But as I mentioned, there is a loop here.

Repeating myself, the hierarchy of Planck constants predicts scaled up versions of weak bosons with unusually large Compton length with same mass but effectively massless below Compton scale and p-adic hierarchy suggests scaled variants with scaled down mass (by half octave) and scaled up Compton length. This predicts that weak interactions can become as strong as em interactions in arbitrarily long length scales.

This provides explanation also for the mysterious chiral selection in living matter requiring parity breaking gigantic as compared to that predicted by standard model with weak bosons with standard masses and standard Planck constant and leads to a plethora of quantitative predictions. Large hbars also explain macroscopic quantum coherence in bio scales for which experimental evidence is increasing rapidly (consider only discoveries about photosynthesis).

The color flux tubes assumed to connect nucleons inside nuclei could be dark a also the quarks at their ends: nuclei wold contain dark part. If one takes parity breaking in living matter seriously these flux tubes interpreted as flux tubes associated with classical color magnetic fields could be of atomic size. keV scale actually corresponds to atomic size scale and even larger. Could the dark weak bosons possibly involved be effectively massless in atomic length scale at these flux tubes?

This is of course speculation, but part of much bigger picture rather just conjecturing some exotic particle with desired properties to explain some particular anomaly.

Matti,

Largely my sense is to wait out the situation and see how the data falls in the end. I must confess I am not sure this will in the end amount to a lot. Again I call this the Fischbach effect, where as you might recall in the mid-1980s there was a lot of noise and flurry over his fifth force, which eventually faded into an historical footnote of wrong physics.

P-adic physics involves the aspects of orientifolds and other structures. I am not sure what is meant by hierarchies of Planck constants. Planck constant and the speed of light are conversion factors, and unitless in naturalized units. ħ converts between one set of commuting observables and the other. Remember that for a quantum system with 2n degrees of freedom q_i and p_i a observer is only able to access half of these. Similarly the speed of light is a conversion factor between time and distance. These are then also units that when scaled up, say you try to increase the speed of light, or if you adjust ħ that other observables scale up in a way so as to mask this appearance. For instance the speed of light is a factor in a projective geometry (PSL(2,C)) and the rescaling has not effect on the structure. The Planck unit is similar in this regards, though how this works is a bit stranger to describe.

The hierarchy of Planck constants is of course consistent with conversion factor idea. This kind of confusion would be horrible blunder for a theoretician above 10 years age;-).

The minimum value of Planck constant can be taken to be unit with suitable choice of units and depending on scenario integer multiples or even rational multiples appear.

If I accept the mechanism how hierarchy of Planck constants emerges from basic TGD without any additional postulate, only integer multiples are possible.

The mechanism would be the extreme nonlinearity and vacuum degeneracy of Kahler action. The correspondence between canonical momentum densities and time derivatives of imbedding space coordinates is 1-to-many, something not encountered in ordinary wave mechanics in practice. This leads to introduction of covering space of imbedding space as a convenient description of the situation

The effective values of the Planck constant describing the situation when sheets of covering are regarded as one and same is integer multiple of the ordinary one and the integer is the number of sheets of the covering. Anyons and fractional quantum Hall effect can be also understood in terms of this mechanism.

I suppose I have trouble seeing how this differs from the S-duality

qg = nħ

for certain values of n. In your case the value of n would be prime valued or p-adic valued. Some form of orbifold or orientifold compactification, or a discrete subgroup on a manifold might then induce this sort of structure.

Maybe it might be possible to understand the quantization in this manner . InTGD framework electric-magnetic duality is however replaced with what I call weak form of electric-magnetic duality. It states that the Kahler electric field at light-like orbits partonic 2-surfaces (identified as wormhole throats at which induced metric changes signature for Euclidian for CP_2 type vacuum extremal to Minkowskian for the background space-time sheet) is proportional to Kahler magnetic field. Partonic 2-surface correspond to CP2 sized wormhole throats and if they are homologically non-trivial in CP_2 homology the magnetic flux which is integer valued so that the classical quantization of Kahler electric charge reduces to that for Kahler magnetic charge. This boundary condition at wormhole throats led to a breakthrough in the mathematical understanding of the theory. I will not go to this however.

One theoretical motivation for the quantization of Planck constant could be the idea that Nature is basically theoretician-friendly and cures the basic head ache of the theoretician caused by the failure of perturbation theory at strong coupling.

The quantization of hbar would mean proportionality of gauge coupling strength to 1/hbar. Therefore the quantization of Planck constant makes possible perturbation theory in a situation when coupling becomes strong or alternatively, almost vacuum extremals of Kahler action are in question so that the exponent of Kahler function does not converge rapidly around its maximum and perturbation theory fails since very large fluctuations contribute.

The phase transition increasing hbar and reducing the value of gauge coupling strength or more general parameter (say Z_1Z_2 alpha in case of electromagnetism or GMm/hbar in the case of gravitation above Planck mass scale) to a small value and makes perturbative description possible in terms of states at multisheeted covering. One can say that the system becomes unstable against splitting to multisheeted structure describable in terms of covering so that the Kahler action and thus Kahler function becomes multiplied by n and convergence of functional integral over 3-surfaces is guaranteed.

Besides the quantal effects of ELF em fields on brain which should not be possible by the fact that energies are below thermal energy for ordinary value of Planck constant, one of the physical motivations for the quantization of hbar was the observation of Nottale that orbits of planets in solar system seem to be Bohr orbits in reasonable approximation for a gigantic value of Planck constant proportional to GMm. The rough idea is that dark matter at space-time sheets mediating gravitation corresponds to this extremely large Planck constant and ordinary matter condenses around it at approximate Bohr orbit.

There could be a connection or analogy with stacks of branes of M-theory which also relate to non-perturbative effects and dynamically generate gauge symmetries but I do not have competence to say anything detailed about this.

Matti,

There is a lot here you write that just does not make much sense to me right off. The matter of wormholes is interesting, though a wormhole has the topology on a spatial manifold of S^1xS^2, or a 3-sphere where two 3-balls are removed and connected by a 3-cylinder. This is different from CP^2. However, the duality between gravitational mass and its dual NUT charge can be worked with. A D3-brane may be constructed with a Dirac-Misner string (a gravitational analogue of the Dirac monopole string) as a Taub-NUT spacetime bolted on. This gives a metric with the sqrt{D5D1) as the tt term and reciprocal of the rr term. Some interesting developments can be explored this way.

I still say there is only one “hbar,” but where some multiple of that can be derived by orbifold winding, which could obey for some systems a prime or Mersenne prime rule. More reasonably maybe one can perform some sort of Godel numbering that has a prime rule or a p-adic rule. However, the idea of hierarchies of Planck constants is a bit strange.

Yes. I did not explain in any detail what I mean with wormhole. What is essentially new is that I am talking about 4-D surfaces rather than abstract metrics of GRT. This is a big deviation from GRT and it is better to forget general relativistic associations altogether. The following explains what I

mean with wormhole throats.

a) CP2 type vacuum extremals are basic solutions of field equations. These vacuum exrremals are warped imbeddings of CP_2 to M^4 xCP_2 with metric and Kahler form of CP_2 but having one-dimensional random light-like curve as M^4 projection. They are excellent candidates for space-time correlates of elementary particles. Note that the Euclidian signature of the induced metric is perfectly sensible since Poincare symmetry is realized at imbedding space level.

b) Their deformations can be glued to background space-time sheet with Minkowskian signature of induced metric. The signature changes at some 3-D surface which has degenerate induced metric and is metrically 2-D. This gives a generalization of conformal invariance of string models. I call this light-like surface wormhole throat.

c) Wormhole throat is a carrier of fermionic quantum numbers (also many fermion states having interpretation as superpartners of basic fermion state) . This is nothing but holography.

d) One can also take two Minkowskian space-time sheets and connect them by wormhole contacts which are pieces of CP_2 type vacuum extremals. This gives a pair of wormhole throats and the interpretation is as a counterpart of a boson or of its superpartner. Bosons emerge.

e) The CP2 type extremals or equivalently these light-like wormhole throats define the lines of generalized Feynman diagrams. This means geometrization/topologization of Feynman diagrammatics. Gluing of lines at ends means gluing along partonic 2-surfaces at ends of 3-D lines. This means deviation from string diagrams which in TGD framework have in terms of propagation along two different routes for single particle rather than decay of particle.

If one accepts the proposed origin of hbar hierarchy one could say that there is single hbar for each sheet of covering. One can however also treat them as single singlet sheet (they have same canonical momentum densities and same action are for practical purpose identical copies of each other) n-fold hbar since action is multiplied by n or equivalently hbar is multiplied by n. My terminology reflects the original proposal that the hierarchy is something completely independent of basic TGD. The understanding in terms of 1-to-many relation between canonical momentum densities and time derivatives of imbedding space coordinates emerged only few months ago as I wrote article series to Prespacetime Journal.

It is quite understandable to try to understand this in terms of superstring or GRT based associations but this easily leads to astray since space-times are 4-surfaces now..

I am still not entirely clear about a lot of this. Is there any connection between this association between wormholes and elementary particles and the BPS charge with black holes?

There is only analogy with black holes. For wormhole throats both induced 4-metric and 3-metric become degenerate because signature changes. For blackhole horizon metric becomes also degenerate. For wormhole throats interior metric is however Euclidian whereas for blackholes it is Minkowskian.

The wormhole throats would however play a role very similar to that proposed for blackhole horizons in holographic scenarios. Holography is very strong since one has effective 2-dimensionality since only 4-D tangent space-time data at partonic 2-surface remain as a remnant of 4-dimensionality (recall that the orbit of partonic 2-surface is extremal of Chern-Simons subject to constraint from weak form of electric-magnetic duality).

This is absolutely essential: otherwise one would have topological QFT with no momentum degrees of freedom. Now one has “almost topological” QFT since Kahler action reduces to Chern-Simons action because Coulomb term in Kahler action vanishes by field equations and only boundaries term reducing to Chern-Simons by duality remains. The vanishing of Coulomb term follows from the assumption that the flow lines of Kahler current define Beltrami flow which by definition defines a global coordinate).

That elementary particles would be basically Kahler monopoles came as one of the many surprises related to the weak form of electric-magnetic duality. The monopole charge is neutralized by throat with opposite mopole charge in weak scale: this throat carries also weak isospin neutralizing weak charge so that only em charge is visible in longer scales. One could speak of electroweak confinement. In the case of color confinement similar mechanism at QCD confinement scale would be at work too.

The presence of Kahler electric and magnetic charges brings in mind SUSYs where similar things happen. Now magnetic charge is however purely homological. That something analogous to self duality is in question means that electric and magnetic monopoles are one and same object. One might perhaps say that magnetic and electric phase are identical.

What would be interesting is if S duality between a gauge charge and its magnetic dual and T duality are in some ways aspects of a general symmetry.

Do you mean like U-duality?

U duality is a mixing of S and T duality, or what results with STSSTS or some such thing, where there are indices on the terms to indicate directions and so forth. What would be interesting is to show that S and T transformations are special cases of a general transformation system that is itself a gauge field, or a field that transform by some general group of modular forms. We might call this U-dualtiy, but what I have in mind is a bit more than the standard idea.

I am not competent in string landscape-ology so that I cannot say anything interesting about S, T or U.

There is however another central duality in TGD framework which I have christened M^8-H -duality, here I have H =M4xCP_2 for brevity. It is crucial in the number theoretic vision. The statement is that surfaces in H can be regarded equivalently as surfaces in M^8. The induced metric and Kahler form are identical, also the value of Kaehler function.

This duality is intuitively analogous to the duality of elementary wave mechanics meaning that one can use either x-space or momentum space to describe particles. What comes also strongly in mind is the quite recent duality of twistor description of N=4 SYM in which conformal symmetries have dual counterparts acting at momentum space instead of M^4. Together these dualities give rise to Yangian symmetry which seems to be extremely powerful symmetry making perhaps N=4 SYM an integrable theory. I have commented this from TGD point of view quite recently. One can of course ask whether this possibly existing Yangian symmetry could correspond to M^8-H duality.

The description of the duality is following.

a) Points of space-time surface in M^8= M^4xE^4 in octonionic M^8 are mapped to points of M^4xCP_2. M^4 part of the map is just projection.

b) CP_2 part is less trivial. The idea is to identify M^8 as a subspace of complexified octonions, I call it hyper-octonionic. Suppose that space-time surface is hyper-quaternionic (in appropriate sense meaning that one can attach to its each point a hyper-quaternionic plane, not necessary tangent plane). Assume that it also contains a preferred hypercomplex plane M^2 of M^8 at each point or more generally a varying plane M^2 which planes however integrate a 2-surface analogous to string world sheet. The interpretation is as a preferred plane of non-physical polarizations so that gauge symmetry has a number theoretic correlate. Note that one would thus have a local hierarchy of octonionic, quaternionic, and complex planes.

Under these assumptions the tangent plane (if action is just the four-volume or its generalization in the case of Kahler action) is characterized by a point of CP(2) = SU(3)/U(2) where SU(3) is automorphism group of octonions respecting preferred plane M^2 of polarizations and U(2) is automorphism group acting in hyper-quaternionic plane. This point can be identified as a point of CP_2 in M^4xCP_2 so that one obtains the duality.

If duality is ok then the descriptions using PoincarexSO(4) as isometries of M^8 and Poincare xSU(3) as isometries of H should be equivalent. The interpretation in hadron physics context would be that SO(4) is the counterpart of color group in low energy hadron physics acting on strong isospin degrees of freedom and and SU(3) that of QCD description useful at high energies. SO(4) is indeed used in old fashioned hadron physics when quarks and gluons had not yet been introduced. Skyrme model is one example.

As already noticed, the generalization of the Yangian symmetry of N=4 SYM by replacing point like particles with partonic 2-surfaces would mean that conformal group of Minkowski space defining Yangian in N=4 SYM is replaced with its Kac-Moody variant and various super conformal algebras are replaced with their Yangians. This would mean a horrible extension of the already impressive symmetries of TGD and might be enough to fix scattering amplitudes more or less completely.

If the connection with M^8-H duality is true then one would however have SO(4) and SU(3) in sector and its dual. The problems is that SU(3) is not SO(4)! One could perhaps think that duality maps SU(3) as octonion automorphisms to color SU(3) acting as isometries of CP_2 and U(2) leaving quaternionic tangent plane invariant to electroweak U(2) acting as holonomies of CP_2. This would mean a rather natural inclusion of super counterpart of electroweak gauge group the Yangian. Maybe this might work.

There is in the Jordan algebra there are 3 copies of the octonions and three scalars. That is 27 dimensions in total. A constraint on the three scalars defines a light cone, which reduces the dimension to 26. This is related to the 26 dimensional bosonic string, but where 10 dimensions is the supergravity sector of type II strings and the other 16 dimensions is an E_8xE_8 heterotic sector. There are dualities (actually trialities) in this system between 8 dimensional spaces. So there are structures which involve dualities between 8 dimensional spaces which are octonionic valued.

The 24 dimensions associated with the three octonions clearly involve gravity. It is the case that CL(16) is a bit big 256^2 = 65536, which is the number of states. However, for the SO(24) group in the bosonic string sector there are a lot of states as it is. For the open string the Regge trajectory predicts states α’M^2 = -1, which are the ground state tachyons. States of the form α’M^2 = 0 are 24 massless polarized vector bosons. From there α’M^2 = 1 states are

α^i_{-2}|0,k>, α^i_{-1}α^j_{-1}|0,k>

which in SO(N) there are N and (N + 1)N/2 states, where N = 24 gives 24 and 300 states. Now if we go to α’M^2 = 2 we have

α^i_{-3}|0,k>, α^i_{-2}α^j_{-1}|0,k>, α^i_{-1}α^i_{-1}α^j_{-1}|0,k>

where by similar counting N, N^2, (N+2)(N+1)N/3! gives 24 + 576 + 2600 = 3200 states. This is the maximum spin, or spin = 2ħ. We then work to include the states of the closed strings with α’M^2 = 4(N-1), with tachyons α’M^2 = -4, then states

α^i_{-1}{tilde-α}^j_{-1}|0,k> = |Ω^{ij}(k)>

The symmetric and antisymmetric portions of these two sets of (N – 1)N/2, or 276, states (552 in total) and the trace terms are 24 dilatons — a total of 576 states. The symmetric off diagonal elements of the tensor Ω^{ij} gives the graviton, and the antisymmetric elements are a gauge-like field.

For the closed string there are 576 states, which is greater than the 256 left and 256 right states we might expect from CL(8). Yet we can impose restrictions on the number of states, by realizing there is some metric condition (gauge-like coordinate condition) on the four dimensional spacetime (10 components per R and L modes) which reduces this to 256! Yet all we have are the states of the graviton and an associated gauge-like field. We don’t have a supergravity multiplet. So to include the superpartners of the graviton (type IIB strings) we need all that open string stuff, and we need to work in the associated 10 and 11 dimensional superspace.

The F_2 and G_2 groups are centralizers in E_8, and G_2 is the automorphism group of E_8 and F_4 of the Jordan exceptional algebra. The 7-sphere plays a central role in this matter, for it defines a holonomy which is crucial in defining a cubic action. I will say that this is holographic, and there are ways of working a matrix theory this way. The best approach is the Jordan exceptional algebra. This is the algebra of the octonions, which extends the E_8 octonions into a triality. The J^2(O) = R (+) V [(+) = oplus] is of the form

J^2(O) =

|z_1 O |

|O z_2|

which is extended to the J^3(O) matrix algebra. The triality in J^3(O) includes an E_8 matrix of vectors and two spinor matrices. These do correspond to a Feynman diagram where a vector (boson) decays into a spinor and its conjugate. The J^3(O) is R (+) J^2(O) (+) θ (+) bar-θ,

J^3(O) =

|z_1 O O’|

|O z_2 O”|

|O’ O” z_3|

for the spinorial (fermionic fields) octonions in O and O”. The vector term given by the ocotinion O, V J^2(O) decays into V –> ψ + bar-ψ. This is a manifestation of the automorphism of G_2, and is an elementary Feynman diagram for a supersymmetric gauge interaction..

The space here is 27 dimensional. The O’s are each 8-dimensional, which gives a general span of 3×8 + 3 = 27 dimensional. The above triality condition, along with some anomaly cancellations of vertex algebras, defines a space of reduced dimension of 8 + 3 = 11 dimensional. On the light cone frame (infinite momentum frame) the space in 27 dimensions is reduced to 26 dimensions and the 11 dimensional space to 10. These are the corresponding bosonic string Lorentizian spacetime and the supersymmetric space of supergravity respectively. The diagonal elements of this matrix define a Chern simons lagrangian of scalar terms for x_i p_i + A_i (the cubic nature of this is apparent) and a general Lagrangian defined as the determinant of J^3(O) under all triality transformations defines a cubic action. This then determines an equivalency between a field theory term and a dual boundary field. This field boundary of dual field is a cornerstone of AdS.CFT. The AdS/CFT can be found for the case where two scalars in J^3(O) define timelike directions.

The G_2 group acts on 7-manifolds as a system of three-forms, and this exceptional group is very interesting. The G_2 group is then an holonomy with R^3 bundles over a quaterionic space. The G_2 group is a determined by space C^5, where for every point a ∈ C^5, let the 2-plane π_a exist in the tangent space T_aC^5. This means the metrics for the 7-manifolds are determined by five parameters plus two abelian isometries. These isometries have fixed points on the G_2 manifold, which are two combinations of Killing vectors with codimension 4. In general we may consider the manifold M^4×M^7, where M^4 may be any spacetime (M, g). The simplest spacetime is a Minkowski spacetime. The structure defines a four dimensional field theory which for N-Killing spinors is N supersymmetric for a G_2 holonomy on M^7. The exceptional group G_2 is the automorphism group of the octonions o = x_0I + x_ae_a for the basis elements e_a obeying the algebra

e_ae_b = -δ_{ab} + ω_{abc} e_c

where the tensor ω_{abc} is determined by products of three octonionic elements which are G_2 invariant. This is the tensor component of a three-form Ω which is expanded according to elements on the M^7 as

Ω = (1/3!)ω_{abc}e_a∧e_b∧e_c

= e_1∧e_2∧e3 + e_4∧e_3∧e_5 + e_5∧e_1∧e_6 + e_6∧e_2∧e_4 + e4∧e_7∧e_1 + e_5∧e_7∧e_2 + e_6∧e_7∧e_3

= e_1∧e_2∧e_3 + (1/2)e_i∧e_m∧J_{i mn}e_n

so the spin tensor J_{i mn} has the element i = 1,2,3 and m,n = 4,5,6,7. This is an aspect of the alternativity of the octonions which define triplets of quaternions as seen in the index i. The product of the octonionic elements means the product of spin tensors obeys J_i*J_j = -δ_{ij} + ε_{ijk}J_k. By definition the G_2 holoomy means the three form is closed dΩ = 0, and the Hopf fibration S^3 – -> S^7 – -> S^4 induces a symmetry between elements in seven dimensions so d*Ω = 0. In addition for the spin connection σ^{ab}, the projection with the tensor is zero ω_{abc}σ^{ab} = 0. This means that Ω is covariantly constant, which is a condition it being a Killing spinor. This gives a set of first order differential equations for the metric elements, The existence of additional covariantly constant field-form restricts the G_2 holonomy so the Killing spinor equation has more than one solution and the 4 dimensional field theory has extended N > 1 supersymmetry.

As far as I understand you talk about G_2 manifolds as they appear in M-theory as 7-D internal spaces. In TGD framework G_2 manifold is somewhat more general notion since M^8 -or rather its tangent space represented by gamma matrices- is dentified as subspace of complexified octonions. Since G_2 acts on imaginary octonionic units (multiplied by commuting imaginary unit) onlly, this does not change the situation in any manner if one considers the algebra generated by octonionic gamma matrices with complex coefficients.

As automorphic group of octonions G_2 leaves real unit intact and this represents preferred time direction so that G_2 must be subgroup of SO(7). G_2 replaces SO(7,1) as the subgroup of isometries preserving given octonion structure and SO(1,7)/G_2 serves as moduli space for non-equivalent octonion structures in E^8 (or M^8 as in my case).

G_2 indeed emerges quite concretely when one replaces gamma matrices of M^8 or H with their octonionic representation: one can still define sigma matrices but they generate G_2 instead of SO(7,1) and acts as as maximal holonomy. I have studied the counterpart of the modified Dirac equation for these gamma matrices – not strictly speaking matrices they are non-associative- and quite interesting results follow. Holonomy is in this case much smaller than the maximal one.

Whether the octonionic variant of Dirac equation really makes sense physically is not clear and it might be that the octonionization is only needed to define what hyper-quaternionic space-time surfaces are as a condition that induced gamma matrices (or their appropriate generalizations) at space-time surface span via the commutators a complexified quaternionic sub-algebra rather than entire complexified octonionic algebra. Hyper-quaternionic gammas allow representation as matrices so that at spacetime level it does not matter.

The other octonion related groups do not have obvious role in my personal theory landscape. The criticism of the work of Lisi however inspired following observation. E_8 Kac-Moody has same number of Cartan generators as the Kac-Moody algebra for the isometries and holonomies of H (Poincare x SU(3)xU(2)_ew) so that the construction of the Kac-Moody algebra as exponentials of Cartan algeba generators would give both E_8 and isometry Cartan algebra by a proper choice of weights.

G_2 holds an S^7 fixed, or acts as a restriction on SO(8). A semidirect product of SO(8) with S^3 or SU(3) gives the F_4 automorphism of J^3(O). So the G_2 acts as a triality operation on SO(8) ~ SO(7,1), that holds F_4 fixed in the E_8, or F_4 and G_2 are centralizers.