### About the art of rediscovery

Lubos has been talking about recent progress related to firewall paradox of blackhole physics (see this and this). Lubos has been especially happy about Maldacena-Susskind proposal for wormhole connections as a correlate of entanglement. I believe that this idea as such is wrong and represents the last attempts to save the general relativity based view about space-time: to make real progress in quantum gravity one must leave the general relativity based view about geometry and replace it with sub-manifold geometry as done in TGD.

The idea about about geometric correlates of entanglement is however deep. The braiding of magnetic flux tubes connecting entangled systems would serve as a geometric and topological space-time correlate of entanglement. It also happens to be ten year old basic ideas of TGD. I have been talking a lot about it also in this blog - and probably also in Lubos blog and viXra log where Lubos has also often visited- and it is nice that my blog is read. Lubos however refused from any public blog communications because he believes that I suffer some fatal infective disease - maybe academic equivalent of leprosy;-).

As a matter of fact, I have been patiently waiting that some name would finally realize the depth of the idea about geometric correlates of entanglement and decide to rediscover it. Now my patience has been repaid. This correspondence has even got a name: ER-EPR correspondence. Maldacena and Susskind apply this idea to solve firewall paradox. This is very nice but to my opinion the idea is applied to solve a wrong problem. The idea of this caliber would deserve something much better.

I see the firewall paradox as a pseudo-problem due to wrong belief about what blackhole interior is (see this and this). In TGD framework blackhole interior is generalized and becomes Euclidian region of space-time surface. Firewall paradox disappears. The Minkowskian-Euclidian horizon is of course something very real: the outer surface of a line of generalised Feynman diagrams thickened to four-surface. If TGD view is correct, the applications are much more wider to every day physics, especially so in biophysics and a detailed vision about quantum biophysics is developing. Here is a something really juicy for a namy-enough rediscoverer!

Susskind already earlier discovered the p-adic number fields and applied them to solve some problem of some hopeless cosmological scenario inspired by string theory - much more intelligent applications are waiting for rediscovery - just visit my hope page and choose your favourite idea! Earlier Susskind rediscovered holography: in TGD framework it follows as a 4-D version from general coordinate invariance (see this). Few years ago TGD version of the holographic principle was replaced with a stronger form in which 2-D surfaces and their 4-D tangent space data carry the data characterising quantum state: effective 2-dimensionality.

Holography represents the oldest layer of quantum TGD born around 1990 when the vision about the geometry of WCW as space of 3-surfaces whose Kähler metric is determined by Kähler function defined by a preferred extremal of Kä:hler action - a 4-surface uniquely associated with a given 3-surface as analog of Bohr orbit: this is just a statement of holographic principle tying together quantum classical correspondence, general coordinate invariance, and making classical physics exact part of quantum physics. This became four years before Susskind's "The world as a hologram". Most importantly, TGD holography is holography in 4-D context and replaces the unphysical 10-D space with 4-D real space-time and - as it became clear much later - also leads to stringy description of elementary particles. I am eagerly waiting that the strong form of holography would be discovered by some name.

Also Tom Banks - the teacher of Lubos - has been busily re-discovering TGD related visions: his CV already contains hyper finite factors of type II_{1} and causal diamonds. I am really happy that big names understand the value of great ideas and are ready to take trouble of rediscovering them. It is of course a pity that they forget to mention the real father of the idea! But I of course understand that big names have much more important things to do than worrying about minor details like this!

## 24 Comments:

http://t.co/SxZbQ7wCto

Dear Matti,

In modified Dirac equation gauge potential generators is not concluded in the covariant derivative term. So there is the question that how can regard the interactions? One can add the Cartan algebra generators of isommetries of imbedding space and it contain strong interactions. Also strong interaction contains electroweak interaction because U(2) is subgroup of SU(3). This view is very odd and interesting.

At quantum TGD, the spinor field in modified Dirac equation is a map from the space of 3-surfaces to elements of G/H?

Matti:

Do not be concerned about not receiving name recognition from these re-discoverers.

You have documented proof that you developed these theories prior to them.

Your recognition will come from somewhere. That much I know.

This comment has been removed by a blog administrator.

To tyy:

please, no personal insults. I want to preserve this blog as a forum for civilized discussion.

Dear Matti,

I make my last question more clear:

At classical level, the spinor field takes the point of space time at imbedding space as argument and gives the spinor associated with the point. Components of the spinor are complex numbers.

At quatum level, seond quantized induced spinor field takes point of WCW(3- surface) and gives WCW spinor. Components of WCW are many fermionic states. The fermionic states are elements of G/H. the algebra of G/H acts on the 3-surfaces of WCW.

is there any incorrect?

To Hamed:

your view looks correct. I just restate from slightly different emphasis.

Covariant derivative term *is* (!) present in modified Dirac equation and of same form as for the counterpart of massless Dirac equation. The gauge potentials are the spinor connection are however *induced* that is components of CP_2 projected to the space-time surface: A_mu= A_k partual_mu s^k.

This is important difference. Everything comes out from geometry. No fields are postulated as primary entities.

This gives couplings to classical *electroweak* gauge potentials. Color gauge potential couplings are not obtained at classical level: since color is not spin like quantum number but analogous to angular momentum. Color partial waves emerge at the level of WCW but not at the level of space-time. Here is distinction between TGD color and QCD color.

The conjecture is that color interactions are at the QFT limit of point like particles necessarily gauge interactions since there is no other option in QFT context. Since the mathematical structure is that of generalized Kac-Moody algebra, and Kac-Moody algebra is very near to gauge algebra there are excellent reasons to believe that this is the case.

More concretely, at WCW level one can assign to given state a color partial wave in cm degrees of freedom of partonic two-surface. In these degrees fermion is represented as a partial wave of imbedding space spinor. The imbedding space coordinates are interpreted as cm coordinates.

For quark chirality imbedding space spinor has triality t=1 ( t=-1 for antiquarks) and for leptons it is triality: this comes from different couplings to induced Kahler gauge potential needed to achieve acceptable spinor structure. This predicts the existence of colored excitations of leptons and quarks: most them have masses with CP_2 mass scake and are un observable in recent day physics.

For spinor harmonics of CP_2 trialities are correct but the correlation of color and electroweak numbers is wrong. The correct correlation is possible to obtain since the analogs color Kac Moody algebra and symplectic algebra of delta M^4xxCP_2 (analog of Kac Moody algebra associated with symplectic group of S^2xCP_2) is needed to build states with vanishing conformal weight from those with negative (tachyonic conformal weight). These allow to have the correct color quantum numbers which do not depend on weak charges.

To Hamed:

There is indeed correlation between colour and electroweak quantum numbers for solutions of ordinary massless Dirac equation in CP_2 and imbedding space. As I explained this is wrong but colour Kac-Moody algebras associated with vibrational degrees of freedom of par tonic 2-surfaces and its centre of mass degrees of freedom help to build massless states as colour singlets for leptons and colour triplets for quarks.

I have been perhaps too lazy: some mathematical work might allow to improve understanding of this connection. This connection between holonomy and isometries is somewhat analogous to the connection between magnetic and electric fields discovered by Maxwell at his time and coming from Lorentz invariance.

About spinor field formalism.

a) Induced spinor fields are analogs of second quantizer free spinor fields and the oscillator operator algebra is used to build the generators of various super algebras. One can say that all bosonic quanta are fermion antifermion bound states so that no second quantized gauge fields appear in the theory. Only the spinors and the purely geometric degrees of freedom assignable to partonic 2-surfaces and their 4-D tangent space data.

b) The space of 3-surfaces is union of sub-WCW:s which are symmetric spaces labelled by zero modes (WCW coordinates appearing in line element as parameters only). Sub-WCW is indeed coset space G/H. G is full symplectic group of delta M^4xCP_2 and H its subgroup. This means huge injection of mathematical well-definedness to the theory. Mathematicians are intensely studying symplectic groups. Again I must however confess my laziness. The would be a lot of learning from what is known.

Dear Matti,

Thanks,

I didn’t see this before. Interesting:

“Negative and positive energy space-time sheets are space-time correlates for bras and kets and the meeting of negative and positive energy space-time sheets is the space-time correlate

for their scalar product. negative and positive energy space-time sheet meet at X3.”

Hence the geometric correlate of the scalar product is X3. What is similarity between them leads to the geometric correlation?

I can only understand from the scalar product the interpretation as probability amplitude for the state ket to collapse into the state bra. So does this interpretation have any similarity with X3?!!!

I have probably said this in positive energy ontology.

It is good to re-articulate it in zero energy ontology. In ZEO the quantum superposition of space-time sheets inside CD is replaced in each qjump with a new one.

They have 3-surfaces at their ends and in quantum jumps the geometric arrow of time changes at imbedding space level. The dissipation for the dynamics of Kahler action as space-time correlate of quantum dissipation takes in opposite directions of imbedding space time.

Given X^3 as end point of space-time evolution becomes initial point of space-time evolution in reverse time direction. In this sense the positive and negative energy space-time sheets indeed meet at X^3.

Matti

Is there any relation between euclidian areas and zero energy states, between minkowskian and positive/negative areas of space-times? What time is it in the euclidian area? ;)

To Anonymous:

Interesting questions.

a) One could define volumes of various sub-manifolds using a) the square root of the determinant of the induced metric or b) of its absolute value. Both are general coordinate invariant definitions.

b) Space-like areas in Minkowskian and Euclidian region obtained using definition a) obey same formula since minus signs cancel. For Minkowskian 2-surfaces the area is imaginary. String world sheets are prediction of the theory and it would not be surprising if they would contribute exponent of imaginary area to the dependence of quantum state on this surface.

c) For definition a) and induced 4-metric the determinant is negative in Minkowskian regions and positive in Eulidian regions. In the definition of exponential of Kahler action I use this definition. Exponential from regions with Euclidian signature is

exponential of negative real valued action and means that the integral over infinite-D world of classical worlds is converging integral and makes sense mathematically. Minkowskian regions give imaginary exponential giving rise to interference effects. The two parts of Kahler action define Kahler function of WCW on one hand and Morse function on the other hand (its saddle points would provide information about the topology of WCW).

Time coordinate in Eucdlian regions is just like spatial coordinates with respect to induced geometry - that is in abstract internal geometry without any information about sub-manifold property.

With respect to imbedding space time the situation is different. For instance, CP_2 type vacuum extremals have same Kahler and symplectic geometry as canonically imbedded CP_2 in M^4xCP_2 (M^4 coordinates constant). They however have light-like random curve as M^4 projection and describe massless particle moving randomly with light velocity. Hence the time coordinate has dynamical meaning at imbedding space level. The light-likeness condition also gives rise to Virasoro conditions so that one has conformal invariance.

This is an interesting paper, although it is about Bohmian wiev. http://arxiv.org/pdf/1307.1714v1.pdf

They talk of priviledged foliation of spacetime, which means an arrow of time if I understand it right.

"the required foliation could be covariantly determined by the wave function" that is time as a deformation and asymmetry, seen in dilation / compression (red/blueshift) which basically is the same as gravity, AND RELATIVITY on microscale? Relativistic massivation is important there. This makes time to an energy question, I think?

On tgd framework imbedding spagetti coordinates delfiinejä naturalistiseen foliations. For spacetime sheets Minkowskian or Robertson-Walker coordinates.

I am sorru for my iPad. If it does something it is something completely mad.

Enjoying the discussion. Passing along this link that Orwin found and shared on viXra log the other day (Matti, why don't you join in, we miss your input :) )

http://arxiv.org/abs/1010.2963

Scalar--flat Kähler metrics with conformal Bianchi V symmetry

Maciej Dunajski, Prim Plansangkate

(Submitted on 14 Oct 2010 (v1), last revised 22 Apr 2011 (this version, v2))

We provide an affirmative answer to a question posed by Tod \cite{Tod:1995b}, and construct all four-dimensional Kahler metrics with vanishing scalar curvature which are invariant under the conformal action of Bianchi V group. The construction is based on the combination of twistor theory and the isomonodromic problem with two double poles. The resulting metrics are non-diagonal in the left-invariant basis and are explicitly given in terms of Bessel functions and their integrals. We also make a connection with the LeBrun ansatz, and characterise the associated solutions of the SU(\infty) Toda equation by the existence a non-abelian two-dimensional group of point symmetries.

http://web.mit.edu/physics/news/spotlight/20130718_zwierlein.html

http://www.newscientist.com/article/mg21228342.400-spaghetti-functions-the-mathematics-of-pasta-shapes.html?full=true

Spaghetti functions: The mathematics of pasta shapes

18 October 2011 by Richard Webb

Magazine issue 2834. Subscribe and save

What possessed an architect to boil down the beauty of pasta to a few bare formulae?

ALPHABETTI spaghetti: now there was a name to conjure with when I was a kid. Succulent little pieces of pasta, each shaped into a letter of the alphabet, served up in a can with lashings of tomato sauce. Delicious, nutritious – and best of all they made playing with your food undeniably educational.

Some thirty years on, in an upscale Italian restaurant near the London offices of New Scientist, I decide against sharing this reminiscence of family mealtimes with my lunching partner. George Legendre doesn't look quite the type. For one thing, he is French, and possibly indisposed to look kindly on British culinary foibles. For another, he is an architect, designer and connoisseur of all things pasta. In fact, he has just compiled the first comprehensive mathematical taxonomy of the stuff.

Quiz: Can you match the pasta with its mathematical equation?

According to a recent survey by the charity Oxfam, pasta is now the world's favourite food. Something like 13 million tonnes are produced annually around the globe, with Italy topping the league of both producers and consumers, according to figures from the International Pasta Organisation, a trade body. The average Italian gets through 26 kilograms – that's the uncooked mass – of pasta each year.

The plate of paccheri in front of me seems positively modest by comparison. To my untrained eye, it consists of large, floppy and slightly misshapen penne. I might not be too wide of the mark. "If you look carefully, there are probably only three basic topological shapes in pasta – cylinders, spheres and ribbons," Legendre says.

Nevertheless, that simplicity has, in the hands of pasta maestros throughout the world, spawned a multiplicity of complex forms – and inspired many a designer before Legendre (see "Primi piatti"). It was a late-night glass of wine too many at his architectural practice in London that inspired Legendre, together with his colleague Jean-Aimé Shu, into using mathematics to bring order to this chaotic world.

"The first thing we did was order lots of pasta," Legendre says. Then, using their design know-how, they set about modelling every shape they could lay their hands on to derive formulae that encapsulate their forms. "It took almost a year and almost bankrupted the company," he says.

For each shape, they needed three expressions, each describing its form in one of the three dimensions. This provides a set of coordinates that, plotted on a graph, faithfully represents the pasta in 3D. The curvaceous shapes of most pasta lend themselves to mathematical representations mainly through oscillating sine and cosine functions.

For some pastas, the right recipe was obvious. Spaghetti, for example, is little more than an extruded circle. The sine and cosine of a single angle serves to define the coordinates of the points enclosing its unvarying cross- section, and a simple constant characterises its length. Similarly, grain-like puntalette are just deformed spheres. The sines and cosines of two angles, together with different multiplying factors to stretch the shape out in three dimensions, supply its mathematical likeness. "The compactness of the expression is beautiful," says Legendre.

Other shapes were harder to crack. Scrunched-up saccottini, for example, looks for all the world like the crocheted representation of a hyperbolic plane that adorns my desk at New Scientist, and its shape is captured by a complex mathematical mould of multiplied sines and cosines. Simple features such as the slanted ends of penne take some low modelling cunning, involving chopping the pasta into pieces, each represented by slightly different equations.

...

http://www.scirp.org/journal/PaperInformation.aspx?PaperID=33960

"A critique of black-hole-black-body radiation, black-hole thermodynamics, entropy bounds, inflation cosmology, and the lack of gravitational aberration is presented. With the exception of the last topic, the common thread is the misuse of entropy and, consequently, the second law..."

Dear Matti,

At the measurement of position of an electron, electron is measured at a certain position. Hence at this moment, one can say it is a point like particle. But in TGD there is no point like particle at all, just there are 3-surfaces. How is it possible?

Suppose the state of an electron is in a linear combination of |z+> and |z-> that are eigen states of spin in Z direction. I mean these eigen states classical degrees of freedom(zero modes) and the linear combination of them a quantum degree of freedom. Is this correct?

I don’t understand the meaning of localization in zero modes. I understand from the “localization”, something is localized to something other. But at last year you noted my misunderstanding that there isn’t something localized to zero modes. So in the case of zero modes, which thing is localized to which thing?

Maybe in the last example of spin, if you explain the localization, I can understand better.

Dear Hamed,

the situation you describe is encountered in string models and much earlier in atomic and nuclear physics. The measurement of position generalizes. In WCW 3-surfaces associated with particle has center of mass coordinates (M^4xCP_2) and "vibrational coordinates" characterizing the shape of the 3-surface.

Localization in position measurement means localization in center of mass degrees of freedom particle like 3-surface labelled by points of M^4. This is just same as treating macroscopic object such as planet as point. In "vibrational" degrees of freedom localization does not occur but one obtains delocalized eigenstate of color charges and other observables.

WCW spinor field becomes localized in M^4 degrees of freedom in position measurement. More precisely, it is cm degrees of freedom associated partonic 2-surface with upper or lower boundary of CD in which localization takes place. This is due to strong form of holography. There are delicate issues related to the Uncertainty Principle: I have talked about this earlier and will not go into this here.

Dear Hamed,

you ask also about zero modes.

Non-zero modes - quantum fluctuating degrees of freedom - by definiotion correspond to degrees of freedom whose complex coordinates contribute to the line element of WCW Kahler metric. Complex character of the coordinates allows description of these degrees of freedom in terms of Kac Moody type algebras constructible using oscillator operators. These degrees of freedom define a coset space of symplectic transformations of delta M^4xCP_2 divided by its suitable subgroup defining measurement resolution.

Zero modes are those degrees of freedom which do not contribute to the line element. For instance, the values of induced Kahler form are zero modes and various magnetic fluxes associated with Kahler form define zero modes.

Matti, can this center of mass be in relation to the "typical point in the mass" as described in http://www.statssa.gov.za/isi2009/ScientificProgramme/IPMS/0182.pdf ?

To Stephen:

It would took long time to dig out the answer from the mathematical jargon of the article.

In any case, what cm means is intuitively obvious: some point roughly in center of M^4 projection of partonic 2-surface or entire 3-surface involving several of them. The notion of "center" is however somewhat fuzzy and the rule defining it is not unique. It must be however consistent with 4-D translation symmetry and Lorentz invariance so that cm coordinates transform like M^4 coordinates themselves. In mechanics the definition of cm is in terms of mass weighted average position for Minkowski coordinates.

Number theoretic constraints requires that the definition reduces to average defined using weighted sum rather than weighted integral which is p-adically problematic.

In braid picture partonic 2-surface contains fermions and antifermions at discrete points (braid ends) and the energy weighted average for M^4 coordinates of these points indeed reduces to a ratio of sums.

This non-uniqueness does not matter since one has general coordinate invariance in WCW.

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