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A ClassicalRadius Black Hole inOrdinary SpaceTime isconnected through a RingSingularity to a Compton RadiusVortex in Exotic SpaceTime.


A ComptonRadius Vortex inOrdinary SpaceTime isconnected through a RingSingularity to a Classical Radius BlackHole in Exotic SpaceTime.



At the Planck Mass, the Classical Radius equals the ComptonRadius, so that a Planck Mass Black Hole is also a Planck MassCompton Radius Vortex, so that

a PlanckRadius Vortex Black Holelives in both OrdinarySpaceTime and ExoticSpaceTime, acting as a Bridge or Window or Pivot betweenOrdinary SpaceTime andExotic SpaceTime, so I call itthe

Planck Pivot Vortex

whose Symmetry Groupis

(K4 \ Z3) \ Z2 =TD


The Planck Pivot Vortex gives rise to Planck FulcrumOrdinary/Exotic Duality Equations for Length L and Mass M:

L(ordinary) L(exotic) = Lplanck^2

M(ordinary) M(exotic) = Mplanck^2


 Planck Pivot Vortex structures are similar toBosonic String T-dualitystructures.

It took several e-mail messages from JackSarfatti to convince me that we can go below the PlanckScale.

One reason that I thought that we could not go below the PlanckScale was what Feynman said in his book QED (Princeton Presspaperback 1988), from footnote 1 on page 129: "... perhaps the ideathat two points can be infinitely close together is wrong ... Ifwe make the minimum possible distance between two points as small as10^(-100) centimeters (the smallest distance involved in anyexperiment today isaround 10^(-16) centimeters), the infinities disappear, all right -but other inconstencies arise, such as the total probability of anevent adds up to slightly more or less than 100%, or we getnegative energies in infinitesimal amounts. It has been suggestedthat these inconsistencies arise because we haven't taken intoaccount the effects of gravity - which are normally very, very weak,but become important at distances of [ the Planck Scale,10^(-5) gm, or ] 10^(-33) cm."

What I had not realized was that, as Kip Thorne says in his bookBlack Holes and Time Warps (Norton 1994, pages 491-492), "... in 1974... Hawking inferred as a byproduct of his discovery of black holeevaporation ... that vacuum fluctuations near a [BlackHole]'s horizon are exotic: They have negativeaverage energy density as seen by outgoing light beams near thehole's horizon. ... it is this exotic property of the vacuumfluctuations that permits the hole's horizon to shrink as the holeevaporates ... The horizon distorts the vacuum fluctuations away fromthe shapes they would have on Earth, and by this distortion it makestheir average energy density negative,that is, that is, it makes thefluctuations exotic. ... Gunar Klinkhammer ... has proved that inflat spacetime ... vacuum fluctuations can never be exotic ... RobertWald and Ulvi Yurtsever have proved that in curved spacetime ... thecurvature distorts the vacuum fluctuations and thereby makes themexotic. ...".

Feynman's Negative Energies below the Planck Scale are dueto Exotic SpaceTime Vacuum Fluctuations.

The Planck-Scale 4-dimensionalHyperDiamond Lattice used in the D4-D5-E6-E7physics model is not fundamental because it is the lattticeat the smallest possible scale, it is fundamental because itis the

Bridge LatticeConnecting Ordinary SpaceTime and Exotic SpaceTime.


There are 3 possible types of particles connectingOrdinary SpaceTime andExotic SpaceTime.

Here are orders of magnitudes of examples of each type:

Electron, Planck Mass Black Hole,Solar Mass Black Hole, and ourUniverse

based on the Planck Fulcrum Ordinary/Exotic Duality Equations:

L(ordinary) L(exotic) = Lplanck^2

M(ordinary) M(exotic) = Mplanck^2

BOTH EXOTIC SPACETIMEElectron Ring Compton Radius Vortex Singularity Classical Black Hole10^(-11) cm 10^(-55) cm10^(-27) gm 10^17 gm
Planck Mass Black HoleCompton Radius Vortex = Classical Black Hole 10^(-33) cm = 10^(-33) cm10^(-5) gm = 10^(-5) gm
Solar Mass Black Hole Ring Classical Black Hole Singularity Compton Radius Vortex10^5 cm 10^(-71) cm10^33 gm 10^(-43) gm
Universe Ring Classical Black Hole Singularity Compton Radius Vortex10^28 cm 10^(-94) cm

In Each of the 3 types, the Structure is a Sarfatti4-Mouth Structure:

Each of the 3 types of 4-Mouth Structures has its ownSymmetry Group:

Compton Radius Vortex in OrdinarySpaceTime: K4

Classical Black Hole in OrdinarySpaceTime: Z3 \ Z2

Planck Pivot Vortex: (K4 \ Z3) \ Z2 =TD


The interplay between Ordinary SpaceTime and Exotic SpaceTime isimportant in

Herbert/Sarfatti NEAR FIELDand FAR FIELD Phenomena.



Start with a

Compton Radius VortexKerr-Newman Black Hole

with a^2 greater than m^2:

Roughly, this looks like


A 1 _____________ _____________ B 2


the lines ___________ are edge-on views of the ringsingularity,

the line between 1 and 2 is the ring singularity in the ordinarypart of the extended spacetime in which distances are positive andgravity is attractive, and

the line between A and B is the same ring singularity in theexotic part of the extended spacetime in which distances are negativeand gravity is repulsive.

Since the A and B sides of the exotic singularity differ from the1 and 2 sides of the ordinary singularity in that distances arenegative or positive, respectively, and

since the A and 1 sides differ from the 1 and 2 sides in that theyare on the top and bottom of the singularity as defined by its spinon its axis,

The External Symmetries of a Compton Radius Vortex are thoseof Position in SpaceTime, Mass=Area, Spin=Angular Momentum, ElectricCharge, and ColorCharge.

The Internal Symmetry Group of the Compton Radius VortexKerr-Newman Black Hole with a^2 greater than m^2 is the Klein 4-groupK4.


For particles such as leptons and quarks that are less massivethan the Planck Mass Mplanck, the Classical Radius given by G M^2 / Ris much smaller than the Compton Radius given by hbar / M c. Someexamples of Classical and Compton Radii are:

If you tried to probe the Electron or Proton within their ComptonRadius Vortex all the way down to its Classical Radius, you wouldhave to use a probe whose energy is on the order of hbar / Rclassicalc. For the Electron, it would be EprobeElectron = 10^41 GeV, and fora Quark it would be EprobeQuark = 10^38 GeV, both far more energeticthan the Planck Energy Eplanck = 10^19 GeV.

Since any energy higher than Eplank = 10^19 GeV would disruptSpaceTime by graviton creation of newSpaceTime forming a Black Hole of mass at least the Planck MassMplanck = 10^19 GeV,

the Classical Radius Vortex of Electrons, Quarks, andother particles less massive than the Planck Mass Mplanck = 10^19 GeVdoes not exist in Ordinary SpaceTime,but lives in Exotic SpaceTime.

The only elementary particles for which the

Classical Radius

is greater than the Compton Radius are BlackHoles with mass greater than the Planck Mass.

The Compton Radius Vortices of Black Holes larger than PlanckMass do not exist in OrdinarySpaceTime, but live in ExoticSpaceTime.

The Maximal Extension of SpaceTime for such a Black Hole is shownin Figure 12.4 from General Relativity by Robert M. Wald (Chicago1984):

At such a Black Hole, you can travel from External SpaceTimeRegion I to Extenal SpaceTime Region IX by going through 3 Regions,Regions II, VI, and VII, that are inside Event Horizons.

Also, you can travel through the Ring Singularity such as fromRegion VI to Region VI' and back to Region VI.


The External Symmetries of a Classical Radius Black Hole are thoseof Position in SpaceTime, Mass=Area, Spin=Angular Momentum, ElectricCharge, and ColorCharge.

The Internal Symmetry Group of a Classical Radius BlackHole is

an extension (denoted by \ ) of

the cyclic group Z3 of the 3 InteriorRegions

of the journey from Region I to Region IX and

the group Z2 of going through the RingSingularity

from Region VI to Region VI' and back

so that the total Symmetry Group is an extension \

Z3 \ Z2


Only for a Planck Mass Black Hole

(of mass 10^19 GeV and radius 10^(-33) cm, for which theClassical Radius equals the Compton Radius)


both the Classical Radius and the ComptonRadius

be observed from both OrdinarySpaceTime and Exotic SpaceTime,

forming a Bridge or Window or Pivot between them,

so that a Planck Mass Black Hole has Symmetry Group that is anextension (denoted by \ ) of the extension Z3 \ Z2 of the ClassicalRadius Black Hole and K4 of the Compton Radius Vortex

so that the ingredients K4, Z3, and Z2 produce T = A4 = K4 \ Z3and TD = T \ Z2, and

(K4 \ Z3) \ Z2 = TD

is the 24-element Symmetry Group of a Planck Mass Black Hole.

TD, the Binary Tetrahedral Group, orDouble A4,

is the McKay group for E6 of theD4-D5-E6-E7 physics model.


E7, whose McKay group is OD,the 48-element Binary Octahedral Group, or Double S4D, appears inthe D4-D5-E6-E7 physics model as thegroup of the Super Implicate OrderMacrospace.

The 24-element Octahedral Group O, which is double-covered by OD,is the Symmetric Group S4.

Jack Sarfatti remarks(with respect to his closely related structures that motivated me towrite this page): "... Note you get the full S4 symmetry at thePlanck mass. The symmetry is broken when you move off the Planckscale. ... That's what we want. ...".

Saul-Paul Sirag remarks(with respect to his closely related structures that motivated me towrite this page): "... Ezekiel saw the 4 cherubim. John's vision ofthe throne of God in the book of Revelation has 4 "living creatures"(zoon in Greek) around the throne, and 4! = 24 elders surrounding thethrone. Of course the main number, repeated over and over is 7, whichgoes back to the 7 days of Creation + Sabboth. But there is a deepconnection between S4 and 7 as we will see. [Aside: For a while,I called the 4 objects permuted by S4 Zons.] ... Carl Jung haspointed out that the 4 cherubim correspond to 4 cardinal figures ofthe Zodiac. (He was undoubtedly not the first to notice this.) FromJung we may pass to Arthur Young, who was a student of Jungiansymbolism (he went through a long Jungian analysis, which he creditedwith the cure of his paralyzed arms -- but that's another story. Junghad emphasized the symbolism of fourness, in addition to the wellknown threeness of the Christian trinity. Because of Arthur Young'sfascination with the fourness, he was very intrigued with thetetrahedron. In March of 1974 he asked me (as his "researchassociate" at the Institute for the Study of Consciousness, which heset up in the fall of 1973) to work out the group table for thesymmetries of the tetrahedron. ... the rotations of the tetrahedronhave the symmetry group consisting of the 12 even permutations of 4objects (this is called the alternating-4 group, A4, and also thetetrahedral group, T. Moreover, the full symmetry group (whichincludes reflections) is the set of all permutations of 4 objects,the symmetric-4 goup, labeled S4, and also called the octahedralgroup, O, because it is the rotational symmetry group of theoctahedron (and cube which is the dual figure). One of the things Ilearned while working out this S4 group table was that I could takeshort cuts by way of the structure of the Klein-4 group K4 as asubgroup of S4. In standard group theory languange, S4 is thesemi-direct product of the K4 group and S3, the Symmeric-3 group.Thus there are 6 cosets of K4 in S4. In other words, I stumbled ontothe concept of cosets without knowing what they were called. Sometimein 1980, Abdas Salam sent Jack a copy of his Nobel Prize address(1973). In it Salam mentions 24 particles (18 quarks in 3 familiesand 3 colors; and 6 leptons in 3 families). Jack made the claim thatthese 24 particles must correspond to the 24 elements of S4. I lookedat my S4 table and saw immediately that since there are 5 classes ofS4 elements, and that there were 1, 3, & 8 elements making up theeven permutations of the A4 subgroup, while the remaining 12 elementsseparate into two classes each containtin 6 elements. It looked likethe even permutations would correspond to gauge bosons, and the oddpermutations would correspond to basic fermions. After all 1, 3, 8,6, 6 had become a particle physics mantra: 1 photon, 3 weakons, 8gluons, 6 quarks, 6 leptons. The multiplication of permutations wouldmatch the basic rule of particle physics: fermions interact byexchanging bosons; bosons can interact with each other, by exchangingbosons. Moreover, the cosets of K4 arranged these 12 odd permutationsas 2 of each class in three separate cosets. The idea that groupmultiplicaton of elements modeled particle interactions was, ofcourse, a radically new idea. This was the jumping off point for thedevelopment of the S4 (Octahedral) group algebra theory of theunification of the forces (other than gravity). The Standard ModelLie groups are imbedded as a Principal fiber bundle (the unitaryelements) in the Group Algebra C[S4], also known as theoctahedral group algbra C[O] In order to bring in gravity, Iwent to the double cover of O, the octahedral double group OD. Thegroup algebra C[OD] = C[O] + P + D, where P is thecomplex Pauli algebra and D is the complex Dirac algebra (which arecomplex Clifford algebras, i.e. complex C(3) and complex C(4). Thereare now 8 classes in OD, which correspond to 8 basic representations,and thus to 8 total matrix algebras of dimensions 1, 2, 3, 4, 3, 2,1, 2. By the correspondence proved by John McKay (1979) these arewhat I call "balance" numbers of the E7 Lie algebra. ... I have beenpushing the idea that the entire set of A-D-ECoxeter graphs is implicated in the ultimatedescription of reality. This is because the A-D-E graphs havebeen shown by mathematicians in recent decades to be a ubiquitousclassification structure. At least 20 different mathematical objectshave been brought into this scheme -- Lie algebras(and groups), Coxeter (Weyl) reflectiongroups, finite subgroups of SU(2), which I call McKaygroups, catastrophe structures, singularities (of differentiablemaps), 2-d conformal field theories, graviational instantons,error-correcting codes -- to name only a fewof the well known (and of great interest to physics). ... Each of theA-D-E classifications is merely a different window into some vastobject (Vast Active Living Inteligent System -- a la Phillip K.Dick?) What is clear through one window is seen only dimly (or not atall) through another. The A-D-E Coxeter graphs provide a way totransform from one type of object to another, or to transform withina particular type. There is an infinite number of A's, and aninfinite number of D's beginning with D4, and only three E's: E6, E7,E8. ... The D series begins with D4, sowe are back to 4 again. ..."

My remarks are that these symmetries are consistent with theHyperDiamond Lattice structure of theD4-D5-E6 physics model, and thatSaul-Paul's work with S4 was a key that led me to construct theD4-D5-E6 physics model. Unlike Jack andSaul-Paul, I use the 24-elementDouble-cover Tetrahedral group TD (also called the Binary TetrahedralGroup) instead of the 24-element Octahedral group O = S4, butthere is much similarity among the various approaches.

All these fascinating symmetries are related to mentalpictures that Jack Sarfatti, Saul-Paul Sirag, Nick Herbert, DimiChakalov, and I have had, and to the imagesand ideas of Mark Thornally:



How deeply have we probed within a Compton RadiusVortex?

What have we seen?

If you tried to probe the Gaja/GaneshaElectron or Proton inside its Compton Radius Vortex all the way downto its Classical Radius, you would have to use a probe whose energyis on the order of hbar / Rclassical c. For the Electron, it would beEprobeElectron = 10^41 GeV, and for a Quark it would be EprobeQuark =10^38 GeV, both far more energetic than the Planck Energy Eplanck =10^19 GeV. Since any energy higher than Eplank = 10^19 GeV woulddisrupt SpaceTime by graviton creation of newSpaceTime forming a Black Hole of mass at least the Planck MassMplanck = 10^19 GeV, you cannot probe all the way down to itsClassical Radius.

When we have probed as deeply as we can with our currentexperiments, down to about 10^(-16) cm at about 100 GeV energies, wehave found pointlike Musa/GaneshaElectrons, Quarks, and Gluons.

Gordon Kane describes what "pointlike" means in this context, inhis book Modern Elementary Particle Physics, Updated Edition, byGordon Kane (Addison-Wesley 1993 pages 217-221):

"... The basic quantity we need to organize the data is the crosssection [ sigma(point) ] for e+ e- -> f fbar where f is apoint-like spin 1/2 fermion [and fbar is the antiparticle off]. By comparison of the actual cross section with the point-likeone, we want to test whether any given fermion is point-like. ...

[equation 19.7] d sigma(point) / d OMEGA = ( Qf^2 alpha^2/ 4 s ) ( 1 + cos^2(theta) )

... [Section] 19.1 Are Quarks, Lepton, and GluonsPoint-Like? How well has the point-like nature of quarks,leptons, andgluons been tested? At LEP, the processes e+ e- to e+ e-, e+ e- tomu+ mu-, and e+ e- to tau+ tau- have been studied for a center ofmass energy up to MZ [about 90 GeV], and behave to anaccuracy of order 1% as expected from equation 19.7 as functions of sand theta. The same result holds for e+ e- to q qbar . It isparticularly impressive here, since the quarks are produced as jets,as described in Chapter 15. The jets have the 1+cos^2(theta) expectedfrom equation 19.7 if they are spin 1/2 fermions. For example, thenumber of jets pointing at 0 degrees or 180 degrees is twice thatpointing at 90 degrees. The sizes of the cross sections are givencorrectly for the fractional electric charges normally assigned tothe quarks. The c quark and b quark can be identified from their weakdecays, so the cross sections for e+ e- to c cbar and e+ e- to b bbarhave been studied to MZ as well, and are point-like. ... Forcomparison, the cross section for e+ e- to p pbar will be about10^(-9) of the point cross section at sqrt(s) = 150 GeV because theproton is not point-like. How can these results be interpreted?Historically, structure has always appeared when the available"particles" were probed with projectiles having energies smallcompared to the mass - for molecules, atoms, nuclei, and nucleons.Here the energies of the probes are of two or more orders ofmagnitude larger than the masses and no evidence for structure hasappeared. Ultimately it will remian an experimental question, but itis already clear that quarks and leptons cannot have structure in thesame sense that atoms or nuclei or protons had structure. The sameresult holds for photons and gluons and W+/- and Z0 bosons, whosecross sections are all point-like. ..."




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