Tony's Home A Classical Radius Black Hole in Ordinary SpaceTime is connected through a Ring Singularity to a Compton Radius Vortex in Exotic SpaceTime. A Compton Radius Vortex in Ordinary SpaceTime is connected through a Ring Singularity to a Classical Radius Black Hole in Exotic SpaceTime.

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

a Planck Radius Vortex Black Hole lives in both Ordinary SpaceTime and Exotic SpaceTime, acting as a Bridge or Window or Pivot between Ordinary SpaceTime and Exotic SpaceTime, so I call it the

# Planck Pivot Vortex

whose Symmetry Group is

## (K4 \ Z3) \ Z2 = TD

The Planck Pivot Vortex gives rise to Planck Fulcrum Ordinary/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 to Bosonic String T-duality structures.

It took several e-mail messages from Jack Sarfatti to convince me that we can go below the Planck Scale.

One reason that I thought that we could not go below the Planck Scale was what Feynman said in his book QED (Princeton Press paperback 1988), from footnote 1 on page 129: "... perhaps the idea that two points can be infinitely close together is wrong ... If we make the minimum possible distance between two points as small as 10^(-100) centimeters (the smallest distance involved in any experiment today is around 10^(-16) centimeters), the infinities disappear, all right - but other inconstencies arise, such as the total probability of an event adds up to slightly more or less than 100%, or we get negative energies in infinitesimal amounts. It has been suggested that these inconsistencies arise because we haven't taken into account 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 book Black Holes and Time Warps (Norton 1994, pages 491-492), "... in 1974 ... Hawking inferred as a byproduct of his discovery of black hole evaporation ... that vacuum fluctuations near a [Black Hole]'s horizon are exotic: They have negative average energy density as seen by outgoing light beams near the hole's horizon. ... it is this exotic property of the vacuum fluctuations that permits the hole's horizon to shrink as the hole evaporates ... The horizon distorts the vacuum fluctuations away from the shapes they would have on Earth, and by this distortion it makes their average energy density negative,that is, that is, it makes the fluctuations exotic. ... Gunar Klinkhammer ... has proved that in flat spacetime ... vacuum fluctuations can never be exotic ... Robert Wald and Ulvi Yurtsever have proved that in curved spacetime ... the curvature distorts the vacuum fluctuations and thereby makes them exotic. ...".

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

The Planck-Scale 4-dimensional HyperDiamond Lattice used in the D4-D5-E6-E7 physics model is not fundamental because it is the latttice at the smallest possible scale, it is fundamental because it is the

### Bridge Lattice Connecting Ordinary SpaceTime and Exotic SpaceTime.

There are 3 possible types of particles connecting Ordinary SpaceTime and Exotic SpaceTime.

Here are orders of magnitudes of examples of each type:

Electron, Planck Mass Black Hole, Solar Mass Black Hole, and our Universe

based on the Planck Fulcrum Ordinary/Exotic Duality Equations:

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

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

```
ORDINARY SPACETIME         BOTH           EXOTIC SPACETIME
Electron                Ring
Compton Radius Vortex      Singularity     Classical Black Hole
10^(-11) cm                               10^(-55) cm
10^(-27) gm                                10^17 gm  ```

```Planck Mass Black Hole
Compton Radius Vortex = Classical Black Hole
10^(-33) cm = 10^(-33) cm
10^(-5) gm = 10^(-5) gm```

```Solar Mass Black Hole        Ring
Classical Black Hole     Singularity     Compton Radius Vortex
10^5 cm                               10^(-71) cm
10^33 gm                              10^(-43) gm```

```      Universe               Ring
Classical Black Hole     Singularity     Compton Radius Vortex
10^28 cm                              10^(-94) cm```

In Each of the 3 types, the Structure is a Sarfatti 4-Mouth Structure:

• Compton/Classical Vortex/Black Hole Mouth in Ordinary SpaceTime
• Ring Singularity Mouth in Ordinary SpaceTime
• Ring Singularity Mouth in Exotic SpaceTime
• Classical/Compton Blackole/Vortex in Exotic SpaceTime
Each of the 3 types of 4-Mouth Structures has its own Symmetry Group:

Compton Radius Vortex in Ordinary SpaceTime: K4

Classical Black Hole in Ordinary SpaceTime: Z3 \ Z2

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

The interplay between Ordinary SpaceTime and Exotic SpaceTime is important in

## Compton Radius Vortex Kerr-Newman Black Hole

with a^2 greater than m^2: Roughly, this looks like

```A                                1

_____________                   _____________

B                                2```
` `

where

the lines ___________ are edge-on views of the ring singularity,

the line between 1 and 2 is the ring singularity in the ordinary part of the extended spacetime in which distances are positive and gravity is attractive, and

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

Since the A and B sides of the exotic singularity differ from the 1 and 2 sides of the ordinary singularity in that distances are negative or positive, respectively, and

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

The External Symmetries of a Compton Radius Vortex are those of Position in SpaceTime, Mass=Area, Spin=Angular Momentum, Electric Charge, and Color Charge.

### The Internal Symmetry Group of the Compton Radius Vortex Kerr-Newman Black Hole with a^2 greater than m^2 is the Klein 4-group K4.

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

• Massless Neutrino - RclassicalNeutrino = 0 - RcomptonNeutrino = scale of Universe
• Electron - RclassicalElectron = 10^(-55) cm - RcomptonElectron = 10^(-11) cm
• Quark - RclassicalQuark = 10^(-52) cm - RcomptonQuark = 10^(-13) cm
• Planck Mass - RclassicalPlanck = 10^(-33) cm = RcomptonPlanck

If you tried to probe the Electron or Proton within their Compton Radius Vortex all the way down to its Classical Radius, you would have to use a probe whose energy is on the order of hbar / Rclassical c. For the Electron, it would be EprobeElectron = 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 would disrupt SpaceTime by graviton creation of new SpaceTime forming a Black Hole of mass at least the Planck Mass Mplanck = 10^19 GeV,

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

The only elementary particles for which the

is greater than the Compton Radius are Black Holes with mass greater than the Planck Mass. The Compton Radius Vortices of Black Holes larger than Planck Mass do not exist in Ordinary SpaceTime, but live in Exotic SpaceTime.

The Maximal Extension of SpaceTime for such a Black Hole is shown in Figure 12.4 from General Relativity by Robert M. Wald (Chicago 1984): At such a Black Hole, you can travel from External SpaceTime Region 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 from Region VI to Region VI' and back to Region VI.

The External Symmetries of a Classical Radius Black Hole are those of Position in SpaceTime, Mass=Area, Spin=Angular Momentum, Electric Charge, and Color Charge.

### The Internal Symmetry Group of a Classical Radius Black Hole is

an extension (denoted by \ ) of

### the cyclic group Z3 of the 3 Interior Regions

of the journey from Region I to Region IX and

### the group Z2 of going through the Ring Singularity

from Region VI to Region VI' and back

so that the total Symmetry Group is an extension \

### Only for a Planck Mass Black Hole

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

can

be observed from both Ordinary SpaceTime and Exotic SpaceTime,

forming a Bridge or Window or Pivot between them,

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

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

### (K4 \ Z3) \ Z2 = TD

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

is the McKay group for E6 of the D4-D5-E6-E7 physics model.

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

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 to write this page): "... Note you get the full S4 symmetry at the Planck mass. The symmetry is broken when you move off the Planck scale. ... That's what we want. ...".

Saul-Paul Sirag remarks (with respect to his closely related structures that motivated me to write this page): "... Ezekiel saw the 4 cherubim. John's vision of the throne of God in the book of Revelation has 4 "living creatures" (zoon in Greek) around the throne, and 4! = 24 elders surrounding the throne. Of course the main number, repeated over and over is 7, which goes back to the 7 days of Creation + Sabboth. But there is a deep connection between S4 and 7 as we will see. [Aside: For a while, I called the 4 objects permuted by S4 Zons.] ... Carl Jung has pointed out that the 4 cherubim correspond to 4 cardinal figures of the Zodiac. (He was undoubtedly not the first to notice this.) From Jung we may pass to Arthur Young, who was a student of Jungian symbolism (he went through a long Jungian analysis, which he credited with the cure of his paralyzed arms -- but that's another story. Jung had emphasized the symbolism of fourness, in addition to the well known threeness of the Christian trinity. Because of Arthur Young's fascination with the fourness, he was very intrigued with the tetrahedron. In March of 1974 he asked me (as his "research associate" at the Institute for the Study of Consciousness, which he set up in the fall of 1973) to work out the group table for the symmetries of the tetrahedron. ... the rotations of the tetrahedron have the symmetry group consisting of the 12 even permutations of 4 objects (this is called the alternating-4 group, A4, and also the tetrahedral group, T. Moreover, the full symmetry group (which includes reflections) is the set of all permutations of 4 objects, the symmetric-4 goup, labeled S4, and also called the octahedral group, O, because it is the rotational symmetry group of the octahedron (and cube which is the dual figure). One of the things I learned while working out this S4 group table was that I could take short cuts by way of the structure of the Klein-4 group K4 as a subgroup of S4. In standard group theory languange, S4 is the semi-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 onto the concept of cosets without knowing what they were called. Sometime in 1980, Abdas Salam sent Jack a copy of his Nobel Prize address (1973). In it Salam mentions 24 particles (18 quarks in 3 families and 3 colors; and 6 leptons in 3 families). Jack made the claim that these 24 particles must correspond to the 24 elements of S4. I looked at my S4 table and saw immediately that since there are 5 classes of S4 elements, and that there were 1, 3, & 8 elements making up the even permutations of the A4 subgroup, while the remaining 12 elements separate into two classes each containtin 6 elements. It looked like the even permutations would correspond to gauge bosons, and the odd permutations would correspond to basic fermions. After all 1, 3, 8, 6, 6 had become a particle physics mantra: 1 photon, 3 weakons, 8 gluons, 6 quarks, 6 leptons. The multiplication of permutations would match the basic rule of particle physics: fermions interact by exchanging bosons; bosons can interact with each other, by exchanging bosons. Moreover, the cosets of K4 arranged these 12 odd permutations as 2 of each class in three separate cosets. The idea that group multiplicaton of elements modeled particle interactions was, of course, a radically new idea. This was the jumping off point for the development of the S4 (Octahedral) group algebra theory of the unification of the forces (other than gravity). The Standard Model Lie groups are imbedded as a Principal fiber bundle (the unitary elements) in the Group Algebra C[S4], also known as the octahedral group algbra C[O] In order to bring in gravity, I went to the double cover of O, the octahedral double group OD. The group algebra C[OD] = C[O] + P + D, where P is the complex Pauli algebra and D is the complex Dirac algebra (which are complex Clifford algebras, i.e. complex C(3) and complex C(4). There are 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 are what I call "balance" numbers of the E7 Lie algebra. ... I have been pushing the idea that the entire set of A-D-E Coxeter graphs is implicated in the ultimate description of reality. This is because the A-D-E graphs have been shown by mathematicians in recent decades to be a ubiquitous classification structure. At least 20 different mathematical objects have been brought into this scheme -- Lie algebras (and groups), Coxeter (Weyl) reflection groups, finite subgroups of SU(2), which I call McKay groups, catastrophe structures, singularities (of differentiable maps), 2-d conformal field theories, graviational instantons, error-correcting codes -- to name only a few of the well known (and of great interest to physics). ... Each of the A-D-E classifications is merely a different window into some vast object (Vast Active Living Inteligent System -- a la Phillip K. Dick?) What is clear through one window is seen only dimly (or not at all) through another. The A-D-E Coxeter graphs provide a way to transform from one type of object to another, or to transform within a particular type. There is an infinite number of A's, and an infinite number of D's beginning with D4, and only three E's: E6, E7, E8. ... The D series begins with D4, so we are back to 4 again. ..."

My remarks are that these symmetries are consistent with the HyperDiamond Lattice structure of the D4-D5-E6 physics model, and that Saul-Paul's work with S4 was a key that led me to construct the D4-D5-E6 physics model. Unlike Jack and Saul-Paul, I use the 24-element Double-cover Tetrahedral group TD (also called the Binary Tetrahedral Group) instead of the 24-element Octahedral group O = S4, but there is much similarity among the various approaches.

All these fascinating symmetries are related to mental pictures that Jack Sarfatti, Saul-Paul Sirag, Nick Herbert, Dimi Chakalov, and I have had, and to the images and ideas of Mark Thornally: ### What have we seen?

If you tried to probe the Gaja/Ganesha Electron or Proton inside its Compton Radius Vortex all the way down to its Classical Radius, you would have to use a probe whose energy is on the order of hbar / Rclassical c. For the Electron, it would be EprobeElectron = 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 would disrupt SpaceTime by graviton creation of new SpaceTime forming a Black Hole of mass at least the Planck Mass Mplanck = 10^19 GeV, you cannot probe all the way down to its Classical Radius.

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

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

"... The basic quantity we need to organize the data is the cross section [ sigma(point) ] for e+ e- -> f fbar where f is a point-like spin 1/2 fermion [and fbar is the antiparticle of f]. By comparison of the actual cross section with the point-like one, 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 Gluons Point-Like? How well has the point-like nature of quarks,leptons, and gluons been tested? At LEP, the processes e+ e- to e+ e-, e+ e- to mu+ mu-, and e+ e- to tau+ tau- have been studied for a center of mass energy up to MZ [about 90 GeV], and behave to an accuracy of order 1% as expected from equation 19.7 as functions of s and theta. The same result holds for e+ e- to q qbar . It is particularly impressive here, since the quarks are produced as jets, as described in Chapter 15. The jets have the 1+cos^2(theta) expected from equation 19.7 if they are spin 1/2 fermions. For example, the number of jets pointing at 0 degrees or 180 degrees is twice that pointing at 90 degrees. The sizes of the cross sections are given correctly for the fractional electric charges normally assigned to the quarks. The c quark and b quark can be identified from their weak decays, so the cross sections for e+ e- to c cbar and e+ e- to b bbar have been studied to MZ as well, and are point-like. ... For comparison, the cross section for e+ e- to p pbar will be about 10^(-9) of the point cross section at sqrt(s) = 150 GeV because the proton 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 small compared to the mass - for molecules, atoms, nuclei, and nucleons. Here the energies of the probes are of two or more orders of magnitude larger than the masses and no evidence for structure has appeared. Ultimately it will remian an experimental question, but it is already clear that quarks and leptons cannot have structure in the same sense that atoms or nuclei or protons had structure. The same result holds for photons and gluons and W+/- and Z0 bosons, whose cross sections are all point-like. ..."