Neutrino Mixing

nu_e (electron neutrino); nu_m (muon neutrino); nu_t

and three neutrino mass states: nu_1 ; nu_2 : nu_3

and

the division of 8-dimensional spacetime into

4-dimensional physical Minkowski spacetime

plus

4-dimensional CP2 internal symmetry space.

The heaviest mass state nu_3 corresponds to a neutrino

whose propagation begins and ends in CP2 internal symmetry space,

lying entirely therein. According to the D4-D5-E6-E7-E8 VoDou

Physics Model the mass of nu_3 is zero at tree-level

but it picks up a first-order correction propagating

entirely through internal symmetry space by

merging with an electron through the weak and electromagnetic forces,

effectively acting not merely as a point

but

as a point plus an electron loop at both beginning and ending points

so

the first-order corrected mass of nu_3 is given by

M_nu_3 x (1/sqrt(2)) = M_e x GW(mproton^2) x alpha_E

where the factor (1/sqrt(2)) comes from the Ut3 component

of the neutrino mixing matrix

so that

M_nu_3 = sqrt(2) x M_e x GW(mproton^2) x alpha_E =

= 1.4 x 5 x 10^5 x 1.05 x 10^(-5) x (1/137) eV =

= 7.35 / 137 = 5.4 x 10^(-2) eV.

Note that the neutrino-plus-electron loop can be anchored

by weak force action through any of the 6 first-generation quarks

at each of the beginning and ending points, and that the

anchor quark at the beginning point can be different from

the anchor quark at the ending point,

so that there are 6x6 = 36 different possible anchorings.

The intermediate mass state nu_2 corresponds to a neutrino

whose propagation begins or ends in CP2 internal symmetry space

and ends or begins in physical Minkowski spacetime,

thus having only one point (either beginning or ending) lying

in CP2 internal symmetry space where it can act not merely

as a point but as a point plus an electron loop.

According to the D4-D5-E6-E7-E8 VoDou Physics Model the mass

of nu_2 is zero at tree-level

but it picks up a first-order correction at only one (but not both)

of the beginning or ending points

so that so that there are 6 different possible anchorings

for nu_2 first-order corrections, as opposed to the 36 different

possible anchorings for nu_3 first-order corrections,

so that

the first-order corrected mass of nu_2 is less than

the first-order corrected mass of nu_3 by a factor of 6,

so

the first-order corrected mass of nu_2 is

M_nu_2 = M_nu_3 / Vol(CP2) = 5.4 x 10^(-2) / 6

= 9 x 10^(-3)eV.

The low mass state nu_1 corresponds to a neutrino

whose propagation begins and ends in physical Minkowski spacetime.

thus having only one anchoring to CP2 interna symmetry space.

According to E8 Physics the mass of nu_1 is zero at tree-level

but it has only 1 possible anchoring to CP2

as opposed to the 36 different possible anchorings for nu_3 first-order corrections

or the 6 different possible anchorings for nu_2 first-order corrections

so that

the first-order corrected mass of nu_1 is less than

the first-order corrected mass of nu_2 by a factor of 6,

so

the first-order corrected mass of nu_1 is

M_nu_1 = M_nu_2 / Vol(CP2) = 9 x 10^(-3) / 6

= 1.5 x 10^(-3)eV.

Therefore:

the mass-squared difference D(M23^2) = M_nu_3^2 - M_nu_2^2 =

= ( 2916 - 81 ) x 10^(-6) eV^2 =

= 2.8 x 10^(-3) eV^2

and

the mass-squared difference D(M12^2) = M_nu_2^2 - M_nu_1^2 =

= ( 81 - 2 ) x 10^(-6) eV^2 =

= 7.9 x 10^(-5) eV^2

The 3 × 3 unitary neutrino mixing matrix neutrino mixing matrix U

nu_1 nu_2 nu_3

nu_e Ue1 Ue2 Ue3

nu_m Um1 Um2 Um3

nu_t Ut1 Ut2 Ut3

can be parameterized (based on the 2010 Particle Data Book)

by 3 angles and 1 Dirac CP violation phase

c12 c13 s12 c13 s13 e−id

U = − s12 c23 − c12 s23 s13 eid c12 c23 − s12 s23 s13 eid s23 c13

s12 s23 − c12 c23 s13 eid − c12 s23 − s12 c23 s13 eid c23 c13

where cij = cos(theta_ij) , sij = sin(theta_ij)

The angles are

theta_23 = pi/4 = 45 degrees

because

nu_3 has equal components of nu_m and nu_t so

that Um3 = Ut3 = 1/sqrt(2) or, in conventional

notation, mixing angle theta_23 = pi/4

so that cos(theta_23) = 0.707 = sqrt(2)/2 = sin(theta_23)

theta_13 = 9.594 degrees = asin(1/6)

and cos(theta_13) = 0.986

because sin(theta_13) = 1/6 = 0.167 = |Ue3| = fraction of nu_3 that is nu_e

theta_12 = pi/6 = 30 degrees

because

sin(theta_12) = 0.5 = 1/2 = Ue2 = fraction of nu_2 begin/end points

that are in the physical spacetime where massless nu_e lives

so that cos(theta_12) = 0.866 = sqrt(3)/2

d = 70.529 degrees is the Dirac CP violation phase

ei(70.529) = cos(70.529) + i sin(70.529) = 0.333 + 0.943 i

This is because the neutrino mixing matrix has 3-generation structure

and so has the same phase structure as the KM quark mixing matrix

in which the Unitarity Triangle angles are:

β = V3.V1.V4 = arccos( 2 sqrt(2) / 3 ) ≅ 19.471 220 634 degrees so sin 2β = 0.6285

α = V1.V3.V4 = 90 degrees

γ = V1.V4.V3 = arcsin( 2 sqrt(2) / 3 ) ≅ 70.528 779 366 degrees

The constructed Unitarity Triangle angles can be seen on the Stella Octangula

configuration of two dual tetrahedra (image from gauss.math.nthu.edu.tw):

Then we have for the neutrino mixing matrix:

nu_1 nu_2 nu_3

nu_e 0.866 x 0.986 0.50 x 0.986 0.167 x e-id

nu_m -0.5 x 0.707 0.866 x 0.707 0.707 x 0.986

-0.866 x 0.707 x 0.167 x eid -0.5 x 0.707 x 0.167 x eid

nu_t 0.5 x 0.707 -0.866 x 0.707 0.707 x 0.986

-0.866 x 0.707 x 0.167 x eid -0.5 x 0.707 x 0.167 x eid

nu_1 nu_2 nu_3

nu_e 0.853 0.493 0.167 e-id

nu_m -0.354 0.612 0.697

-0.102 eid -0.059 eid

nu_t 0.354 -0.612 0.697

-0.102 eid -0.059 eid

Since ei(70.529) = cos(70.529) + i sin(70.529) = 0.333 + 0.943 i

and .333e-i(70.529) = cos(70.529) - i sin(70.529) = 0.333 - 0.943 i

nu_1 nu_2 nu_3

nu_e 0.853 0.493 0.056 - 0.157 i

nu_m -0.354 0.612 0.697

-0.034 - 0.096 i -0.020 - 0.056 i

nu_t 0.354 -0.612 0.697

-0.034 - 0.096 i -0.020 - 0.056 i

for a result of

nu_1 nu_2 nu_3

nu_e 0.853 0.493 0.056 - 0.157 i

nu_m -0.388 - 0.096 i 0.592 - 0.056 i 0.697

nu_t 0.320 - 0.096 i 0.632 - 0.056 i 0.697

which is consistent with the approximate experimental values of mixing angles

shown in the Michaelmas Term 2010 Particle Physics handout of Prof Mark Thomson

nu_1 nu_2 nu_3

nu_e 0.853 0.493 0.056 - 0.157 i

nu_m -0.388 - 0.096 i 0.592 - 0.056 i 0.697

nu_t 0.320 - 0.096 i 0.632 - 0.056 i 0.697

nu_1 nu_2 nu_3

nu_e 0.85 0.53 0

nu_m -0.37 0.60 0.71

nu_t 0.37 -0.60 0.71

if the matrix is modified by taking into account

the March 2012 results from Daya Bay observing non-zero theta_13 = 9.54 degrees.

Here is a pdf version of this page.

Ken Shoulders's EVOs and Ball Lightning

For reference, here are values of some useful physical quantities:

The effective G* induced by the zero point energy core needed

to stabilize a single spatially extended electron is ~ 10^40 G.

G* m / r = e / r G* m = e G* = e/m = 10^42

e Electron charge [Q] 1.381 E-34 cm

m_e Electron mass [M] 9.1095 E-28 gm

6.764 E-56 cm

r_e Electron radius [L] 2.81794 E-13 cm

classical (= alpha(h-bar/(m_e c))

r_es Electron Schwarzschild radius [L] 1.35264 E-55 cm

(= 2G_0 m_e/c^2)

22 orders of magnitude *smaller* than the Planck length

a_0 Bohr radius [L] 0.529177 E-08 cm

( = h-bar^2/(m_e e^2) )

Ken
Shoulders and Steve Shoulders said in 1996: "... Highly
organized, **micron-sized clusters of electrons** having soliton
behavior ... have been investigated by K. Shoulders since 1980 ... a
short Latin acronym has been adopted and the structure is called an
EV, for strong electron. Their organizational properties have been
theoretically studied and reported by P. Beckmann
[... Petr Beckmann, "Electron Clusters," Galilean
Electrodynamics, Sept./Oct., Vol. 1, No. 5, pp. 55-58, 1990
...] and R. Ziolkowski [... Richard W.
Ziolkowski and Michael K. Tippett, "Collective effect in an electron
plasma system catalyzed by a localized electromagnetic wave,"
Physical Review A, vol. 43, no.6, pp. 3066-3072, 15 mar., 1991
...] ... What is seen in the laboratory is an extremely
energetic entity ... Measurements ... measuring the charge-to-mass
ratio of the structure ...[by]... time-of-flight ... have
been made showing there are no included ions to a limit of at least
one ion per million electrons. **The total number of electrons in a
one micrometer diameter EV is 10^11**. ...". In
1999
they
said: "... Throughout much of this work on EV
energetics it has been obvious that we get more energy out of certain
experiments than we put in. ...".

In August 2004 e-mail messages about Shoulders's EVOs, Jack Sarfatti said:

"... picture is of a self-assembled spherical shell or maybe a kind of Buckyball of N close-packed electrons each of effective surface area ~ (h/mc)^2. This forms a closed cavity - with some leakage perhaps, but the leakage rate decreases as N increases. Obviously there will be a cavity boundary condition Casimir effect but I am pretty sure it is usually negligible in comparison with my strong gravity effect from Einstein's general relativity. ...... The KEY IDEA is as follows:

1. The repulsive electro-static self energy per unit electron mass for the N poly-electron cluster is V(Coulomb Self-Energy) ~ N^2e^2/mr > 0 where the N electrons are arranged in a mono-layer thin spherical shell of thickness h/mc ~ 10^-11 cm

i.e. Euclidean area of the shell is A = 4pir^2 = N(h/mc)^2 r ~ N^1/2(h/mc) = Schwarzschild radial coordinate if large space warp ... from G* ~ 10^40G at short-range.

That is, N on-mass-shell bare electrons each of radius e^2/mc^2 ~ 10^-13 cm in a soup of virtual plasma of virtual photons and virtual electron-positron pairs - the latter partially condensed as a vacuum condensate!

... a Casimir force ... plays a minor secondary role. The Casimir potential energy per unit electron mass will be of the form V(Casimir) ~ C(hc/mr)N(h/mcr)^2 Where C is a dimensionless coefficient that can be positive or negative ... Note that V(Casimir) scales only as N because it depends on the surface area of the N poly-electron thin shell. This is a boundary effect!

Ignoring rotational and vibrational modes - to be added later. All we have next is the GR correction term ... V(Dark Energy) = c^2/\zpfr^2 a 3D Harmonic Oscillator Potential like a ball in a tunnel through center of Earth

Note that /\zpf > 0 i.e. an anti-gravity repulsive "dark energy" exotic vacuum core that COUNTER-INTUITIVELY BINDS the N electrons into a metastable BOUNDARY WALL THIN POLY-ELECTRON SHELL making the QED Casimir force in the first place ... Adding all three potential energies Coulomb, Casimir & General Relativity with PW Anderson's "More is Different"

V(total) = BN^2(e^2/mr) + CN(hc/mr)(h/mcr)^2 + c^2/\zpfr^2

B is also a dimensionless coefficient The critical point for dynamical equilibrium is dV(total)/dr = 0 i.e. the total acceleration must vanish in metastable equilibrium where r --> r* -BN^2(e^2/mr*^2) - 3CN(hc/mr*^2)(h/mcr*)^2 + 2c^2/\zpfr* = 0

So I do not care about Casimir force, which when N >> 1 is obviously a small perturbation!

We now have a more accurate formula for r*, or rather, if you want to keep r* = N^1/2(h/mc) then you can compute /\zpf.

We also have the stability constraint: d^V(total)/dr^2 > 0

When this constraint is violated WE HAVE WHAT IS BEGINNING TO SUGGEST A BOMB! ...

... you must explain why the boundary forms! You cannot impose it by fiat. The boundary is the thin shell of charge itself of radius a ~ N^1/2(h/mc). If N ~ 10^12 that gives a ~ 10^-5 cm. ... I don't think it works well for 2 electrons. You need, in simplest model, N >> 1 electrons close-packed to form a sphere ...".

My model for EVOs also makes a spherical shell, but it is a two-layer shell, motivated by the formation of a blastocyst two-layer shell in embryology, and it also explains how the door to the high-energy vacuum is opened.

Here is an 8-step description of my model:

1 - A bunch of electrons are zapped in Ken Shoulders's apparatus

with a complicated electromagnetic field.

2 - One of the electrons finds another with opposite spin

and they form a Cooper pair of two electrons

in a dumbbell configuration.

3 - They find another Cooper pair, and the 4 of them form

a double-dumbbell tetrahedral configuration.

4 - The tetrahedron finds (or catalyzes the formation of)

another opposite-oriented tetrahedron, and the 8 of them

form a cube.

5 - Each of the 8 vertices of the cube finds from the cloud

an opposite-spin electron, and the 16 of them look like

Cooper pairs at each of the 8 cube vertices

with the long axis of each pair on a diagonal of the cube.

( At age 4 days, a human embryo consists of a solid ball of 16 cells, called the morula. At the next stage of cell division, the blasocyst forms. Here is a blastocyst image

from http://www.visembryo.com/baby/stage3.html which states: "... Cell division continues, and a cavity known as a blastocele forms in the center of the morula. Cells flatten and compact on the inside of the cavity ... the appearance of the cavity in the center the entire structure is now called a blastocyst. ... two cell types are forming: the embryoblast (inner cell mass on the inside of the blastocele), and the trophoblast (the cells on the outside of the blastocele). ...". )

THE CENTER OF THE CUBE IS A HOLLOW INTERIOR,

with a 2-layer boundary of 8 inner electrons of each Cooper pair

and 8 outer electrons of each Cooper pair.

The 8 inner electrons can be thought of as being bounded by

the 8 outer electrons.

6 - Any energy (kinetic or repulsive electromagnetic) of

the 8 inner electrons confined by the boundary of the 8 outer electrons

is transferred to the Bohm Quantum Potential by the process

described in Bohm's Hidden Variable Paper II, section 5,

(reprinted at page 387 of Quantum Theory and Measurement,

edited by Wheeler and Zurek (Princeton 1983))

in which Bohm says:

"... the PSI-field is able to bring the particle to rest

and to transform the entire kinetic energy into potential energy

of interaction with the PSI-field. ...".

Bohm discusses specifically the situation of

"... a "free" particle contained between two impenetrable and

perfectly reflecting walls, separated by a distance L. ...",

but

perhaps a similar analysis might apply to a spherical cluster.

Bohm goes on to say:

"... at first sight, it may seem puzzling

that a particle having a high energy should be at rest

in the empty space between two walls.

Let us recall, however, that the space is not really empty,

but contains

an objectively real PSI-field that can act on the particle. ...".

7 - The increased energy of the Bohm Quantum Potential is

now enough to open the door to the high-energy vacuum,

which effectively gives the electron configuration

access to conformal degrees of freedom of of vacuum dark energy etc.

8 - The electron double-layer with central vacuum energy configuration,

which is the EVO, then begins to collect the other electrons in

the cloud, making them into Cooper pairs and sticking them into

the sort-of-spherical double-layer.

The outer layer of electrons acts as a protective boundary for

the EVO, because if a hostile electron/positive ion system

attacks the EVO, an outer boundary EVO electron neutralizes

the positive ion and the EVO captures the remaining electron

to replace the boundary electron.

The entire EVO system continues to grow until the electrons

of the cloud are all assimilated into it (about 10^12 electrons

in the case of EVOs manufactured by Ken Shoulders).

Ball lightning can be a lot larger than the size of the Ken Shoulders manufactured EVO because lightning can be more energetic than his machines.

A typical Ball Lightning has r ~ 10 cm, N = 10^21.

Use the hydrogen atom as the basis of comparison

where r ~ 10^-8 cm and N = 1

with self-electrical force ~ 10^+16

compared to

the Ball Lightning self-electrical force 10^42 x 10^-2 = 10^40

in these relative dimensionless units.

That is,

the self-electrical force at the

surface of the Ball Lightning assumed to be in a spherical thin shell

is ~ 10^24 stronger than the electrical force on

the atomic electron in the ground state of the hydrogen atom.

Next consider a single electron as a shell of charge e

at the classical electron radius 10^-13cm.

The relative self-electric force is then 10^+26.

Therefore,

the electrical force of the Ball Lightning is

about 10^14 larger than that on a single electron.

The effective G* induced by the zero point energy core needed

to stabilize a single spatially extended electron is ~ 10^40 G.

That is

the effective Planck length Lp* in

the interior of a single electron is ~ 10^-13 cm.

The effective Planck length in the interior of the Ball Lightning

is therefore ~ 10^-6 cm since G* ~ Lp^*2.

Tony Smith's Home Page - Here is a pdf version of this page.

......